Electrical, Electromagnetic, And Optical Characterization Of The InP/InGaAs Alloy System Guide

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Electrical, Electromagnetic, and Optical Characterization of the InP/InGaAs Alloy System
A Thesis
Presented to the Faculty of the
Department of Electronics and Communications Engineering
Gokongwei College of Engineering
De La Salle University
In Partial Fulfillment of the
Requirements for the Degree of
Bachelor of Science in Electronics and Communications Engineering
by
DELA CRUZ, Juan Z.
FRANCO, Nat Y.
GARCIA, Sebastian X.
MARTINEZ, Isabella W.
RIANZARES, Max V.
August, 2016
ORAL DEFENSE RECOMMENDATION SHEET
This thesis, entitled
Electrical, Electromagnetic, and Optical Characterization of the
InP/InGaAs Alloy System
, prepared and submitted by thesis group, ESG-04, composed
of:
DELA CRUZ, Juan Z.
FRANCO, Nat Y.
GARCIA, Sebastian X.
MARTINEZ, Isabella W.
RIANZARES, Max V.
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Elec-
tronics and Communications Engineering
(
BS-ECE
) has been examined and is recom-
mended for acceptance and approval for ORAL DEFENSE.
Dr. Francisco D. Baltasar
Adviser
August 5, 2016
THESIS APPROVAL SHEET
This thesis entitled
Electrical, Electromagnetic, and Optical Characterization of the
InP/InGaAs Alloy System, prepared and submitted by:
DELA CRUZ, Juan Z.
FRANCO, Nat Y.
GARCIA, Sebastian X.
MARTINEZ, Isabella W.
RIANZARES, Max V.
with group number ESG-04 in partial fulfillment of the requirements for the degree of
Bachelor of Science in Electronics and Communications Engineering
(
BS-ECE
) has
been examined and is recommended for acceptance and approval.
PANEL OF EXAMINERS
Dr. Amado Z. Hernandez
Chair
Dr. Jose Y. Alonzo Dr. Mariana X. Mercado
Member Member
Dr. Francisco D. Baltasar
Adviser
Date: August 5, 2016
2016
All Rights Reserved. No part of this publication may be reproduced, stored in an information retrieval system,
or transmitted, in any form or by any means, electronic, mechanical, by photocopying, scanning, recording,
or otherwise, except under the terms of the applicable law.
ACKNOWLEDGMENT
Write this prior to binding your thesis if you have submitted necessary requirements and
are told by the university that you have passed.
v
ABSTRACT
Keep your abstract short by giving the gist/nutshell of your thesis. Use the following
checklist questions to help you in crafting your abstract.
Did you briefly state what you intend to do?
Did you concisely discuss the problem statement?
Did you tersely mention the objectives in general terms?
Did you succinctly describe the methodology for the target audience?
Did you strongly describe your significant results and your conclusions?
Index Terms—alloy system, characterization, InP, InGaAs.
vi
TABLE OF CONTENTS
Oral Defense Recommendation Sheet ii
Thesis Approval Sheet iii
Acknowledgment v
Abstract vi
Table of Contents vii
List of Figures x
List of Tables xi
Abbreviations xii
Notation xiii
Glossary xiv
Listings xv
Chapter 1 INTRODUCTION 1
1.1 Background of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 PriorStudies................................. 4
1.3 ProblemStatement ............................. 5
1.4 Objectives.................................. 6
1.4.1 General Objective(s) . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Specific Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Significance of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Assumptions, Scope and Delimitations . . . . . . . . . . . . . . . . . . . 7
1.6.1 Assumptions ............................ 8
1.6.2 Scope ................................ 8
1.6.3 Delimitations ............................ 8
1.7 Description and Methodology . . . . . . . . . . . . . . . . . . . . . . . . 8
1.8 Overview .................................. 9
vii
Table of Contents
Chapter 2 LITERATURE REVIEW 10
2.1 ExistingWork................................ 11
2.2 Lacking in the Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Summary .................................. 15
Chapter 3 THEORETICAL CONSIDERATIONS 16
3.1 Summary .................................. 19
Chapter 4 DESIGN CONSIDERATIONS 20
4.1 Summary .................................. 23
Chapter 5 METHODOLOGY 24
5.1 Implementation ............................... 25
5.2 Evaluation.................................. 27
5.3 Summary .................................. 29
Chapter 6 RESULTS AND DISCUSSION 30
6.1 Summary .................................. 32
Chapter 7 CONCLUSIONS, RECOMMENDATIONS, AND FUTURE DIREC-
TIVES 33
7.1 ConcludingRemarks ............................ 34
7.2 Contributions ................................ 34
7.3 Recommendations.............................. 34
7.4 FutureProspects............................... 36
References 37
Appendix A ANSWERS TO QUESTIONS TO THIS THESIS 46
Appendix B USAGE EXAMPLES 55
Appendix C SOME LIST OF MATH SYMBOLS 94
Appendix D DISLAYING MATH EXPRESSIONS 112
Appendix E IEEE EDITORIAL STYLE MANUAL 144
Appendix F IEEE CITATION REFERENCE 176
Appendix G IEEE PUBLICATION ABBREVIATIONS 184
viii
Table of Contents
Appendix H IEEE INDEX TERMS 192
Appendix I PUBLICATION LIST AND AWARD 260
Appendix J VITA 261
Index 263
ix
LIST OF FIGURES
3.1 A quadrilateral image example. . . . . . . . . . . . . . . . . . . . . . . . . . 19
B.1 A quadrilateral image example. . . . . . . . . . . . . . . . . . . . . . . . . . 68
B.2 Figures on top of each other. See List. B.6 for the corresponding L
A
T
E
X code. 70
B.3 Four figures in each corner. See List. B.7 for the corresponding L
A
T
E
X code. . 72
x
LIST OF TABLES
B.1 Feasible triples for highly variable grid . . . . . . . . . . . . . . . . . . . . . 74
B.2 Calculation of y=xn.............................. 78
xi
ABBREVIATIONS
AC AlternatingCurrent................................................64
CSS CascadingStyleSheet.............................................64
HTML Hyper-textMarkupLanguage......................................64
XML eXtensibleMarkupLanguage......................................64
xii
NOTATION
|S| the number of elements in the set S..................................66
∅thesetwithnoelements............................................66
h(t)impulseresponse...................................................56
Sacollectionofdistinctobjects.......................................66
Uthesetcontainingeverything........................................66
x(t)input signal represented in the time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
y(t)output signal represented in the time domain . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Throughout this thesis, mathematical notations conform to ISO 80000-2 standard, e.g.
variable names are printed in italics, the only exception being acronyms like e.g.
SNR
,
which are printed in regular font. Constants are also set in regular font like
j
. Functions are
also set in regular font, e.g. in
sin (·)
. Commonly used notations are
t
,
f
,
j = √−1
,
n
and
exp (·)
, which refer to the time variable, frequency variable, imaginary unit,
n
th variable,
and exponential function, respectively.
xiii
GLOSSARY
Functional Analysis
the branch of Mathematics concerned with the study of spaces
of functions
matrix
a concise and useful way of uniquely representing and working
with linear transformations; a rectangular table of elements
xiv
LISTINGS
B.1 Sample L
A
T
E
X code for equations and notations usage . . . . . . . . . . . 57
B.2 Sample L
A
T
E
X code for notations usage . . . . . . . . . . . . . . . . . . . 61
B.3 Sample L
A
T
E
X code for abbreviations usage . . . . . . . . . . . . . . . . . 65
B.4 Sample L
A
T
E
X code for glossary and notations usage . . . . . . . . . . . . 67
B.5 Sample L
A
T
E
X code for a single figure . . . . . . . . . . . . . . . . . . . 69
B.6 Sample L
A
T
E
X code for three figures on top of each other . . . . . . . . . 71
B.7 Sample L
A
T
E
X code for the four figures . . . . . . . . . . . . . . . . . . . 73
B.8 Sample L
A
T
E
X code for making typical table environment . . . . . . . . . 76
B.9 Sample L
A
T
E
X code for algorithm or pseudocode listing usage . . . . . . . 79
B.10 Computing Fibonacci numbers . . . . . . . . . . . . . . . . . . . . . . . 80
B.11 Sample L
A
T
E
X code for program listing . . . . . . . . . . . . . . . . . . . 81
B.12 Sample L
A
T
E
X code for referencing sections . . . . . . . . . . . . . . . . 82
B.13 Sample L
A
T
E
X code for referencing subsections . . . . . . . . . . . . . . 83
B.14 Sample L
A
T
E
X code for referencing sub-subsections . . . . . . . . . . . . 84
B.15 Sample L
A
T
E
X code for Index usage . . . . . . . . . . . . . . . . . . . . . 89
B.16 Sample L
A
T
E
X code for including PDF pages . . . . . . . . . . . . . . . . 90
xv
Chapter 1
INTRODUCTION
Contents
1.1 Background of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 PriorStudies................................. 4
1.3 ProblemStatement ............................. 5
1.4 Objectives.................................. 6
1.4.1 General Objective(s) . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 Specific Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Significance of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Assumptions, Scope and Delimitations . . . . . . . . . . . . . . . . . . . 7
1.6.1 Assumptions ............................ 8
1.6.2 Scope ................................ 8
1.6.3 Delimitations ............................ 8
1.7 Description and Methodology . . . . . . . . . . . . . . . . . . . . . . . . 8
1.8 Overview .................................. 9
1
1. Introduction
1.1 Background of the Study
Aside from the usual text descriptions of the background, put here figures that will cast
images to your audience about the context of your work.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
2
1. Introduction
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
3
1. Introduction
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
1.2 Prior Studies
Put here a summary of your literature review. Preferably, a table showing the summary
would be helpful.
Prior Studies or Literature Review (expansion of the Prior Studies) is basically about
competition. Competition.
So the goals are:
1. to mention briefly the problem;
2. to show the features of the existing literature in solving the problem
3. to show the weakness of the solutions of existing literature
4. to show how your solution is better (can be better (for proposals))
For the table that is placed here, please discuss it in light of the above-mentioned goals. The
main difference between the Prior Studies and Literature Review is that the Prior Studies is
done in a concise manner.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
4
1. Introduction
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
1.3 Problem Statement
The problem statement needs to be very clear and to the point.
A persuasive problem statement from a contextualized and intended-audience-awareness
perspective consists of:
1. PS1: description of the ideal scenario for your intended audience
•
Describe the goals, desired state, or the values that your audience considers
important and that are relevant to the problem.
2. PS2: reality of the situation
•
Describe a condition that prevents the goal, state, or value discussed in PS1
from being achieved or realized at the present time.
•It is imperative to make the audience feel the pain point.
3. PS3: consequences for the audience
•
Using specific details, show how the situation contains little promise of im-
provement unless something is done.
After the above-mentioned items, succinctly describe your approach/solution (”approach”
for proposal theses; ”solution” for “final” theses). You must be terse here because your
5
1. Introduction
approach/solution is like a seed/kernel in terms of its description here, which you expand
more through your objectives, and it grows larger in your description and methodology,
and its full explanation in the Methodology chapter.
A well constructed problem statement will convince your audience that the problem is real
and worth having you solve it.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
1.4 Objectives
Your objectives are the states that you desire to achieve in solving the problem. The general
objective is the main state to be achieved whereas the specific ones are sub-states to be
achieved.
1.4.1 General Objective(s)
To . . . ;
6
1. Introduction
1.4.2 Specific Objectives
1. To . . . ;
2. To . . . ;
3. To . . . ;
4. To . . . ;
5. To . . . ;
1.5 Significance of the Study
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
1.6 Assumptions, Scope and Delimitations
Bulletize your assumptions in one group, and then bulletize the scope in another, and do
the same for your delimitations.
7
1. Introduction
1.6.1 Assumptions
1. . . . ;
2. . . . ;
3. . . . ;
1.6.2 Scope
1. . . . ;
2. . . . ;
3. . . . ;
1.6.3 Delimitations
1. . . . ;
2. . . . ;
3. . . . ;
1.7 Description and Methodology
A purpose of the description here is to re-steer/remind the panelist/reader again by tersely
describing what your thesis is about (i.e. its problem and the main goal you want to achieve).
Your methodology is your means of achieving your stated objectives.
Note that each stated objective should have a corresponding methodology.
8
1. Introduction
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
1.8 Overview
Provide here a brief summary and what the reader should expect from each succeeding
chapter. Show how each chapter is connected with each other.
9
Chapter 2
LITERATURE REVIEW
Contents
2.1 ExistingWork................................ 11
2.2 Lacking in the Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Summary .................................. 15
10
2. Literature Review
2.1 Existing Work
Cite and summarize here relevant and significant literature (dissertations, theses, journals,
patents, notable conference papers) through a table and descriptions to prove that no one
has done your work yet. Your focus here is what has been done.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
11
2. Literature Review
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
12
2. Literature Review
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
2.2 Lacking in the Approaches
You can summarize the weaknesses of existing approaches by a tabular comparison of the
literature. Your focus here is what has not been done, and/or what features were missed,
and then introduce the necessity for doing your proposed solution.
Briefly include here the following in order to remind the reader why you are highlighting
the weakness of the solutions of existing literature.
•mentioning of the problem
•showing how your solution is better (can be better (for proposals))
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
13
2. Literature Review
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
14
2. Literature Review
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
2.3 Summary
15
Chapter 3
THEORETICAL CONSIDERATIONS
Contents
3.1 Summary .................................. 19
16
3. Theoretical Considerations
Before starting the first section, provide an overview of the purpose of this chapter and
its contents, and how they are relevant to your methodology.
This chapter is for providing the context to your panelist/reader. It is actually an
expanded form of the Background of the Study that you have put in Chapter 1.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
17
3. Theoretical Considerations
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
18
3. Theoretical Considerations
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Fig. 3.1 A quadrilateral image example.
3.1 Summary
19
Chapter 4
DESIGN CONSIDERATIONS
Contents
4.1 Summary .................................. 23
20
4. Design Considerations
Before starting the first section, provide an overview of the purpose of this chapter and
its contents, and how they are relevant to your methodology.
Your primary goal in the Design Considerations is to describe to your panelist/readers
the key topics that fall under Theoretical Considerations. These key topics are those that
you have directly adopted in making your solution/methodology.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
21
4. Design Considerations
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
22
4. Design Considerations
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
4.1 Summary
23
Chapter 5
METHODOLOGY
Contents
5.1 Implementation ............................... 25
5.2 Evaluation.................................. 27
5.3 Summary .................................. 29
24
5. Methodology
Mention here your methodology flow through a figure (preferably) and provide an
overview of it and how your methodology achieves your objectives. How your methodology
achieves each of your specific objective is what your panelists/examiners will be looking for.
Also make sure that you refer clearly to the chapters on the Literature Review, Theoretical
Considerations, and Design Considerations showing how your methodology ties with those
that you have discussed in those chapters.
5.1 Implementation
Summarize the process used to create/set-up the work with an explanation of such process,
instruments, and materials that you used if any. If the description is lengthy, use condensed
bullet points.
Rule of thumb: Implementation is how you made your work; (keywords: implemented,
created, made, soldered, programmed, etc.).
If you wrote a program or made a simulation, you must state how the program or
simulation functions in this section. An algorithm or a pseudocode as shown in Table B.2
is a good example.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
25
5. Methodology
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
26
5. Methodology
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
5.2 Evaluation
Describe the procedures for evaluating the correct behavior and outcome of your work,
including what information you need to gather and how you will obtain or measure it.
Rule of thumb: Evaluation is how you tested your work; (keywords: measured, tested,
compared, simulated, etc.).
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
27
5. Methodology
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
28
5. Methodology
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
5.3 Summary
29
Chapter 6
RESULTS AND DISCUSSION
Contents
6.1 Summary .................................. 32
30
6. Results and Discussion
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
31
6. Results and Discussion
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
6.1 Summary
32
Chapter 7
CONCLUSIONS, RECOMMENDATIONS,
AND FUTURE DIRECTIVES
Contents
7.1 ConcludingRemarks ............................ 34
7.2 Contributions ................................ 34
7.3 Recommendations.............................. 34
7.4 FutureProspects............................... 36
33
7. Conclusions, Recommendations, and Future Directives
7.1 Concluding Remarks
In this Thesis, . . .
7.2 Contributions
The interrelated contributions and supplements that have been developed in this Thesis are
listed as follows.
•the ;
•the ;
•the ;
7.3 Recommendations
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
34
7. Conclusions, Recommendations, and Future Directives
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
35
7. Conclusions, Recommendations, and Future Directives
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
7.4 Future Prospects
There are several prospect related in this research that may be extended for further studies.
. . . So the suggested topics are listed in the following.
1. the . . . .
2. the . . . .
3. the . . . .
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L
A
T
E
X-comment this and the following texts after you have implemented them. See the
following references for helpful guides for the bibliography and script editing in general.
Note that the links might be unavailable, but the names can be searched in the Web.
1. IEEE Citation Reference: www.ieee.org/documents/ieeecitationref.pdf
2. IEEE Editorial Style manual: www.ieee.org/documents/style manual.pdf
3.
IEEE Abbreviations for Transactions, Journals, Letters, and Magazines: www.ieee.
org/documents/trans journal names.pdf
Also in your BibTeX file, enclose letters or words that should all be in uppercase in curly
brackets. Example: IBM, Philippines, eXtensible Markup Language.
Produced: August 5, 2016, 23:45
45
Appendix A
ANSWERS TO QUESTIONS TO THIS
THESIS
46
A. Answers to Questions to this Thesis
How important is the problem to practice?
A possible answer to this question is the summary of your Significance of the Study, and
that portion of the Problem Statement where you describe the ideal scenario for your
intended audience.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
How will you know if the solution/s that you will achieve
would be better than existing ones?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
How will you measure the improvement/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
47
A. Answers to Questions to this Thesis
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
What is/are your basis/bases for the improvement/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Why did you choose that/those basis/bases?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
How significant are your measure/s of the improvement/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
48
A. Answers to Questions to this Thesis
What is the difference of the solution/s from existing
ones?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
How is it different from previous and existing ones?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
What are the assumptions made (that are behind for
your proposed solution to work)?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
49
A. Answers to Questions to this Thesis
Will your proposed solution/s be sensitive to these assump-
tions?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Can your proposed solution/s be applied to more general cases
when some of the assumptions are eliminated? If so, how?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
What is the necessity of your approach / proposed
solution/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
50
A. Answers to Questions to this Thesis
What will be the limits of applicability of your proposed solu-
tion/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
What will be the message of the proposed solution to technical
people? How about to non-technical managers and business
men?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
How will you know if your proposed solution/s is/are
correct?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
51
A. Answers to Questions to this Thesis
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Will your results warrant the level of mathematics used (i.e., will
the end justify the means)?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Is/are there an/ alternative way/s to get to the same
solution/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Can you come up with illustrating examples, or even better,
counter examples to your proposed solution/s?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
52
A. Answers to Questions to this Thesis
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
Is there an approximation that can arrive at the essentially the
same proposed solution/s more easily?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
If you were the examiner of your Thesis, how would
you present the Thesis in another way? Give your
remarks, especially for your methodology and the re-
sults and discussions.
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
What are the weaknesses of your Thesis, specifically your method-
ology and the results and discussions?
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
53
A. Answers to Questions to this Thesis
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
54
Appendix B
USAGE EXAMPLES
55
B. Usage Examples
The user is expected to have a working knowledge of L
A
T
E
X. A good introduction is
in [4]. Its latest version can be accessed at http://www.ctan.org/tex-archive/info/lshort.
Equations
The following examples show how to typeset equations in L
A
T
E
X. This section also shows
examples of the use of
\gls{ }
commands in conjunction with the items that are in
the
notation.tex
file.
Please make sure that the entries in notation.tex are
those that are referenced in the L
A
T
E
X document files used by this Thesis. Please
comment out unused notations and be careful with the commas and brackets in
notation.tex .
In
(B.1)
, the output signal
y(t)
is the result of the convolution of the input signal
x(t)
and the impulse response h(t).
y(t) = h(t)∗x(t) = Z+∞
−∞
h(t−τ)x(τ) dτ(B.1)
Other example equations are as follows.
V1
I1="A B
C D#V2
I2(B.2)
1
2<jmod jy
17k2−17bxc−mod(byc,17),2k,(B.3)
|ζ(x)3ζ(x+iy)4ζ(x+ 2iy)|= exp X
n,p
3 + 4 cos(ny log p) + cos(2ny log p)
npnx ≥1(B.4)
56
B. Usage Examples
The verbatim L
A
T
E
X code of Sec. B is in List. B.1.
Listing B.1: Sample L
A
T
E
X code for equations and notations usage
1The foll owi ng exa mple s show how to ty pes et eq uati ons in \ LaTeX . This
secti on also shows ex ampl es of the use of \ verb | \ gls { } | co mman ds
in conju n ction with the items that are in the \ verb | nota tion . tex |
file . \ tex tbf { P lea se make su re that the en tri es in } \ ve rb | nota tio n .
tex |\ textbf { are those that are re feren c ed in the \ LaTeX \
do cume nt files used by this \ d ocum entT ype . Please comme nt out
unused n otat ions and be careful with the commas and br acke ts in } \
verb | n ot ati on . tex |.
2
3In ~\ e qr ef { eq : conv } , th e ou tpu t sig nal \ gls { not : o ut put _ s ig t } is the
re sul t of th e c on vol ut io n of the inp ut si gn al \ gls { not : i npu t _ sig t }
and the im pul se res po nse \ gls { not : ir }.
4
5\ begin { eqna rra y }
6y\ left ( t \ right ) = h\ left ( t \ right ) * x \ left ( t \ right ) =\ int _{ -\
infty }^{+\ infty } h\ left ( t -\ tau \ rig ht ) x\ left ( \ tau \ right ) \
ma th rm { d }\ tau
7\ label { eq : conv }
8\ end { e qnar ray }
9
10 Other ex am ple e quat ion s are as follows .
11
12 \ begin { eqna rra y }
13 \ left [ \ dfra c { V _{1} }{ I _{1} } \ right ] =
14 \ begin { bma tri x }
15 A & B \\
16 C&D
17 \ end { b mat rix }
18 \ left [ \ dfra c { V _{2} }{ I _{2} } \ right ]
19 \ label { eq : ABCD }
20 \ end { e qnar ray }
21
22 \ begin { eqna rra y }
23 \ dfrac {1}{2} < \ left \ lfloor \ mat hrm { mod }\ left (\ left \ lf lo or \ dfrac { y }{1 7}
\ right \ rf lo or 2^{ -17 \ lfloor x \ rf lo or - \ m at hr m {mod }(\ l fl oo r y \
rfloor , 17) } ,2\ ri ght ) \ righ t \rfloor ,
24 \ end { e qnar ray }
25
26 \ begin { eqna rra y }
27 | \ zeta (x )^3 \ zeta ( x + iy )^4 \ zeta ( x + 2 iy ) | =
28 \ exp \ sum _{ n ,p } \ frac {3 + 4 \ cos ( ny \ log p ) + \ cos (2 ny \ log p ) }{ np ^{ nx
}} \ ge 1
29 \ end { e qnar ray }
57
B. Usage Examples
Notations
In order to use the standardized notation, the user is highly suggested to see the ISO 80000-2
standard [5].
See https://en.wikipedia.org/wiki/Help:Displaying a formula and https://en.wikipedia.
org/wiki/List of mathematical symbols for L
A
T
E
X maths and other notations, respectively.
The following were taken from isomath-test.tex .
Math alphabets
If there are other symbols in place of Greek letters in a math alphabet, it uses T1 or OT1
font encoding instead of OML.
mathnormal A, B, Γ, ∆, Θ, Λ, Ξ, Π, Σ, Φ, Ψ, Ω, α, β, π, ν, ω, v, w, 0,1,9
mathit A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathrm A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathbf A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathsf A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathtt A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,↑,↓,ß,˚,!,v,w,0,1,9
New alphabets bold-italic, sans-serif-italic, and sans-serif-bold-italic.
mathbfit A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,α,β,π,ν,ω,v,w,,,
mathsfit , , , , , , , , , , , , , , , , , , , , ,
mathsfbfit , , , , , , , , , , , , , , , , , , , , ,
Do the math alphabets match?
axαωaxαω T CΘΓ T CΘΓ
Vector symbols
Alphabetic symbols for vectors are boldface italic,
λ=e1·a
, while numeric ones (e.g.
the zero vector) are bold upright, a+0=a.
Matrix symbols
Symbols for matrices are boldface italic, too:1Λ=E·A.
1
However, matrix symbols are usually capital letters whereas vectors are small ones. Exceptions are
physical quantities like the force vector For the electrical field E.
58
B. Usage Examples
Tensor symbols
Symbols for tensors are sans-serif bold italic,
=· ⇐⇒ αijl =eijk ·akl.
The permittivity tensor describes the coupling of electric field and displacement:
D=0 rE
59
B. Usage Examples
Bold math version
The “bold” math version is selected with the commands
\boldmath
or
\mathversion{bold}
mathnormal A, B, Γ, ∆, Θ, Λ, Ξ, Π, Σ, Φ, Ψ, Ω, α, β, π, ν, ω, v, w, 0,1,9
mathit A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathrm A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathbf A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathsf A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,ff,fi,ß,˚,!,v,w,0,1,9
mathtt A,B,Γ,∆,Θ,Λ,Ξ,Π,Σ,Φ,Ψ,Ω,↑,↓,ß,˚,!,v,w,0,1,9
New alphabets bold-italic, sans-serif-italic, and sans-serif-bold-italic.
mathbfit A, B, Γ , ∆, Θ, Λ, Ξ, Π, Σ, Φ, Ψ , Ω, α, β, π, ν, ω, v, w, , , 
mathsfit , , , , , , , , , , , , , , , , , , , , ,
mathsfbfit , , , , , , , , , , , , , , , , , , , , ,
Do the math alphabets match?
axαωaxαω T CΘΓ T CΘΓ
Vector symbols
Alphabetic symbols for vectors are boldface italic,
λ=e1·a
, while numeric ones (e.g.
the zero vector) are bold upright, a+ 0 = a.
Matrix symbols
Symbols for matrices are boldface italic, too:2Λ=E·A.
Tensor symbols
Symbols for tensors are sans-serif bold italic,
=· ⇐⇒ αijl =eijk ·akl.
The permittivity tensor describes the coupling of electric field and displacement:
D=0 rE
2
However, matrix symbols are usually capital letters whereas vectors are small ones. Exceptions are
physical quantities like the force vector For the electrical field E.
60
B. Usage Examples
The verbatim L
A
T
E
X code of Sec. B is in List. B.2.
Listing B.2: Sample L
A
T
E
X code for notations usage
1% A test s tring with Latin and Greek lett ers ::
2\ newco mmand {\ t e ststr ing }{ %
3% capital Latin letters
4% A , B ,C ,
5A ,B ,
6% capital Greek letters
7%\ Gamma ,\ Delta ,\ Theta ,\ Lambda ,\ Xi ,\ Pi ,\ Sigma ,\ Upsilon ,\ Phi ,\ Psi ,
8\ Gamma ,\ Delta ,\ Theta ,\ Lambda ,\ Xi ,\ Pi ,\ Sigma ,\ Phi ,\ Psi ,\ Omega ,
9% small Greek le tters
10 \ alpha ,\ beta ,\ pi ,\ nu ,\ omega ,
11 % small Latin letter s :
12 % com pare \nu , \omega , v , and w
13 v ,w ,
14 % digits
15 0 ,1 ,9
16 }
17
18
19 \ su bsec tion *{ Math al phab ets }
20
21 If there are other symbols in place of Greek letters in a math
22 alphabet , it uses T 1 or OT 1 font enc odin g ins tead of OML .
23
24 \ begin { eqna rra y *}
25 \ mbox { mathno rmal } & & \ t est str ing \\
26 \ mbox { mathit } & & \ mathit {\ te sts trin g }\\
27 \ mbox { mathrm } & & \ mathrm {\ te sts trin g }\\
28 \ mbox { mathbf } & & \ mathbf {\ te sts trin g }\\
29 \ mbox { mathsf } & & \ mathsf {\ te sts trin g }\\
30 \ mbox { mathtt } & & \ mathtt {\ te sts trin g }
31 \ end { e qnar ray *}
32 New alp habet s bold - italic , sans - serif - italic , and sans - serif - bold -
italic.
33 \ begin { eqna rra y *}
34 \ mbox { mathb fi t } & & \ mathb fit {\ tests tri ng }\\
35 \ mbox { maths fi t } & & \ maths fit {\ tests tri ng }\\
36 \ mbox { mathsf bfit } & & \ m ath sfb fit {\ testst ring }
37 \ end { e qnar ray *}
38 %
39 Do the math alph abet s m atch ?
40
41 $
42 \ math norm al { a x \ alpha \ o mega }
43 \ mat hbf it {a x \ alpha \ omega }
44 \ math sfbf it { a x \ alpha \ omega }
45 \quad
46 \ math sfbf it { T C \ Theta \ Gamma }
47 \ mat hbf it {T C \ Theta \ Gamma }
48 \ math norm al { T C \ Theta \ G amma }
49 $
50
51 \ sub sec tion *{ Vector symb ols }
52
61
B. Usage Examples
53 Al p habet ic sym bols for vector s are bol dface italic ,
54 $\ vec {\ lam bda }=\ vec { e }_ {1 }\ cd ot \ ve c {a }$ ,
55 while nu meric ones ( e . g. the zero vec tor ) are bold upright ,
56 $\ ve c {a } + \ vec {0 } = \ vec { a }$ .
57
58 \ sub sec tion *{ Matrix symb ols }
59
60 Symbo ls for m atri ces are bold face italic , too :%
61 \ fo otno te { However , matrix symbols are usually c apital le tters whe rea s
vectors
62 are small ones . Ex cepti ons are physica l quant i ties like the force
63 ve cto r $\ vec { F }$ or t he ele ct rica l fie ld $\ vec { E }$ . %
64 }
65 $\ matri xsym {\ Lam bda }=\ matri xsym { E}\ cdot \ matr ixs ym {A }.$
66
67
68 \ sub sec tion *{ Tensor symb ols }
69
70 Symbo ls for t ensors are sans - serif bold italic ,
71
72 \[
73 \ te nso rsym {\ alpha } = \ ten sors ym {e }\ cdot \ tenso rsym {a}
74 \ quad \ L on gleftrig ht ar row \ quad
75 \ alpha _{ ijl } = e _{ ijk }\ cdot a _{ kl }.
76 \]
77
78
79 The permi t tivity t ensor d escri bes the cou plin g of elec tric field and
80 displacement: \[
81 \ vec { D }=\ epsi lon _{ 0} \ t enso rs ym {\ epsi lon }_{\ math rm { r }}\ v ec { E }\]
82
83
84
85 \newpage
86 \ sub sec tion *{ Bold math versio n }
87
88 The ‘‘bold ’’ math version is s elec ted with the c omma nds
89 \ verb +\ boldm ath + or \ verb +\ mathve rsion { bold }+
90
91 {\ bo ldma th
92 \ begin { eqna rra y *}
93 \ mbox { mathno rmal } & & \ t est str ing \\
94 \ mbox { mathit } & & \ mathit {\ te sts trin g }\\
95 \ mbox { mathrm } & & \ mathrm {\ te sts trin g }\\
96 \ mbox { mathbf } & & \ mathbf {\ te sts trin g }\\
97 \ mbox { mathsf } & & \ mathsf {\ te sts trin g }\\
98 \ mbox { mathtt } & & \ mathtt {\ te sts trin g }
99 \ end { e qnar ray *}
100 New alp habet s bold - italic , sans - serif - italic , and sans - serif - bold -
italic.
101 \ begin { eqna rra y *}
102 \ mbox { mathb fit } & & \ math bfit {\ t ests tri ng }\\
103 \ mbox { maths fit } & & \ math sfit {\ t ests tri ng }\\
104 \ mbox { mathsf bfit } & & \ m ath sfb fit {\ testst ring }
105 \ end { e qnar ray *}
106 %
107 Do the math alph abet s m atch ?
62
B. Usage Examples
108
109 $
110 \ math norm al { a x \ alpha \ o mega }
111 \ mat hbf it {a x \ alpha \ omega }
112 \ math sfbf it { a x \ alpha \ omega }
113 \quad
114 \ math sfbf it { T C \ Theta \ Gamma }
115 \ mat hbf it {T C \ Theta \ Gamma }
116 \ math norm al { T C \ Theta \ G amma }
117 $
118
119 \ sub sec tion *{ Vector symb ols }
120
121 Al p habet ic sym bols for vector s are bol dface italic ,
122 $\ ve c {\ lam bda }=\ v ec { e }_ {1} \ c do t \ vec { a}$ ,
123 while nu meric ones ( e . g. the zero vec tor ) are bold upright ,
124 $\ ve c {a } + \ vec {0 } = \ vec { a }$ .
125
126
127
128
129 \ sub sec tion *{ Matrix symb ols }
130
131 Symbo ls for m atri ces are bold face italic , too :%
132 \ fo otno te { However , matri x sym bols are usu ally capi tal letters wh ereas
vectors
133 are small ones . Ex cepti ons are physica l quant i ties like the force
134 ve cto r $\ vec { F }$ or t he ele ct rica l fie ld $\ vec { E }$ . %
135 }
136 $\ matri xsym {\ Lam bda }=\ matri xsym { E}\ cdot \ matr ixs ym {A }.$
137
138
139 \ sub sec tion *{ Tensor symb ols }
140
141 Symbo ls for t ensors are sans - serif bold italic ,
142
143 \[
144 \ te nso rsym {\ alpha } = \ ten sors ym {e }\ cdot \ tenso rsym {a}
145 \ quad \ L on gleftrig ht ar row \ quad
146 \ alpha _{ ijl } = e _{ ijk }\ cdot a _{ kl }.
147 \]
148
149 The permi t tivity t ensor d escri bes the cou plin g of elec tric field and
150 displacement: \[
151 \ vec { D }=\ epsi lon _{ 0} \ t enso rs ym {\ epsi lon }_{\ math rm { r }}\ v ec { E }\]
152 }
63
B. Usage Examples
Abbreviation
This section shows examples of the use of L
A
T
E
Xcommands in conjunction with the
items that are in the
abbreviation.tex
and in the
glossary.tex
files. Please
see List. B.3.
To lessen the L
A
T
E
X compilation time, it is suggested that you use
\acr{ } only for the first occurrence of the word to be abbreviated.
Again please see List. B.3. Here is an example of first use: alternating current (ac).
Next use: ac. Full: alternating current (ac). Here’s an acronym referenced using
\acr
:
hyper-text markup language (html). And here it is again: html. If you are used to the
glossaries
package, note the difference in using
\gls
: hyper-text markup language
(html). And again (no difference): hyper-text markup language (html). Here are some more
entries:
•extensible markup language (xml) and cascading style sheet (css).
•Next use: xml and css.
•Full form: extensible markup language (xml) and cascading style sheet (css).
•Reset again.
•Start with a capital. Hyper-text markup language (html).
•Next: Html. Full: Hyper-text markup language (html).
•
Prefer capitals? Extensible markup language (XML). Next: XML. Full: extensible
markup language (XML).
•
Prefer small-caps? Cascading style sheet (CSS). Next: CSS. Full: cascading style
sheet (CSS).
•Resetting all acronyms.
•Here are the acronyms again:
•
Hyper-text markup language (HTML), extensible markup language (XML) and cas-
cading style sheet (CSS).
•Next use: HTML,XML and CSS.
•
Full form: Hyper-text markup language (HTML), extensible markup language (XML)
and cascading style sheet (CSS).
64
B. Usage Examples
•Provide your own link text: style sheet.
The verbatim L
A
T
E
X code of Sec. B is in List. B.3.
Listing B.3: Sample L
A
T
E
X code for abbreviations usage
1Ag ai n p lea se se e List .~\ ref { lst : ab brv }. Her e is an ex amp le of fir st u se :
\ acr { ac }. Nex t use : \ ac r {ac }. F ul l : \ g ls { ac }. Here ’ s an ac rony m
re fe renc ed usi ng \ verb | \ acr |: \ acr { html }. An d here it is again : \
acr { html }. If you are used to the \ tex ttt { gloss ari es } package , note
the d iff er ence in usi ng \ verb | \ gls |: \ gls { h tm l }. An d ag ain ( no
di ff eren ce ) : \ gls { html }. Here are s om e mo re e ntr ies :
2
3\ begin { ite miz e }
4
5\ it em \ acr { xml } and \ acr { c ss }.
6
7\ it em Next use : \ acr { xml } and \ a cr { css }.
8
9\ it em Full for m : \ g ls { xm l } and \ gls { css }.
10
11 \ item Reset again . \ glsre set all { ab bre viat ion }
12
13 \ it em St art with a c apit al . \ Ac r { ht ml }.
14
15 \ it em Next : \ Acr { ht ml }. Fu ll : \ Gls { ht ml }.
16
17 \ item Prefer capitals ? \ rene w command {\ a cronym f ont }[1]{\
Mak eT ex tU pp er ca se {# 1} } \ Acr { xml }. Nex t : \ acr { xml }. Full : \ gls { xml
}.
18
19 \ item Pr efer small - ca ps ? \ r enewco mm and {\ a cr onym font }[1 ]{\ te xts c {#1}}
\ Acr { css }. Nex t : \ acr { css }. Full : \ gls { css }.
20
21 \ item Resett ing all acronyms .\ glsres e tall { ab brev iati o n }
22
23 \ item Her e are the ac ron yms again :
24
25 \ it em \ Acr { ht ml } , \ acr { xml } and \ acr { css }.
26
27 \ it em Next use : \ Acr { html } , \ acr { xml } and \ acr { c ss }.
28
29 \ it em Full for m : \ G ls { h tm l }, \ gls { xml } an d \ gls { cs s }.
30
31 \ it em Pro vide yo ur own link tex t : \ g lsl ink {[ tex tbf ] css }{ st yle }
32
33 \ end { i tem ize }
65
B. Usage Examples
Glossary
This section shows examples of the use of
\gls{ }
commands in conjunction with the
items that are in the
glossary.tex
and
notation.tex
files. Note that entries in
notation.tex are prefixed with “ not: ” label (see List. B.4).
Please make sure that the entries in notation.tex are those that are referenced
in the L
A
T
E
X document files used by this Thesis. Please comment out unused notations
and be careful with the commas and brackets in notation.tex .
•
Matrices are usually denoted by a bold capital letter, such as
A
. The matrix’s
(i, j)
th
element is usually denoted aij . Matrix Iis the identity matrix.
•A set, denoted as S, is a collection of objects.
•The universal set, denoted as U, is the set of everything.
•The empty set, denoted as ∅, contains no elements.
•
Functional Analysis is seen as the study of complete normed vector spaces, i.e.,
Banach spaces.
•The cardinality of a set, denoted as |S| , is the number of elements in the set.
The verbatim L
A
T
E
X code for the part of Sec. B is in List. B.4.
66
B. Usage Examples
Listing B.4: Sample L
A
T
E
X code for glossary and notations usage
1\ begin { ite miz e }
2
3\ item \ Gl sp l { ma trix } are usu all y deno ted by a bold capi tal letter ,
such as $\ math bfit { A }$. Th e \ gls { m atr ix } ’s $( i ,j )$ th elem ent is
us ua lly deno te d $ a_{ ij }$. \ Gls { mat ri x } $\ mat hb f {I }$ is the
id en tit y \ gls { m atr ix }.
4
5\ it em A set , den ote d as \ gls { not : set } , is a c ol lec ti on of ob jec ts .
6
7\ it em The uni ve rsa l set , den oted as \ gls { not : u ni ve rsal Se t } , is the
set of ev eryth ing .
8
9\ it em The empt y set , d enot ed as \ gls { not : e mpty Se t }, cont ai ns no
elements.
10
11 \ it em \ Gls { F un ctio na l Anal ys is } is seen as the stu dy of c om ple te
normed vector spaces , i.e., Banach spaces.
12
13 \ it em The car di na lity of a set , den oted as \ gls { not : c ar di nal it y } , is
the nu mbe r of elem ents in the s et .
14
15 \ end { e nume ra te }
67
B. Usage Examples
Figure
This section shows several ways of placing figures. PDFL
A
T
E
X compatible files are PDF,
PNG, and JPG. Please see the figure subdirectory.
Fig. B.1 A quadrilateral image example.
68
B. Usage Examples
Fig. B.1 is a gray box enclosed by a dark border. List. B.5 shows the corresponding
L
A
T
E
X code.
Listing B.5: Sample L
A
T
E
X code for a single figure
1\ begin { figure }[! htbp ]
2\ ce nte ring
3\ inc ludeg raphi cs [ width =0.5\ text width ]{ exa mple }
4\ capti on {A quadril atera l image example .}
5\ la bel { fig : e xam ple }
6\ end { f ig ure }
7\ cle ardou blepa ge
8
9Fig .~\ ref { fig : example } is a gray box enclo sed by a dark border . List .~\
ref { ls t : one fig } s hows the co rr es pond in g \ La TeX \ c od e .
10 \ end { f ig ure }
69
B. Usage Examples
(a) A sub-figure in the top row.
(b) A sub-figure in the middle row.
(c) A sub-figure in the bottom row.
Fig. B.2 Figures on top of each other. See List. B.6 for the corresponding L
A
T
E
X code.
70
B. Usage Examples
Listing B.6: Sample L
A
T
E
X code for three figures on top of each other
1\ begin { figure }[! htbp ]
2\ ce nte ring
3\ su bbo ttom [ A sub - figure in the top row .]{
4\ i nc lu de gr aphic s [ w idth =0. 35\ tex tw idt h ]{ exam ple _ gray _ bo x }
5\ la bel { fig : top }
6}
7\ vfill
8\ su bbo ttom [ A sub - figure in the mid dle row .]{
9\ i nc lu de gr aphic s [ w idth =0. 35\ tex tw idt h ]{ exam ple _ gray _ bo x }
10 \ la bel { fig : mid }
11 }
12 \ vfill
13 \ su bbo ttom [ A sub - figure in the bot tom row .]{
14 \ i nc lu de gr aphic s [ w idth =0. 35\ tex tw idt h ]{ exam ple _ gray _ bo x }
15 \ la bel { fig : bo tm }
16 }
17 \ capti on { Figur es on top of each other }
18 \ la bel { fig : tmb }
19 \ end { f ig ure }
71
B. Usage Examples
(a) A sub-figure in the upper-left corner. (b) A sub-figure in the upper-right corner.
(c) A sub-figure in the lower-left corner. (d) A sub-figure in the lower-right corner
Fig. B.3 Four figures in each corner. See List. B.7 for the corresponding L
A
T
E
X code.
72
B. Usage Examples
Listing B.7: Sample L
A
T
E
X code for the four figures
1\ begin { figure }[! htbp ]
2\ ce nte ring
3\ su bbo ttom [ A sub - figure in the upper - left co rner .]{
4\ i nc lu de gr aphic s [ w idth =0. 45\ tex tw idt h ]{ exam ple _ gray _ bo x }
5\ la bel { fig : u ppr le ft }
6}
7\ hfill
8\ su bbo ttom [ A sub - figure in the upper - right corne r .]{
9\ i nc lu de gr aphic s [ w idth =0. 45\ tex tw idt h ]{ exam ple _ gray _ bo x }
10 \ la bel { fig : u ppr ig ht }
11 }
12 \ vfill
13 \ su bbo ttom [ A sub - figure in the lower - left co rner .]{
14 \ i nc lu de gr aphic s [ w idth =0. 45\ tex tw idt h ]{ exam ple _ gray _ bo x }
15 \ la bel { fig : l ower le ft }
16 }
17 \ hfill
18 \ su bbo ttom [ A sub - figure in the lower - right corne r ]{
19 \ i nc lu de gr aphic s [ w idth =0. 45\ tex tw idt h ]{ exam ple _ gray _ bo x }
20 \ la bel { fig : l owr ig ht }
21 }
22 \ c apt ion { Fo ur f igu res in eac h c or ner . Se e List .~\ re f { lst : f ourf ig s } for
the corre spondin g \ L aTeX \ code .}
23 \ la bel { fig : f our fig }
24 \ end { f ig ure }
73
B. Usage Examples
Table
This section shows an example of placing a table (a long one). Table B.1 are the triples.
TABLE B.1 FEASIBLE TRIPLES FOR HIGHLY VARIABLE GRID
Time (s) Triple chosen Other feasible triples
0 (1, 11, 13725) (1, 12, 10980), (1, 13, 8235), (2, 2, 0), (3, 1, 0)
2745 (1, 12, 10980) (1, 13, 8235), (2, 2, 0), (2, 3, 0), (3, 1, 0)
5490 (1, 12, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
8235 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
10980 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
13725 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
16470 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
19215 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
21960 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
24705 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
27450 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
30195 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
32940 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
35685 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
38430 (1, 13, 10980) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
41175 (1, 12, 13725) (1, 13, 10980), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
43920 (1, 13, 10980) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
46665 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
49410 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
52155 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
54900 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
57645 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
60390 (1, 12, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
63135 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
65880 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
68625 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
71370 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
74115 (1, 12, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
76860 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
79605 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
82350 (1, 12, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
85095 (1, 12, 13725) (1, 13, 10980), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
87840 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
90585 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
93330 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
96075 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
98820 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
101565 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
104310 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
107055 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
109800 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
112545 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
115290 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
118035 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
120780 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
123525 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
Continued on next page
74
B. Usage Examples
Continued from previous page
Time (s) Triple chosen Other feasible triples
126270 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
129015 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
131760 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
134505 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
137250 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
139995 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
142740 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
145485 (1, 12, 16470) (1, 13, 13725), (2, 2, 2745), (2, 3, 0), (3, 1, 0)
148230 (2, 2, 2745) (2, 3, 0), (3, 1, 0)
150975 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
153720 (1, 12, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
156465 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
159210 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
161955 (1, 13, 16470) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
164700 (1, 13, 13725) (2, 2, 2745), (2, 3, 0), (3, 1, 0)
75
B. Usage Examples
List. B.8 shows the corresponding L
A
T
E
X code.
Listing B.8: Sample L
A
T
E
X code for making typical table environment
1\ begin { center }
2{\ sc r iptsi ze
3\ begin { tabu lar x }{\ t ext widt h }{ p {0.1\ text wid th }| p {0 .2\ textw idth }| p {0.5 \
te xtwid th }}
4\ c apt ion { F easi bl e t ripl es for high ly va riab le grid } \ lab el { ta b : tri ple _
grid } \\
5\ hline
6\ hline
7\ te xtb f { Ti me ( s) } &
8\textbf{Triple chosen} &
9\ te xt bf { Other fe asib le tr ip les } \\
10 \ hline
11 \endfirsthead
12 \ multi colum n {3}{ c}%
13 {\ textit { Conti nued from pre viou s page }} \\
14 \ hline
15 \ hline
16 \ te xtb f { Ti me ( s) } &
17 \textbf{Triple chosen} &
18 \ te xt bf { Other fe asib le tr ip les } \\
19 \ hline
20 \endhead
21 \ hline
22 \ m ul tico lu mn {3}{ r }{\ te xt it { C onti nu ed on ne xt pa ge }} \\
23 \endfoot
24 \ hline
25 \endlastfoot
26 \ hline
27
28 0 & (1 , 11 , 137 25) & (1 , 12 , 10 98 0) , (1 , 13 , 823 5) , (2 , 2 , 0) , (3 , 1 , 0)
\\
29 27 45 & (1 , 12 , 1 09 80) & (1 , 13 , 8 235 ) , (2 , 2 , 0) , (2 , 3 , 0) , (3 , 1 , 0)
\\
30 54 90 & (1 , 12 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
31 82 35 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
32 10 980 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
33 13 725 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
34 16 470 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
35 19 215 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
36 21 960 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
37 24 705 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
38 27 450 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
39 30195 & (2 , 2, 2745) & (2 , 3, 0) , (3 , 1, 0) \\
40 32 940 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
41 35 685 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
42 38 430 & (1 , 13 , 1 09 80) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
76
B. Usage Examples
43 41 175 & (1 , 12 , 1 37 25) & (1 , 13 , 109 80) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
44 43 920 & (1 , 13 , 1 09 80) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
45 46665 & (2 , 2, 2745) & (2 , 3, 0) , (3 , 1, 0) \\
46 49410 & (2 , 2, 2745) & (2 , 3, 0) , (3 , 1, 0) \\
47 52 155 & (1 , 12 , 1 64 70) & (1 , 13 , 137 25) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
48 54 900 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
49 57 645 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
50 60 390 & (1 , 12 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
51 63 135 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
52 65 880 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
53 68625 & (2 , 2, 2745) & (2 , 3, 0) , (3 , 1, 0) \\
54 71 370 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
55 74 115 & (1 , 12 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
56 76 860 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
57 79 605 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
58 82 350 & (1 , 12 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
59 85 095 & (1 , 12 , 1 37 25) & (1 , 13 , 109 80) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 , 1 ,
0) \\
60 87 840 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
61 90 585 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
62 93 330 & (1 , 13 , 1 37 25) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
63 96 075 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
64 98 820 & (1 , 13 , 1 64 70) & (2 , 2 , 2 745 ) , (2 , 3 , 0) , (3 , 1 , 0) \\
65 10 156 5 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
66 10 431 0 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
67 10 705 5 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
68 10 980 0 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
69 11 254 5 & (1 , 12 , 164 70) & (1 , 13 , 1 372 5) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 ,
1, 0) \\
70 11 529 0 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
71 11 803 5 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
72 12 078 0 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
73 12 352 5 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
74 12 627 0 & (1 , 12 , 164 70) & (1 , 13 , 1 372 5) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 ,
1, 0) \\
75 12 901 5 & (2 , 2 , 2 745 ) & (2 , 3 , 0) , (3 , 1 , 0) \\
76 13 176 0 & (2 , 2 , 2 745 ) & (2 , 3 , 0) , (3 , 1 , 0) \\
77 13 450 5 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
78 13 725 0 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
79 13 999 5 & (2 , 2 , 2 745 ) & (2 , 3 , 0) , (3 , 1 , 0) \\
80 14 274 0 & (2 , 2 , 2 745 ) & (2 , 3 , 0) , (3 , 1 , 0) \\
81 14 548 5 & (1 , 12 , 164 70) & (1 , 13 , 1 372 5) , (2 , 2 , 27 45) , (2 , 3 , 0) , (3 ,
1, 0) \\
82 14 823 0 & (2 , 2 , 2 745 ) & (2 , 3 , 0) , (3 , 1 , 0) \\
83 15 097 5 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
84 15 372 0 & (1 , 12 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
85 15 646 5 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
86 15 921 0 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
87 16 195 5 & (1 , 13 , 164 70) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
88 16 470 0 & (1 , 13 , 137 25) & (2 , 2 , 2 74 5) , (2 , 3 , 0) , (3 , 1 , 0) \\
89 \ end { t abul arx }
90 }
91 \ end { c en ter }
77
B. Usage Examples
Algorithm or Pseudocode Listing
Table B.2 shows an example pseudocode. Note that if the pseudocode exceeds one page, it
can mean that its implementation is not modular. List. B.9 shows the corresponding L
A
T
E
X
code.
TABLE B.2 CALCULATION OF y=xn
Input(s):
n:nth power; n∈Z+
x: base value; x∈R+
Output(s):
y: result; y∈R+
Require: n≥0∨x6= 0
Ensure: y=xn
1: y⇐1
2: if n < 0then
3: X⇐1/x
4: N⇐ −n
5: else
6: X⇐x
7: N⇐n
8: end if
9: while N6= 0 do
10: if Nis even then
11: X⇐X×X
12: N⇐N/2
13: else {Nis odd}
14: y⇐y×X
15: N⇐N−1
16: end if
17: end while
78
B. Usage Examples
Listing B.9: Sample L
A
T
E
X code for algorithm or pseudocode listing usage
1\ begin { ta ble }[! htbp ]
2\ capti on { Cal cula tion of $ y = x ^n $}
3\ la bel { tab : cal cxn }
4{\footnotesize
5\ begin { tab ula r }{ lll }
6\ hline
7\ hline
8{\ b fs er ies I npu t ( s) :} & & \\
9$n$ & : & $n $ th power ; $n \ in \ mathbb {Z }^ {+} $ \\
10 $x$ & : & base value ; $x \ in \ mathbb {R }^ {+}$ \\
11 \ hline
12 {\ b fs er ies O ut put ( s ) :} & & \\
13 $y$ & : & result ; $ y \ in \ mathbb { R }^{+}$ \\
14 \ hline
15 \ hline
16 \\
17 \ end { t abu lar }
18 }
19 \ begin { a lgo rithm ic }[1]
20 {\footnotesize
21 \ R EQU IRE $n \ geq 0 \ vee x \ neq 0$
22 \ ENSURE $y = x ^ n $
23 \ STATE $ y \ L efta rrow 1$
24 \ IF {$ n < 0$ }
25 \ STATE $X \ Left arro w 1 / x$
26 \ STATE $ N \ L efta rrow -n $
27 \ ELSE
28 \ STATE $ X \ L efta rrow x$
29 \ STATE $ N \ L efta rrow n$
30 \ ENDIF
31 \ W HIL E {$ N \ n eq 0$}
32 \ IF {$ N $ is eve n }
33 \ STATE $ X \ L efta rrow X \ t imes X$
34 \ STATE $N \ Left arro w N / 2$
35 \ E LS E [$ N $ is o dd ]
36 \ STATE $ y \ L efta rrow y \ t imes X$
37 \ STATE $N \ Left arro w N - 1$
38 \ ENDIF
39 \ENDWHILE
40 }
41 \ end { a lg orit hm ic }
42 \ end { tab le }
79
B. Usage Examples
Program/Code Listing
List. B.10 is a program listing of a C code for computing Fibonacci numbers by calling the
actual code. Please see the code subdirectory.
Listing B.10: Computing Fibonacci numbers in C (./code/fibo.c)
1/* fibo .c -- It pr in ts out the first N F ibon acci
2* numbers.
3*/
4
5# i nc lu de < s td io . h >
6
7int mai n (void ) {
8int n ; /* Number of fibo nacci n umb ers we will print */
9int i ; /* Index of f ibona cci number to be printed next */
10 int cu rrent ; /* Val ue o f th e ( i) th f ibo na cc i nu mbe r */
11 int nex t ; /* Val ue of th e (i +1) th fi bo nac ci n um ber */
12 int tw oaway ; /* Val ue of the ( i +2) th fi bo nac ci num ber */
13
14 printf (" How many Fibon acci n umb ers do you want to c ompute ? ");
15 sc anf ( " %d " , & n );
16 if (n <=0)
17 printf (" The number should be posi tive .\ n");
18 else {
19 printf ("\ n \ n \ tI \ t Fibon acci (I) \ n \ t =============== = = = = = = \ n ") ;
20 next = current = 1;
21 for ( i =1; i <= n ; i ++) {
22 printf ("\t % d \t % d \ n" , i , current ) ;
23 tw oaw ay = c urr ent + next ;
24 cu rre nt = next ;
25 next = two awa y ;
26 }
27 }
28 }
29
30 /* The output from a run of this progra m was :
31
32 How many Fibo nacci n umbers do you want to com pute ? 9
33
34 I Fi bon acci ( I)
35 =====================
36 1 1
37 2 1
38 3 2
39 4 3
40 5 5
41 6 8
42 7 13
43 8 21
44 9 34
45
46 */
80
B. Usage Examples
List. B.11 shows the corresponding L
A
T
E
X code.
Listing B.11: Sample L
A
T
E
X code for program listing
1List .~\ ref { lst : fib _ c} is a pro gram l ist ing of a C co de for c omp ut ing
Fi bona cci nu mbe rs by call ing the act ua l code . Pl eas e see the \ ve rb |
code | subdirectory.
81
B. Usage Examples
Referencing
Referencing chapters: This appendix is in Appendix B, which is about examples in using
various L
A
T
E
X commands.
Referencing sections: This section is Sec. B, which shows how to refer to the locations
of various labels that have been placed in the L
A
T
E
X files. List. B.12 shows the corresponding
L
A
T
E
X code.
Listing B.12: Sample L
A
T
E
X code for referencing sections
1Re fe re ncin g se ctio ns : T hi s s ect ion is Sec .~ \ ref { sec : ref } , wh ich sh ows
how to refer to the locat ions of various labels that have been
placed in the \ LaTeX \ files . List .~\ ref { lst : refsec } shows the
cor re spon di ng \ LaT eX \ code .
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
82
B. Usage Examples
A subsection
Referencing subsections: This section is Sec. B, which shows how to refer to a subsection.
List. B.13 shows the corresponding L
A
T
E
X code.
Listing B.13: Sample L
A
T
E
X code for referencing subsections
1Re fe re ncin g su bs ec tion s : Th is s ec tion is Sec . ~\ r ef { se c : sub sec } , wh ic h
sh ow s how to ref er to a subs ec ti on . List .~\ ref { lst : r efs ub } s ho ws the
co rr espon di ng \ LaT eX \ code .
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
83
B. Usage Examples
A sub-subsection
Referencing sub-subsections: This section is Sec. B, which shows how to refer to a sub-
subsection. List. B.14 shows the corresponding L
A
T
E
X code.
Listing B.14: Sample L
A
T
E
X code for referencing sub-subsections
1Re fe re ncin g sub - su bs ec tion s : Th is s ec tion is Sec . ~\ r ef { se c : su bsub se c },
wh ic h s ho ws how to ref er to a sub - su bs ec tio n . Li st .~ \ ref { ls t :
re fsubs ub } shows the corre s p onding \ LaTeX \ code .
Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam lobortis facilisis sem.
Nullam nec mi et neque pharetra sollicitudin. Praesent imperdiet mi nec ante. Donec
ullamcorper, felis non sodales commodo, lectus velit ultrices augue, a dignissim nibh lectus
placerat pede. Vivamus nunc nunc, molestie ut, ultricies vel, semper in, velit. Ut porttitor.
Praesent in sapien. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Duis fringilla
tristique neque. Sed interdum libero ut metus. Pellentesque placerat. Nam rutrum augue
a leo. Morbi sed elit sit amet ante lobortis sollicitudin. Praesent blandit blandit mauris.
Praesent lectus tellus, aliquet aliquam, luctus a, egestas a, turpis. Mauris lacinia lorem sit
amet ipsum. Nunc quis urna dictum turpis accumsan semper.
84
B. Usage Examples
Citing
Citing bibliography content is done using BibTeX. It requires the creation of a BibTeX
file (.bib extension name), and then added in the argument of \bibliography{ } . For
each .bib file, separate them by a comma in the argument
\bibliography{ }
without
the extension name. Building your BibTeX file (references.bib) can be done easily with a
tool called JabRef (www.jabref.org).
The following subsections are examples of citations.
Books
•[6]
•[7]
•[8]
•[9]
•[10]
•[11]
•[12]
•[13]
•[14]
•[15]
•[16]
•[17]
•[18]
•[19]
•[20]
•[21]
•[22]
•[23]
•[24]
•[25]
•[26]
•[27]
•[28]
•[29]
•[30]
•[31]
•[32]
•[33]
•[34]
•[35]
•[36]
•[37]
•[38]
•[39]
•[40]
•[4]
•[41]
•[42]
85
B. Usage Examples
•[43]
•[44]
•[45]
•[46]
•[47]
•[1]
Booklets
•[48]
Proceedings
•[49]
•[50]
•[2]
In books
•[51]
•[52]
•[53]
•[54]
•[55]
•[56]
•[57]
•[58]
•[59]
•[60]
•[61]
•[62]
•[63]
•[64]
•[65]
•[66]
•[67]
•[68]
•[69]
•[70]
•[71]
•[72]
•[73]
•[74]
•[75]
•[76]
In proceedings
•[77]
•[78]
•[79]
•[80]
•[81]
•[82]
•[83]
86
B. Usage Examples
Journals
•[84]
•[85]
•[86]
•[87]
•[88]
•[89]
•[90]
•[91]
•[92]
•[93]
•[94]
•[95]
•[96]
•[97]
•[98]
•[99]
•[100]
•[101]
•[102]
•[103]
•[104]
•[105]
•[5]
•[106]
•[107]
•[108]
•[109]
•[110]
•[111]
•[112]
•[113]
•[114]
•[115]
•[116]
•[3]
Theses/dissertations
•[117]
•[118]
•[119]
•[120]
•[121]
•[122]
•[123]
87
B. Usage Examples
Technical Reports and Others
•[124]
•[125]
•[126]
•[127]
•[128]
•[129]
•[130]
•[131]
•[132]
•[133]
•[134]
•[135]
•[136]
•[137]
•[138]
Miscellaneous
•[139]
•[140]
•[141]
•[?]
•[142]
•[143]
•[144]
•[145]
•[146]
•[147]
•[148]
•[149]
•[150]
•[151]
•[152]
•[153]
•[154]
88
B. Usage Examples
Index
For key words or topics that are expected (or the user would like) to appear in the Index, use
index{key}
, where
key
is an example keyword to appear in the Index. For example,
Fredholm integral and Fourier operator of the following paragraph are in the Index.
If we make a very large matrix with complex exponentials in the rows (i.e., cosine real
parts and sine imaginary parts), and increase the resolution without bound, we approach
the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator
that defines the continuous Fourier transform.
List. B.15 is a program listing of the above-mentioned paragraph.
Listing B.15: Sample L
A
T
E
X code for Index usage
1If we make a very large matrix with co mplex expone n tials in the rows (i.
e., cosine real parts and sine imagi nary parts ) , and inc reas e the
re solu tion wi thout bound , we ap pro ach the ker nel of the \ inde x {
Fr edho lm int egra l } Fredholm integral equation of the 2 nd kind ,
namely the \ index { Four ier } Fourier o per ato r that defi nes the
co nti nuo us Fo urier tran sfo rm .
89
B. Usage Examples
Adding Relevant PDF Pages
Examples of such PDF pages are Standards, Datasheets, Specification Sheets, Application
Notes, etc. Selected PDF pages can be added (see List. B.16), but note that the options
must be tweaked. See the manual of pdfpages for other options.
Listing B.16: Sample L
A
T
E
X code for including PDF pages
1\ in clu dep df [ pages ={8 -10} ,%
2offset =3.5 mm -10 mm ,%
3sc al e =0 .73 , %
4frame ,%
5pa gec omm and ={} ,]
6{./ refere nce / X il in x 2015 - UltraScale - Arc hi te ct ur e - Ove rvi ew . pdf }
90
UltraScale Architecture and Product Overview
DS890 (v2.1) April 27, 2015 www.xilinx.com
Preliminary Product Specification 8
Virtex UltraScale FPGA Feature Summary
Table 6: Virtex UltraScale FPGA Feature Summary
VU065 VU080 VU095 VU125 VU160 VU190 VU440
Logic Cells 626,640 780,000 940,800 1,253,280 1,621,200 1,879,920 4,432,680
CLB Flip-Flops 716,160 891,424 1,075,200 1,432,320 1,852,800 2,148,480 5,065,920
CLB LUTs 358,080 445,712 537,600 716,160 926,400 1,074,240 2,532,960
Maximum Distributed RAM (Mb) 4.8 3.9 4.8 9.7 12.7 14.5 28.7
Block RAM/FIFO w/ECC (36Kb each) 1,260 1,421 1,728 2,520 3,276 3,780 2,520
Total Block RAM (Mb) 44.3 50.0 60.8 88.6 115.2 132.9 88.6
CMT (1 MMCM, 2 PLLs) 10161620303030
I/O DLLs 40 64 64 80 120 120 120
Fractional PLLs 5 8 8 10 15 15 0
Maximum HP I/Os(1) 468 780 780 780 650 650 1,404
Maximum HR I/Os(2) 52 52 52 104 52 52 52
DSP Slices 600 672 768 1,200 1,560 1,800 2,880
System Monitor 1112333
PCIe Gen3 x8 2444566
150G Interlaken 3666890
100G Ethernet 3446993
GTH 16.3Gb/s Transceivers 20 32 32 40 52 60 48
GTY 30.5Gb/s Transceivers 20 32 32 40 52 60 0
Notes:
1. HP = High-performance I/O with support for I/O voltage from 1.0V to 1.8V.
2. HR = High-range I/O with support for I/O voltage from 1.2V to 3.3V.
B. Usage Examples
91
UltraScale Architecture and Product Overview
DS890 (v2.1) April 27, 2015 www.xilinx.com
Preliminary Product Specification 9
Virtex UltraScale Device-Package Combinations and Maximum I/Os
Table 7: Virtex UltraScale Device-Package Combinations and Maximum I/Os
Package(1)(2)(3) Package
Dimensions
(mm)
VU065 VU080 VU095 VU125 VU160 VU190 VU440
HR, HP
GTH, GTY HR, HP
GTH, GTY HR, HP
GTH, GTY HR, HP
GTH, GTY HR, HP
GTH, GTY HR, HP
GTH, GTY HR, HP
GTH, GTY
FFVC1517 40x40 52, 468
20, 20 52, 468
20, 20 52, 468
20, 20
FFVD1517 40x40 52, 286
32, 32 52, 286
32, 32
FLVD1517 40x40 52, 286
40, 32
FFVB1760 42.5x42.5 52, 650
32, 16 52, 650
32, 16
FLVB1760 42.5x42.5 52, 650
36, 16
FFVA2104 47.5x47.5 52, 780
28, 24 52, 780
28, 24
FLVA2104 47.5x47.5 52, 780
28, 24
FFVB2104 47.5x47.5 52, 650
32, 32 52, 650
32, 32
FLVB2104 47.5x47.5 52, 650
40, 36
FLGB2104 47.5x47.5 52, 650
40, 36 52, 650
40, 36
FFVC2104 47.5x47.5 52, 364
32, 32
FLVC2104 47.5x47.5 52, 364
40, 40
FLGC2104 47.5x47.5 52, 364
52, 52 52, 364
52, 52
FLGB2377 50x50 52, 1248
36, 0
FLGA2577 52.5x52.5 0, 448
60, 60
FLGA2892 55x55 52, 1404
48, 0
Notes:
1. Go to Ordering Information for package designation details.
2. All packages have 1.0mm ball pitch.
3. Packages with the same last letter and number sequence, e.g., A2104, are footprint compatible with all other UltraScale
architecture-based devices with the same sequence. The footprint compatible devices within this family are outlined. See
the UltraScale Architecture Product Selection Guide for details on inter-family migration.
B. Usage Examples
92
UltraScale Architecture and Product Overview
DS890 (v2.1) April 27, 2015 www.xilinx.com
Preliminary Product Specification 10
Virtex UltraScale+ FPGA Feature Summary
Virtex UltraScale+ Device-Package Combinations and Maximum I/Os
Table 8: Virtex UltraScale+ FPGA Feature Summary
VU3P VU5P VU7P VU9P VU11P VU13P
Logic Cells 689,640 1,051,010 1,379,280 2,068,920 2,147,040 2,862,720
CLB Flip-Flops 788,160 1,201,154 1,576,320 2,364,480 2,453,760 3,271,680
CLB LUTs 394,080 600,577 788,160 1,182,240 1,226,880 1,635,840
Max. Distributed RAM (Mb) 12.0 18.3 24.1 36.1 34.8 46.4
Block RAM/FIFO w/ECC
(36Kb each) 720 1,024 1,440 2,160 2,016 2,688
Block RAM (Mb) 25.3 36.0 50.6 75.9 70.9 94.5
UltraRAM Blocks 320 470 640 960 1,152 1,536
UltraRAM (Mb) 90.0 132.2 180.0 270.0 324.0 432.0
CMTs (1 MMCM and 2 PLLs) 10 20 20 30 12 16
Max. HP I/O(1) 520 832 832 832 624 832
DSP Slices 2,280 3,474 4,560 6,840 8,928 11,904
System Monitor 122334
GTY Transceivers 32.75Gb/s 40 80 80 120 96 128
PCIe Gen3 x16 and Gen4 x8 2 4 4 6 3 4
150G Interlaken 3 4 6 9 9 12
100G Ethernet w/RS-FEC 3 4 6 9 6 8
Notes:
1. HP = High-performance I/O with support for I/O voltage from 1.0V to 1.8V.
Table 9: Virtex UltraScale+ Device-Package Combinations and Maximum I/Os
Package
(1)(2)(3) Package
Dimensions
(mm)
VU3P VU5P VU7P VU9P VU11P VU13P
HP, GTY HP, GTY HP, GTY HP, GTY HP, GTY HP, GTY
FFVC1517 40x40 520, 40
FLVF1924 45x45 624, 64
FLVA2104 47.5x47.5 832, 52 832, 52 832, 52
FHVA2104 52.5x52.5(4) 832, 52
FLVB2104 47.5x47.5 702, 76 702, 76 702, 76 624, 76
FHVB2104 52.5x52.5(4) 702, 76
FLVC2104 47.5x47.5 416, 80 416, 80 416, 104 416, 96
FHVC2104 52.5x52.5(4) 416, 104
FLVA2577 52.5x52.5 448, 120 448, 96 448, 128
Notes:
1. Go to Ordering Information for package designation details.
2. All packages have 1.0mm ball pitch.
3. Packages with the same last letter and number sequence, e.g., A2104, are footprint compatible with all other UltraScale
devices with the same sequence. The footprint compatible devices within this family are outlined.
4. These 52.5x52.5mm overhang packages have the same PCB ball footprint as the corresponding 47.5x47.5mm packages (i.e., the
same last letter and number sequence) and are footprint compatible.
B. Usage Examples
93
Appendix C
SOME LIST OF MATH SYMBOLS
94
List of mathematical symbols
From Wikipedia, the free encyclopedia
This is a list of symbols found within all branches of mathematics to express a formula or to represent a constant.
When reading the list, it is important to recognize that a mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually
synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations a different convention may
be used. For example, depending on context, the triple bar "≡" may represent congruence or a definition. Further, in mathematical logic, numerical equality is sometimes represented by
"≡" instead of "=", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning.
Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and typeset as an image using TeX.
Contents
1 Guide
2 Basic symbols
3 Symbols based on equality
4 Symbols that point left or right
5 Brackets
6 Other non-letter symbols
7 Letter-based symbols
7.1 Letter modifiers
7.2 Symbols based on Latin letters
7.3 Symbols based on Hebrew or Greek letters
8 Variations
9 See also
10 References
11 External links
Guide
This list is organized by symbol type and is intended to facilitate finding an unfamiliar symbol by its visual appearance. For a related list organized by mathematical topic, see List of
mathematical symbols by subject. That list also includes LaTeX and HTML markup and Unicode code points for each symbol.
Basic symbols: Symbols widely used in mathematics, roughly through first-year calculus. More advanced meanings are included with some symbols listed here.
Symbols based on equality "=": Symbols derived from or similar to the equal sign, including double-headed arrows. Not surprisingly these symbols are often associated with an
equivalence relation.
Symbols that point left or right: Symbols, such as < and >, that appear to point to one side or another.
Brackets: Symbols that are placed on either side of a variable or expression, such as | x |.
Other non-letter symbols: Symbols that do not fall in any of the other categories.
Letter-based symbols: Many mathematical symbols are based on, or closely resemble, a letter in some alphabet. This section includes such symbols, including symbols that
resemble upside-down letters. Many letters have conventional meanings in various branches of mathematics and physics. These are not listed here. The See also section, below, has
several lists of such usages.
Letter modifiers: Symbols that can be placed on or next to any letter to modify the letter's meaning.
Symbols based on Latin letters, including those symbols that resemble or contain an X
Symbols based on Hebrew or Greek letters e.g. א, ב, δ, Δ, π, Π, σ, Σ, Φ. Note: symbols resembling Λ are grouped with "V" under Latin letters.
Variations: Usage in languages written right-to-left
Basic symbols
C. Some List of Math Symbols
95
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
+
addition
plus;
add
arithmetic
4 + 6 means the sum of 4 and 6.2 + 7 = 9
disjoint union
the disjoint
union of ... and
...
set theory
A1 + A2 means the disjoint union of sets A1 and A2.A1 = {3, 4, 5, 6} ∧ A2 = {7, 8, 9, 10} ⇒
A1 + A2 = {(3, 1), (4, 1), (5, 1), (6, 1), (7, 2), (8, 2), (9, 2), (10, 2)}
−
subtraction
minus;
take;
subtract
arithmetic
9 − 4 means the subtraction of 4 from 9.8 − 3 = 5
negative sign
negative;
minus;
the opposite of
arithmetic
−3 means the additive inverse of the number 3.−(−5) = 5
set-theoretic
complement
minus;
without
set theory
A − B means the set that contains all the elements of A
that are not in B.
(∖can also be used for set-theoretic complement as
described below.)
{1, 2, 4} − {1, 3, 4} = {2}
±
plus-minus
plus or minus
arithmetic
6 ± 3 means both 6 + 3 and 6 − 3.
The equation x = 5 ± √4, has two solutions, x = 7 and x = 3.
Note: {{sqrt|4}} was used to get √4 .
plus-minus
plus or minus
measurement
10 ± 2 or equivalently 10 ± 20% means the range from
10 − 2 to 10 + 2.If a = 100 ± 1 mm, then a ≥ 99 mm and a ≤ 101 mm.
∓
minus-plus
minus or plus
arithmetic
6 ± (3 ∓ 5) means 6 + (3 − 5) and 6 − (3 + 5).cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y).
×
⋅
·
multiplication
times;
multiplied by
arithmetic
3 × 4 or 3 ⋅ 4 means the multiplication of 3 by 4.7 ⋅ 8 = 56
dot product
scalar product
dot
linear algebra
vector algebra
u ⋅ v means the dot product of vectors u and v(1, 2, 5) ⋅ (3, 4, −1) = 6
cross product
vector product
cross
linear algebra
vector algebra
u × v means the cross product of vectors u and v(1, 2, 5) × (3, 4, −1) =
i j k
125
3 4 −1
= (−22, 16, −2)
placeholder
(silent)
functional
analysis
A · means a placeholder for an argument of a function.
Indicates the functional nature of an expression without
assigning a specific symbol for an argument.
| · |
÷
⁄
division
(Obelus)
divided by;
over
arithmetic
6 ÷ 3 or 6 ⁄ 3 means the division of 6 by 3.
2 ÷ 4 = 0.5
12 ⁄ 4 = 3
quotient group
mod
group theory
G / H means the quotient of group Gmodulo its subgroup
H.{0, a, 2a, b, b + a, b + 2a} / {0, b} = {{0, b}, {a, b + a}, {2a, b + 2a}}
quotient set
mod
set theory
A/~ means the set of all ~equivalence classes in A. If we define ~ by x ~ y ⇔ x − y ∈ ℤ, then ℝ/~ = {x + n : n ∈ ℤ, x ∈ [0,1)}.
√
square root
the (principal)
square root of
real numbers
√x means the nonnegative number whose square is x.√4 = 2
complex square
root
the (complex)
square root of
complex
numbers
If z = r exp(iφ) is represented in polar coordinates with
−π < φ ≤ π, then √z = √r exp(iφ/2).√−1 = i
∑
summation
sum over ...
from ... to ... of
arithmetic
means .
indefinite
integral or
antiderivative
indefinite
integral of
f(x) dx means a function whose derivative is f.x2dx = x3
3 + C
∫∫∫
C. Some List of Math Symbols
96
- OR -
the
antiderivative of
calculus
definite integral
integral from ...
to ... of ... with
respect to
calculus
f(x) dx means the signed area between the x-axis and
the graph of the function f between x = a and x = b.x2dx = b3 − a3
3
line integral
line/ path/ curve/
integral of ...
along ...
calculus
f ds means the integral of f along the curve C,
f(r(t)) | r'(t) | dt, where r is a parametrization of C. (If
the curve is closed, the symbol may be used instead, as
described below.)
Contour
integral;
closed line
integral
contour integral
of
calculus
Similar to the integral, but used to denote a single
integration over a closed curve or loop. It is sometimes
used in physics texts involving equations regarding Gauss's
Law, and while these formulas involve a closed surface
integral, the representations describe only the first
integration of the volume over the enclosing surface.
Instances where the latter requires simultaneous double
integration, the symbol would be more appropriate. A
third related symbol is the closed volume integral, denoted
by the symbol .
The contour integral can also frequently be found with a
subscript capital letter C, C, denoting that a closed loop
integral is, in fact, around a contour C, or sometimes
dually appropriately, a circle C. In representations of
Gauss's Law, a subscript capital S, S, is used to denote
that the integration is over a closed surface.
If C is a Jordan curve about 0, then C1
zdz = 2πi.
∴
therefore
therefore;
so;
hence
everywhere
Sometimes used in proofs before logical consequences. All humans are mortal. Socrates is a human. ∴ Socrates is mortal.
∵
because
because;
since
everywhere
Sometimes used in proofs before reasoning. 11 is prime ∵ it has no positive integer factors other than itself and one.
!
factorial
factorial
combinatorics
n! means the product 1 × 2 × ... × n.
logical negation
not
propositional
logic
The statement !A is true if and only if A is false.
A slash placed through another operator is the same as "!"
placed in front.
(The symbol ! is primarily from computer science. It is
avoided in mathematical texts, where the notation ¬A is
preferred.)
!(!A) ⇔ A
x ≠ y ⇔ !(x = y)
¬
˜
logical negation
not
propositional
logic
The statement ¬A is true if and only if A is false.
A slash placed through another operator is the same as "¬"
placed in front.
(The symbol ~ has many other uses, so ¬ or the slash
notation is preferred. Computer scientists will often use !
but this is avoided in mathematical texts.)
¬(¬A) ⇔ A
x ≠ y ⇔ ¬(x = y)
∝
proportionality
is proportional
to;
varies as
everywhere
y ∝ x means that y = kx for some constant k. if y = 2x, then y ∝ x.
∞infinity
infinity
numbers
∞ is an element of the extended number line that is greater
than all real numbers; it often occurs in limits.
■
□
∎
▮
‣
end of proof
QED;
tombstone;
Halmos finality
symbol
everywhere
Used to mark the end of a proof.
(May also be written Q.E.D.)
(1) a + 0 := a(def.)
(2) a + succ(b) := succ(a + b)(def.)
Proposition. 3 + 2 = 5.
Proof.
3 + 2 = 3 + succ(1) (definition of succ)
3 + succ(1) = succ(3 + 1) (2)
succ(3 + 1) = succ(3 + succ(0)) (definition of succ)
succ(3 + succ(0)) = succ(succ(3 + 0)) (2)
succ(succ(3 + 0)) = succ(succ(3)) (1)
succ(succ(3)) = succ(4) = 5 (definition of succ) ▮
Symbols based on equality
∫b
a∫b
a
∫C
∫b
a
∮
∮
∯
∰
∮
∮
∮
C. Some List of Math Symbols
97
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
=
equality
is equal to;
equals
everywhere
means and represent the same math object (Both symbols have the same value).
≠
inequality
is not equal to;
does not equal
everywhere
means that and do not represent the same math object (Both symbols do not have
the same value).
(The forms !=, /= or <> are generally used in programming languages where ease of typing
and use of ASCII text is preferred.)
≈
approximately equal
is approximately equal to
everywhere
x ≈ y means x is approximately equal to y.
This may also be written ≃, ≅, ~, ♎ (Libra Symbol), or ≒.
π ≈ 3.14159
isomorphism
is isomorphic to
group theory
G ≈ H means that group G is isomorphic (structurally identical) to group H.
(≅ can also be used for isomorphic, as described below.)
Q8 / C2 ≈ V
~
probability distribution
has distribution
statistics
X ~ D, means the random variable X has the probability distribution D.X ~ N(0,1), the standard normal
distribution
row equivalence
is row equivalent to
matrix theory
A ~ B means that B can be generated by using a series of elementary row operations on A
same order of magnitude
roughly similar;
poorly approximates;
is on the order of
approximation theory
m ~ n means the quantities m and n have the same order of magnitude, or general size.
(Note that ~ is used for an approximation that is poor, otherwise use ≈ .)
2 ~ 5
8 × 9 ~ 100
but π2 ≈ 10
similarity
is similar to[1]
geometry
△ABC ~ △DEF means triangle ABC is similar to (has the same shape) triangle DEF.
asymptotically equivalent
is asymptotically
equivalent to
asymptotic analysis
f ~ g means . x ~ x+1
equivalence relation
are in the same equivalence
class
everywhere
a ~ b means (and equivalently ). 1 ~ 5 mod 4
=:
:=
≡
:⇔
≜
≝
≐
definition
is defined as;
is equal by definition to
everywhere
x := y, y =: x or x ≡ y means x is defined to be another name for y, under certain assumptions
taken in context.
(Some writers use ≡ to mean congruence).
P ⇔ Q means P is defined to be logically equivalent to Q. P ⇔ Q means if and only if (iff)
≅
congruence
is congruent to
geometry
△ABC ≅ △DEF means triangle ABC is congruent to (has the same measurements as) triangle
DEF.
isomorphic
is isomorphic to
abstract algebra
G ≅ H means that group G is isomorphic (structurally identical) to group H.
(≈ can also be used for isomorphic, as described above.)
V ≅ C2 × C2
≡
congruence relation
... is congruent to ...
modulo ...
modular arithmetic
a ≡ b (mod n) means a − b is divisible by n5 ≡ 2 (mod 3)
⇔
↔
material equivalence
if and only if;
iff
propositional logic
A ⇔ B means A is true if B is true and A is false if B is false. x + 5 = y + 2 ⇔ x + 3 = y
Symbols that point left or right
C. Some List of Math Symbols
98
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
<
>
strict inequality
is less than,
is greater than
order theory
means x is less than y.
means x is greater than y.
proper subgroup
is a proper subgroup of
group theory
means H is a proper subgroup of G.
≪
≫
significant (strict)
inequality
is much less than,
is much greater than
order theory
x ≪ y means x is much less than y.
x ≫ y means x is much greater than y.
0.003 ≪ 1000000
asymptotic comparison
is of smaller order than,
is of greater order than
analytic number theory
f ≪ g means the growth of f is asymptotically bounded by g.
(This is I. M. Vinogradov's notation. Another notation is the Big
O notation, which looks like f = O(g).)
x ≪ ex
absolute continuity
is absolutely continuous
with respect to
measure theory
means that is absolutely continuous with respect to ,
i.e., whenever , we have .
If is the counting measure on and is the Lebesgue
measure, then .
≤
≥
inequality
is less than or equal to,
is greater than or equal to
order theory
x ≤ y means x is less than or equal to y.
x ≥ y means x is greater than or equal to y.
(The forms <= and >= are generally used in programming
languages, where ease of typing and use of ASCII text is
preferred.)
3 ≤ 4 and 5 ≤ 5
5 ≥ 4 and 5 ≥ 5
subgroup
is a subgroup of
group theory
H ≤ G means H is a subgroup of G.Z ≤ Z
A3 ≤ S3
reduction
is reducible to
computational complexity
theory
A ≤ B means the problem A can be reduced to the problem B.
Subscripts can be added to the ≤ to indicate what kind of
reduction.
If
then
≦
≧
congruence relation
... is less than ... is greater
than ...
modular arithmetic
7k ≡ 28 (mod 2) is only true if k is an even integer. Assume
that the problem requires k to be non-negative; the domain is
defined as 0 ≦ k ≦ ∞.
10a ≡ 5 (mod 5) for 1 ≦ a ≦ 10
vector inequality
... is less than or equal... is
greater than or equal...
order theory
x ≦ y means that each component of vector x is less than or
equal to each corresponding component of vector y.
x ≧ y means that each component of vector x is greater than or
equal to each corresponding component of vector y.
It is important to note that x ≦ yremains true if every element is
equal. However, if the operator is changed, x ≤ yis true if and
only if x ≠ yis also true.
≺
≻
Karp reduction
is Karp reducible to;
is polynomial-time
many-one reducible to
computational complexity
theory
L1 ≺ L2 means that the problem L1 is Karp reducible to L2.[2] If L1 ≺ L2 and L2 ∈ P, then L1 ∈ P.
Nondominated order
is nondominated by
Multi-objective
optimization
P ≺ Q means that the element P is nondominated by element
Q.[3] If P1 ≺ Q2 then
◅
▻
normal subgroup
is a normal subgroup of
group theory
N ◅ G means that N is a normal subgroup of group G.Z(G) ◅ G
ideal
is an ideal of
ring theory
I ◅ R means that I is an ideal of ring R.(2) ◅ Z
antijoin
the antijoin of
relational algebra
R ▻ S means the antijoin of the relations R and S, the tuples in
R for which there is not a tuple in S that is equal on their
common attribute names.
⇒
→
⊃
material implication
implies;
if ... then
propositional logic,
Heyting algebra
A ⇒ B means if A is true then B is also true; if A is false then
nothing is said about B.
(→ may mean the same as ⇒, or it may have the meaning for
functions given below.)
(⊃ may mean the same as ⇒,[4] or it may have the meaning for
superset given below.)
x = 2 ⇒ x2 = 4 is true, but x2 = 4 ⇒ x = 2 is in general false
(since x could be −2).
⊆
⊂
subset
is a subset of
set theory
(subset) A ⊆ B means every element of A is also an element of
B.[5]
(proper subset) A ⊂ B means A ⊆ B but A ≠ B.
(Some writers use the symbol ⊂ as if it were the same as ⊆.)
(A ∩ B) ⊆ A
ℕ ⊂ ℚ
ℚ ⊂ ℝ
C. Some List of Math Symbols
99
⊇
⊃
superset
is a superset of
set theory
A
⊇
B means every element of B is also an element of A.
A ⊃ B means A ⊇ B but A ≠ B.
(Some writers use the symbol ⊃ as if it were the same as ⊇.)
(A ∪ B) ⊇ B
ℝ ⊃ ℚ
→function arrow
from ... to
set theory, type theory
f: X → Y means the function f maps the set X into the set Y.Let f: ℤ → ℕ ∪ {0} be defined by f(x) := x2.
↦
function arrow
maps to
set theory
f: a ↦ b means the function f maps the element a to the element
b.Let f: x ↦ x + 1 (the successor function).
<:
<·
subtype
is a subtype of
type theory
T1 <: T2 means that T1 is a subtype of T2.If S <: T and T <: U then S <: U (transitivity).
cover
is covered by
order theory
x <• y means that x is covered by y.{1, 8} <• {1, 3, 8} among the subsets of {1, 2, ..., 10}
ordered by containment.
⊧
entailment
entails
model theory
A ⊧ B means the sentence A entails the sentence B, that is in
every model in which A is true, B is also true. A ⊧ A ∨ ¬A
⊢
inference
infers;
is derived from
propositional logic,
predicate logic
x ⊢ y means y is derivable from x.A → B ⊢ ¬B → ¬A
partition
is a partition of
number theory
p ⊢ n means that p is a partition of n.(4,3,1,1) ⊢ 9,
⟨|
bra vector
the bra ...;
the dual of ...
Dirac notation
⟨φ| means the dual of the vector |φ⟩, a linear functional which
maps a ket |ψ⟩ onto the inner product ⟨φ|ψ⟩.
|⟩
ket vector
the ket ...;
the vector ...
Dirac notation
|φ⟩ means the vector with label φ, which is in a Hilbert space. A qubit's state can be represented as α|0⟩+ β|1⟩, where α and β are
complex numbers s.t. |α|2 + |β|2 = 1.
Brackets
C. Some List of Math Symbols
100
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
combination;
binomial
coefficient
n choose k
combinatorics
means (in the case of n = positive integer) the number of
combinations of k elements drawn from a set of n elements.
(This may also be written as C(n, k), C(n; k), nCk, nCk, or .)
multiset
coefficient
u multichoose
k
combinatorics
(when u is positive integer)
means reverse or rising binomial coefficient.
|...|
absolute
value;
modulus
absolute
value of;
modulus of
numbers
|x| means the distance along the real line (or across the complex
plane) between x and zero.
|3| = 3
|–5| = |5| = 5
| i | = 1
| 3 + 4i | = 5
Euclidean
norm or
Euclidean
length or
magnitude
Euclidean
norm of
geometry
|x| means the (Euclidean) length of vector x.For x = (3,−4)
determinant
determinant
of
matrix theory
|A| means the determinant of the matrix A
cardinality
cardinality of;
size of;
order of
set theory
|X| means the cardinality of the set X.
(# may be used instead as described below.)
|{3, 5, 7, 9}| = 4.
ǁ...ǁ
norm
norm of;
length of
linear algebra
ǁ x ǁ means the norm of the element x of a normed vector space.[6] ǁ x + y ǁ ≤ ǁ x ǁ + ǁ y ǁ
nearest
integer
function
nearest
integer to
numbers
ǁxǁ means the nearest integer to x.
(This may also be written [x], ⌊x⌉, nint(x) or Round(x).)
ǁ1ǁ = 1, ǁ1.6ǁ = 2, ǁ−2.4ǁ = −2, ǁ3.49ǁ = 3
{ , } set brackets
the set of ...
set theory
{a,b,c} means the set consisting of a, b, and c.[7] ℕ = { 1, 2, 3, ... }
{ : }
{ | }
{ ; }
set builder
notation
the set of ...
such that
set theory
{x : P(x)} means the set of all x for which P(x) is true.[7] {x | P(x)}
is the same as {x : P(x)}. {n ∈ ℕ : n2 < 20} = { 1, 2, 3, 4 }
⌊...⌋
floor
floor;
greatest
integer;
entier
numbers
⌊x⌋ means the floor of x, i.e. the largest integer less than or equal
to x.
(This may also be written [x], floor(x) or int(x).)
⌊4⌋ = 4, ⌊2.1⌋ = 2, ⌊2.9⌋ = 2, ⌊−2.6⌋ = −3
⌈...⌉
ceiling
ceiling
numbers
⌈x⌉ means the ceiling of x, i.e. the smallest integer greater than or
equal to x.
(This may also be written ceil(x) or ceiling(x).)
⌈4⌉ = 4, ⌈2.1⌉ = 3, ⌈2.9⌉ = 3, ⌈−2.6⌉ = −2
⌊...⌉
nearest
integer
function
nearest
integer to
numbers
⌊x⌉ means the nearest integer to x.
(This may also be written [x], ||x||, nint(x) or Round(x).)
⌊2⌉ = 2, ⌊2.6⌉ = 3, ⌊-3.4⌉ = -3, ⌊4.49⌉ = 4
[ : ]
degree of a
field
extension
the degree of
field theory
[K : F] means the degree of the extension K : F.
[ℚ(√2) : ℚ] = 2
[ℂ : ℝ] = 2
[ℝ : ℚ] = ∞
[ ]
[ , ]
equivalence
class
the
equivalence
class of
[a] means the equivalence class of a, i.e. {x : x ~ a}, where ~ is an
equivalence relation.
[a]R means the same, but with R as the equivalence relation.
Let a ~ b be true iff a ≡ b (mod 5).
Then [2] = {..., −8, −3, 2, 7, ...}.
C. Some List of Math Symbols
101
[ , , ]
abstract
algebra
floor
floor;
greatest
integer;
entier
numbers
[x] means the floor of x, i.e. the largest integer less than or equal to
x.
(This may also be written ⌊x⌋, floor(x) or int(x). Not to be
confused with the nearest integer function, as described below.)
[3] = 3, [3.5] = 3, [3.99] = 3, [−3.7] = −4
nearest
integer
function
nearest
integer to
numbers
[x] means the nearest integer to x.
(This may also be written ⌊x⌉, ||x||, nint(x) or Round(x). Not to be
confused with the floor function, as described above.)
[2] = 2, [2.6] = 3, [-3.4] = -3, [4.49] = 4
Iverson
bracket
1 if true, 0
otherwise
propositional
logic
[S] maps a true statement S to 1 and a false statement S to 0. [0=5]=0, [7>0]=1, [2 ∈ {2,3,4}]=1, [5 ∈ {2,3,4}]=0
image
image of ...
under ...
everywhere
f[X] means { f(x) : x ∈ X }, the image of the function f under the
set X ⊆ dom(f).
(This may also be written as f(X) if there is no risk of confusing the
image of f under X with the function application f of X. Another
notation is Im f, the image of f under its domain.)
closed
interval
closed
interval
order theory
.0 and 1/2 are in the interval [0,1].
commutator
the
commutator
of
group theory,
ring theory
[g, h] = g−1h−1gh (or ghg−1h−1), if g, h ∈ G (a group).
[a, b] = ab − ba, if a, b ∈ R (a ring or commutative algebra).
xy = x[x, y] (group theory).
[AB, C] = A[B, C] + [A, C]B (ring theory).
triple scalar
product
the triple
scalar product
of
vector
calculus
[a, b, c] = a × b · c, the scalar product of a×b with c. [a, b, c] = [b, c, a] = [c, a, b].
( )
( , )
function
application
of
set theory
f(x) means the value of the function f at the element x.If f(x) := x2, then f(3) = 32 = 9.
image
image of ...
under ...
everywhere
f(X) means { f(x) : x ∈ X }, the image of the function f under the
set X ⊆ dom(f).
(This may also be written as f[X] if there is a risk of confusing the
image of f under X with the function application f of X. Another
notation is Im f, the image of f under its domain.)
precedence
grouping
parentheses
everywhere
Perform the operations inside the parentheses first. (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
tuple
tuple; n-tuple;
ordered
pair/triple/etc;
row vector;
sequence
everywhere
An ordered list (or sequence, or horizontal vector, or row vector)
of values.
(Note that the notation (a,b) is ambiguous: it could be an ordered
pair or an open interval. Set theorists and computer scientists
often use angle brackets ⟨ ⟩ instead of parentheses.)
(a, b) is an ordered pair (or 2-tuple).
(a, b, c) is an ordered triple (or 3-tuple).
( ) is the empty tuple (or 0-tuple).
highest
common
factor
highest
common
factor;
greatest
common
divisor; hcf;
gcd
number
theory
(a, b) means the highest common factor of a and b.
(This may also be written hcf(a, b) or gcd(a, b).)
(3, 7) = 1 (they are coprime); (15, 25) = 5.
( , )
] , [
open interval
open interval
order theory
.
(Note that the notation (a,b) is ambiguous: it could be an ordered
pair or an open interval. The notation ]a,b[ can be used instead.)
4 is not in the interval (4, 18).
(0, +∞) equals the set of positive real numbers.
( , ]
] , ]
left-open
interval
half-open
interval;
left-open
interval
order theory
.(−1, 7] and (−∞, −1]
C. Some List of Math Symbols
102
[ , )
[ , [
right-open
interval
half-open
interval;
right-open
interval
order theory
.[4, 18) and [1, +∞)
⟨⟩
⟨,⟩
inner product
inner product
of
linear algebra
⟨u,v⟩ means the inner product of u and v, where u and v are
members of an inner product space.
Note that the notation ⟨u, v⟩ may be ambiguous: it could mean the
inner product or the linear span.
There are many variants of the notation, such as ⟨u | v⟩ and (u | v),
which are described below. For spatial vectors, the dot product
notation, x · y is common. For matrices, the colon notation A : B
may be used. As ⟨ and ⟩ can be hard to type, the more "keyboard
friendly" forms < and > are sometimes seen. These are avoided in
mathematical texts.
The standard inner product between two vectors x = (2, 3) and y = (−1, 5) is:
⟨x, y⟩ = 2 × −1 + 3 × 5 = 13
average
average of
statistics
let S be a subset of N for example, represents the average of
all the element in S.
for a time series :g(t) (t = 1, 2,...)
we can define the structure functions Sq( ):
linear span
(linear) span
of;
linear hull of
linear algebra
⟨S⟩ means the span of S ⊆ V. That is, it is the intersection of all
subspaces of V which contain S.
⟨u1, u2, ...⟩ is shorthand for ⟨{u1, u2, ...}⟩.
Note that the notation ⟨u, v⟩ may be ambiguous: it could mean the
inner product or the linear span.
The span of S may also be written as Sp(S).
.
subgroup
generated by
a set
the subgroup
generated by
group theory
means the smallest subgroup of G (where S ⊆ G, a group)
containing every element of S.
is shorthand for .
In S3, and .
tuple
tuple; n-tuple;
ordered
pair/triple/etc;
row vector;
sequence
everywhere
An ordered list (or sequence, or horizontal vector, or row vector)
of values.
(The notation (a,b) is often used as well.)
is an ordered pair (or 2-tuple).
is an ordered triple (or 3-tuple).
is the empty tuple (or 0-tuple).
⟨|⟩
(|)
inner product
inner product
of
linear algebra
⟨u | v⟩ means the inner product of u and v, where u and v are
members of an inner product space.[8] (u | v) means the same.
Another variant of the notation is ⟨u, v⟩ which is described above.
For spatial vectors, the dot product notation, x · y is common. For
matrices, the colon notation A : B may be used. As ⟨ and ⟩ can be
hard to type, the more "keyboard friendly" forms < and > are
sometimes seen. These are avoided in mathematical texts.
Other non-letter symbols
C. Some List of Math Symbols
103
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
*
convolution
convolution;
convolved with
functional analysis
f ∗ g means the convolution of f and g..
complex conjugate
conjugate
complex numbers
z∗ means the complex conjugate of z.
(can also be used for the conjugate of z, as described below.)
.
group of units
the group of units
of
ring theory
R∗ consists of the set of units of the ring R, along with the operation
of multiplication.
This may also be written R×as described above, or U(R).
hyperreal numbers
the (set of)
hyperreals
non-standard
analysis
∗R means the set of hyperreal numbers. Other sets can be used in
place of R.∗N is the hypernatural numbers.
Hodge dual
Hodge dual;
Hodge star
linear algebra
∗v means the Hodge dual of a vector v. If v is a k-vector within an
n-dimensional oriented inner product space, then ∗v is an (n−k)-
vector.
If are the standard basis vectors of ,
∝
proportionality
is proportional to;
varies as
everywhere
y ∝ x means that y = kx for some constant k. if y = 2x, then y ∝ x.
Karp reduction[9]
is Karp reducible
to;
is polynomial-time
many-one
reducible to
computational
complexity theory
A ∝ B means the problem A can be polynomially reduced to the
problem B.If L1 ∝ L2 and L2 ∈ P, then L1 ∈ P.
∖
set-theoretic
complement
minus;
without;
throw out;
not
set theory
A ∖ B means the set that contains all those elements of A that are not
in B.[5]
(− can also be used for set-theoretic complement as described
above.)
{1,2,3,4} ∖ {3,4,5,6} = {1,2}
|
conditional event
given
probability
P(A|B) means the probability of the event A occurring given that B
occurs.
if X is a uniformly random day of the year P(X is May 25 | X is in
May) = 1/31
restriction
restriction of ... to
...;
restricted to
set theory
f|A means the function f is restricted to the set A, that is, it is the
function with domain A ∩ dom(f) that agrees with f.
The function f : R → R defined by f(x) = x2 is not injective, but f|R+ is
injective.
such that
such that;
so that
everywhere
| means "such that", see ":" (described below). S = {(x,y) | 0 < y < f(x)}
The set of (x,y) such that y is greater than 0 and less than f(x).
∣
∤
divisor, divides
divides
number theory
a ∣ b means a divides b.
a ∤ b means a does not divide b.
(The symbol ∣ can be difficult to type, and its negation is rare, so a
regular but slightly shorter vertical bar | character is often used
instead.)
Since 15 = 3 × 5, it is true that 3 ∣ 15 and 5 ∣ 15.
∣∣
exact divisibility
exactly divides
number theory
pa ∣∣ n means pa exactly divides n (i.e. pa divides n but pa+1 does
not). 23 ∣∣ 360.
∥
∦
⋕
parallel
is parallel to
geometry
x ∥ y means x is parallel to y.
x ∦ y means x is not parallel to y.
x ⋕ y means x is equal and parallel to y.
(The symbol ∥ can be difficult to type, and its negation is rare, so
two regular but slightly longer vertical bar || characters are often
used instead.)
If l ∥ m and m ⊥ n then l ⊥ n.
incomparability
is incomparable to
order theory
x ∥ y means x is incomparable to y. {1,2} ∥ {2,3} under set containment.
#
cardinality
cardinality of;
size of;
order of
set theory
#X means the cardinality of the set X.
(|...| may be used instead as described above.)
#{4, 6, 8} = 3
connected sum
connected sum of;
knot sum of;
knot composition
of
topology, knot
theory
A#B is the connected sum of the manifolds A and B. If A and B are
knots, then this denotes the knot sum, which has a slightly stronger
condition.
A#Sm is homeomorphic to A, for any manifold A, and the sphere Sm.
C. Some List of Math Symbols
104
primorial
primorial
number theory
n# is product of all prime numbers less than or equal to n. 12# = 2 × 3 × 5 × 7 × 11 = 2310
:
such that
such that;
so that
everywhere
: means "such that", and is used in proofs and the set-builder
notation (described below). ∃ n ∈ ℕ: n is even.
field extension
extends;
over
field theory
K : F means the field K extends the field F.
This may also be written as K ≥ F.
ℝ : ℚ
inner product of
matrices
inner product of
linear algebra
A : B means the Frobenius inner product of the matrices A and B.
The general inner product is denoted by ⟨u, v⟩, ⟨u | v⟩ or (u | v), as
described below. For spatial vectors, the dot product notation, x·y is
common. See also bra–ket notation.
index of a
subgroup
index of subgroup
group theory
The index of a subgroup H in a group G is the "relative size" of H in
G: equivalently, the number of "copies" (cosets) of H that fill up G
division
divided by
over
everywhere
A : B means the division of A with B (dividing A by B) 10 : 2 = 5
⋮
vertical ellipsis
vertical ellipsis
everywhere
Denotes that certain constants and terms are missing out (e.g. for
clarity) and that only the important terms are being listed.
≀
wreath product
wreath product of
... by ...
group theory
A ≀ H means the wreath product of the group A by the group H.
This may also be written A wr H.
is isomorphic to the automorphism group of the complete
bipartite graph on (n,n) vertices.
↯
※
downwards zigzag
arrow
contradiction; this
contradicts that
everywhere
Denotes that contradictory statements have been inferred. For
clarity, the exact point of contradiction can be appended.
x + 4 = x - 3 ※
Statement: Every finite, non-empty, ordered set has a largest element.
Otherwise, let's assume that is a finite, non-empty, ordered set with
no largest element. Then, for some , there exists an
with , but then there's also an with , and so
on. Thus, are distinct elements in . ↯ is finite.
⊕
⊻
exclusive or
xor
propositional
logic, Boolean
algebra
The statement A ⊕ B is true when either A or B, but not both, are
true. A ⊻ B means the same. (¬A) ⊕ A is always true, A ⊕ A is always false.
direct sum
direct sum of
abstract algebra
The direct sum is a special way of combining several objects into
one general object.
(The bun symbol ⊕, or the coproduct symbol
∐
, is used;
⊻
is only
for logic.)
Most commonly, for vector spaces U, V, and W, the following
consequence is used:
U = V ⊕ W ⇔ (U = V + W) ∧ (V ∩ W = {0})
Kulkarni–Nomizu
product
Kulkarni–Nomizu
product
tensor algebra
Derived from the tensor product of two symmetric type (0,2)
tensors; it has the algebraic symmetries of the Riemann tensor.
has components
.
□
D'Alembertian;
wave operator
non-Euclidean
Laplacian
vector calculus
It is the generalisation of the Laplace operator in the sense that it is
the differential operator which is invariant under the isometry group
of the underlying space and it reduces to the Laplace operator if
restricted to time independent functions.
Letter-based symbols
Includes upside-down letters.
Letter modifiers
Also called diacritics.
C. Some List of Math Symbols
105
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
a
mean
overbar;
... bar
statistics
(often read as "x bar") is the mean (average value of ). .
finite sequence,
tuple
finite sequence,
tuple
model theory
means the finite sequence/tuple . .
algebraic closure
algebraic closure
of
field theory
is the algebraic closure of the field F.The field of algebraic numbers is sometimes denoted as because it is the
algebraic closure of the rational numbers .
complex conjugate
conjugate
complex numbers
means the complex conjugate of z.
(z∗can also be used for the conjugate of z, as described
above.)
.
topological closure
(topological)
closure of
topology
is the topological closure of the set S.
This may also be denoted as cl(S) or Cl(S).
In the space of the real numbers, (the rational numbers are dense in the
real numbers).
â
unit vector
hat
geometry
(pronounced "a hat") is the normalized version of vector ,
having length 1.
estimator
estimator for
statistics
is the estimator or the estimate for the parameter . The estimator produces a sample estimate for the mean .
′
derivative
... prime;
derivative of
calculus
f ′(x) means the derivative of the function f at the point x, i.e.,
the slope of the tangent to f at x.
(The single-quote character ' is sometimes used instead,
especially in ASCII text.)
If f(x) := x2, then f ′(x) = 2x.
•
derivative
... dot;
time derivative of
calculus
means the derivative of x with respect to time. That is
.If x(t) := t2, then .
Symbols based on Latin letters
C. Some List of Math Symbols
106
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
∀
universal quantification
for all;
for any;
for each;
for every
predicate logic
∀ x: P(x) means P(x) is true for all x.∀ n ∈ ℕ:n2 ≥ n.
ℂ
C
complex numbers
C;
the (set of) complex
numbers
numbers
ℂ means {a + b i : a,b ∈ ℝ}.i = √−1 ∈ ℂ
cardinality of the
continuum
cardinality of the
continuum;
c;
cardinality of the real
numbers
set theory
The cardinality of is denoted by or by the symbol (a lowercase Fraktur letter
C).
∂
partial derivative
partial;
d
calculus
∂f/∂xi means the partial derivative of f with respect to xi, where f is a function on (x1,
..., xn). If f(x,y) := x2y, then ∂f/∂x = 2xy,
boundary
boundary of
topology
∂M means the boundary of M∂{x : ||x|| ≤ 2} = {x : ||x|| = 2}
degree of a polynomial
degree of
algebra
∂f means the degree of the polynomial f.
(This may also be written deg f.)
∂(x2 − 1) = 2
E
expected value
expected value
probability theory
the value of a random variable one would "expect" to find if one could repeat the
random variable process an infinite number of times and take the average of the
values obtained
∃
existential quantification
there exists;
there is;
there are
predicate logic
∃ x: P(x) means there is at least one x such that P(x) is true. ∃ n ∈ ℕ: n is even.
∃!uniqueness quantification
there exists exactly one
predicate logic
∃! x: P(x) means there is exactly one x such that P(x) is true. ∃! n ∈ ℕ: n + 5 = 2n.
∈
∉
set membership
is an element of;
is not an element of
everywhere, set theory
a ∈ S means a is an element of the set S;[7] a ∉ S means a is not an element of S.[7]
(1/2)−1 ∈ ℕ
2−1 ∉ ℕ
∌
set membership
does not contain as an
element
set theory
S ∌ e means the same thing as e ∉ S, where S is a set and e is not an element of S.
∋
such that symbol
such that
mathematical logic
often abbreviated as "s.t."; : and | are also used to abbreviate "such that". The use of ∋
goes back to early mathematical logic and its usage in this sense is declining.
Choose ∋ 2| and 3| . (Here | is used in the
sense of "divides".)
set membership
contains as an element
set theory
S ∋ e means the same thing as e ∈ S, where S is a set and e is an element of S.
ℍ
H
quaternions or
Hamiltonian quaternions
H;
the (set of) quaternions
numbers
ℍ means {a + bi + cj + dk : a,b,c,d ∈ ℝ}.
ℕ
N
natural numbers
the (set of) natural
numbers
numbers
N means either { 0, 1, 2, 3, ...} or { 1, 2, 3, ...}.
The choice depends on the area of mathematics being studied; e.g. number theorists
prefer the latter; analysts, set theorists and computer scientists prefer the former. To
avoid confusion, always check an author's definition of N.
Set theorists often use the notation ω (for least infinite ordinal) to denote the set of
natural numbers (including zero), along with the standard ordering relation ≤.
ℕ = {|a| : a ∈ ℤ} or ℕ = {|a| > 0: a ∈ ℤ}
oHadamard product
entrywise product
linear algebra
For two matrices (or vectors) of the same dimensions the Hadamard
product is a matrix of the same dimensions with elements given by
.
In MATLAB this operation is expressed by A.*B.
∘
function composition
composed with
set theory
f ∘ g is the function such that (f ∘ g)(x) = f(g(x)).[10] if f(x) := 2x, and g(x) := x + 3, then (f ∘ g)(x) =
2(x + 3).
O
Big O notation
big-oh of
Computational
complexity theory
The Big O notation describes the limiting behavior of a function, when the argument
tends towards a particular value or infinity.
If f(x) = 6x4 − 2x3 + 5 and g(x) = x4, then
C. Some List of Math Symbols
107
ℙ
P
projective space
P;
the projective space;
the projective line;
the projective plane
topology
ℙ means a space with a point at infinity. ,
probability
the probability of
probability theory
ℙ(X) means the probability of the event X occurring.
This may also be written as P(X), Pr(X), P[X] or Pr[X].
If a fair coin is flipped, ℙ(Heads) = ℙ(Tails) =
0.5.
Power set
the Power set of
Powerset
Given a set S, the power set of S is the set of all subsets of the set S. The power set of
S0 is
denoted by P(S).
The power set P({0, 1, 2}) is the set of all
subsets of {0, 1, 2}. Hence,
P({0, 1, 2}) = {∅, {0}, {1}, {2}, {0, 1}, {0,
2}, {1, 2}, {0, 1, 2. }}
ℚ
Q
rational numbers
Q;
the (set of) rational
numbers;
the rationals
numbers
ℚ means {p/q : p ∈ ℤ, q ∈ ℕ}.
3.14000... ∈ ℚ
π ∉ ℚ
ℝ
R
real numbers
R;
the (set of) real numbers;
the reals
numbers
ℝ means the set of real numbers.
π ∈ ℝ
√(−1) ∉ ℝ
†
conjugate transpose
conjugate transpose;
adjoint;
Hermitian
adjoint/conjugate
/transpose/dagger
matrix operations
A† means the transpose of the complex conjugate of A.[11]
This may also be written A∗T, AT∗, A∗, ATor AT.
If A = (aij) then A† = (aji).
Ttranspose
transpose
matrix operations
AT means A, but with its rows swapped for columns.
This may also be written A′, Ator Atr.
If A = (aij) then AT = (aji).
⊤
top element
the top element
lattice theory
⊤ means the largest element of a lattice. ∀x : x ∨ ⊤ = ⊤
top type
the top type; top
type theory
⊤ means the top or universal type; every type in the type system of interest is a
subtype of top. ∀ types T, T <: ⊤
⊥
perpendicular
is perpendicular to
geometry
x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y. If l ⊥ m and m ⊥ n in the plane, then l || n.
orthogonal complement
orthogonal/
perpendicular
complement of;
perp
linear algebra
W⊥ means the orthogonal complement of W (where W is a subspace of the inner
product space V), the set of all vectors in V orthogonal to every vector in W.Within , .
coprime
is coprime to
number theory
x ⊥ y means x has no factor greater than 1 in common with y. 34 ⊥ 55
independent
is independent of
probability
A ⊥ B means A is an event whose probability is independent of event B. If A ⊥ B, then P(A|B) = P(A).
bottom element
the bottom element
lattice theory
⊥ means the smallest element of a lattice. ∀x : x ∧ ⊥ = ⊥
bottom type
the bottom type;
bot
type theory
⊥ means the bottom type (a.k.a. the zero type or empty type); bottom is the subtype
of every type in the type system. ∀ types T, ⊥ <: T
comparability
is comparable to
order theory
x ⊥ y means that x is comparable to y. {e, π} ⊥ {1, 2, e, 3, π} under set containment.
∪
set-theoretic union
the union of ... or ...;
union
set theory
A ∪ B means the set of those elements which are either in A, or in B, or in both.[5] A ⊆ B ⇔ (A ∪ B) = B
∩
set-theoretic intersection
intersected with;
intersect
set theory
A ∩ B means the set that contains all those elements that A and B have in common.[5] {x ∈ ℝ : x2 = 1} ∩ ℕ = {1}
∨
logical disjunction or
join in a lattice
or;
max;
join
propositional logic,
lattice theory
The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement
is false.
For functions A(x) and B(x), A(x) ∨ B(x) is used to mean max(A(x), B(x)).
n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural
number.
∧
logical conjunction or
meet in a lattice
and;
The statement A ∧ B is true if A and B are both true; else it is false.
For functions A(x) and B(x), A(x) ∧ B(x) is used to mean min(A(x), B(x)).
n < 4 ∧ n > 2 ⇔ n = 3 when n is a natural
number.
C. Some List of Math Symbols
108
min;
meet
propositional logic,
lattice theory
wedge product
wedge product;
exterior product
exterior algebra
u ∧ v means the wedge product of any multivectors u and v. In three-dimensional
Euclidean space the wedge product and the cross product of two vectors are each
other's Hodge dual.
exponentiation
... (raised) to the power
of ...
everywhere
a ^ b means a raised to the power of b
(a ^ b is more commonly written ab. The symbol ^ is generally used in programming
languages where ease of typing and use of plain ASCII text is preferred.)
2^3 = 23 = 8
×
multiplication
times;
multiplied by
arithmetic
3 × 4 means the multiplication of 3 by 4.
(The symbol * is generally used in programming languages, where ease of typing and
use of ASCII text is preferred.)
7 × 8 = 56
Cartesian product
the Cartesian product of
... and ...;
the direct product of ...
and ...
set theory
X × Y means the set of all ordered pairs with the first element of each pair selected
from X and the second element selected from Y. {1,2} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}
cross product
cross
linear algebra
u × v means the cross product of vectors u and v(1,2,5) × (3,4,−1) =
(−22, 16, − 2)
group of units
the group of units of
ring theory
R× consists of the set of units of the ring R, along with the operation of multiplication.
This may also be written R∗as described below, or U(R).
⊗
tensor product, tensor
product of modules
tensor product of
linear algebra
means the tensor product of V and U.[12] means the tensor product of
modules V and U over the ring R.
{1, 2, 3, 4} ⊗ {1, 1, 2} =
{{1, 1, 2}, {2, 2, 4}, {3, 3, 6}, {4, 4, 8}}
⋉
⋊
semidirect product
the semidirect product of
group theory
N ⋊φH is the semidirect product of N (a normal subgroup) and H (a subgroup), with
respect to φ. Also, if G = N ⋊φH, then G is said to split over N.
(⋊ may also be written the other way round, as ⋉, or as ×.)
semijoin
the semijoin of
relational algebra
R ⋉ S is the semijoin of the relations R and S, the set of all tuples in R for which there
is a tuple in S that is equal on their common attribute names. R S = a1,..,an(R S)
⋈
natural join
the natural join of
relational algebra
R ⋈ S is the natural join of the relations R and S, the set of all combinations of tuples
in R and S that are equal on their common attribute names.
ℤ
Z
integers
the (set of) integers
numbers
ℤ means {..., −3, −2, −1, 0, 1, 2, 3, ...}.
ℤ+ or ℤ> means {1, 2, 3, ...} .
ℤ* or ℤ≥ means {0, 1, 2, 3, ...} .
ℤ = {p, −p : p ∈ ℕ ∪ {0}}
ℤn
ℤp
Zn
Zp
integers mod n
the (set of) integers
modulo n
numbers
ℤn means {[0], [1], [2], ...[n−1]} with addition and multiplication modulo n.
Note that any letter may be used instead of n, such as p. To avoid confusion with
p-adic numbers, use ℤ/pℤ or ℤ/(p) instead.
ℤ3 = {[0], [1], [2]}
p-adic integers
the (set of) p-adic
integers
numbers Note that any letter may be used instead of p, such as n or l.
Symbols based on Hebrew or Greek letters
C. Some List of Math Symbols
109
Symbol
in
HTML
Symbol
in TeX
Name
Explanation Examples
Read as
Category
ℵ
aleph number
aleph
set theory
ℵα represents an infinite cardinality (specifically, the α-th one, where α
is an ordinal). |ℕ| = ℵ0, which is called aleph-null.
ℶ
beth number
beth
set theory
ℶα represents an infinite cardinality (similar to ℵ, but ℶ does not
necessarily index all of the numbers indexed by ℵ. ).
δ
Dirac delta
function
Dirac delta of
hyperfunction
δ(x)
Kronecker
delta
Kronecker
delta of
hyperfunction
δij
Functional
derivative
Functional
derivative of
Differential
operators
∆
⊖
symmetric
difference
symmetric
difference
set theory
A ∆ B (or A ⊖ B) means the set of elements in exactly one of A or B.
(Not to be confused with delta, Δ, described below.)
{1,5,6,8} ∆ {2,5,8} = {1,2,6}
{3,4,5,6} ⊖ {1,2,5,6} = {1,2,3,4}
Δ
delta
delta;
change in
calculus
Δx means a (non-infinitesimal) change in x.
(If the change becomes infinitesimal, δ and even d are used instead.
Not to be confused with the symmetric difference, written ∆, above.)
is the gradient of a straight line.
Laplacian
Laplace
operator
vector
calculus
The Laplace operator is a second order differential operator in
n-dimensional Euclidean space
If ƒ is a twice-differentiable real-valued function, then the Laplacian of ƒ
is defined by
∇
gradient
del;
nabla;
gradient of
vector
calculus
∇f (x1, ..., xn) is the vector of partial derivatives (∂f / ∂x1, ..., ∂f / ∂xn). If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)
divergence
del dot;
divergence of
vector
calculus
If , then .
curl
curl of
vector
calculus
If , then .
π
Pi
pi;
3.1415926...;
≈355÷113
mathematical
constant
Used in various formulas involving circles; π is equivalent to the
amount of area a circle would take up in a square of equal width with
an area of 4 square units, roughly 3.14159. It is also the ratio of the
circumference to the diameter of a circle.
A = πR2 = 314.16 → R = 10
projection
Projection of
relational
algebra
restricts to the attribute set.
Homotopy
group
the nth
Homotopy
group of
Homotopy
theory
consists of homotopy equivalence classes of base point
preserving maps from an n-dimensional sphere (with base point) into
the pointed space X.
∏
product
product over
... from ... to ...
of
arithmetic
means .
Cartesian
product
the Cartesian
product of;
the direct
product of
set theory
means the set of all (n+1)-tuples
(y0, ..., yn).
∐
coproduct
coproduct
over ... from ...
A general construction which subsumes the disjoint union of sets and
of topological spaces, the free product of groups, and the direct sum of
modules and vector spaces. The coproduct of a family of objects is
C. Some List of Math Symbols
110
to ... of
category
theory
essentially the "least specific" object to which each object in the family
admits a morphism.
σ
selection
Selection of
relational
algebra
The selection selects all those tuples in for which holds
between the and the attribute. The selection selects all
those tuples in for which holds between the attribute and the
value .
∑
summation
sum over ...
from ... to ...
of
arithmetic
means .
∅
{ }
empty set
the empty set
set theory
∅ means the set with no elements.[7] { } means the same. {n ∈ ℕ : 1 < n2 < 4} = ∅
Variations
In mathematics written in Arabic, some symbols may be reversed to make right-to-left writing and reading easier.[13]
See also
Greek letters used in mathematics, science, and engineering
Diacritic
ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
Latin letters used in mathematics
List of mathematical abbreviations
List of mathematical symbols by subject
Mathematical Alphanumeric Symbols (Unicode block)
Mathematical constants and functions
Mathematical notation
Mathematical operators and symbols in Unicode
Notation in probability and statistics
Physical constants
Table of logic symbols
Table of mathematical symbols by introduction date
Typographical conventions in mathematical formulae
References
"Math is Fun website".1.
Rónyai, Lajos (1998), Algoritmusok(Algorithms), TYPOTEX, ISBN 963-9132-16-02.
Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. (2002). "A fast and elitist multiobjective genetic algorithm: NSGA-II". IEEE Transactions on Evolutionary Computation 6 (2): 182.
doi:10.1109/4235.996017.
3.
Copi, Irving M.; Cohen, Carl (1990) [1953], "Chapter 8.3: Conditional Statements and Material Implication", Introduction to Logic (8th ed.), New York: Macmillan Publishers (United States),
pp. 268–269, ISBN 0-02-325035-6, LCCN 89037742
4.
Goldrei, Derek (1996), Classic Set Theory, London: Chapman and Hall, p. 4, ISBN 0-412-60610-05.
Nielsen, Michael A; Chuang, Isaac L (2000), Quantum Computation and Quantum Information, New York: Cambridge University Press, p. 66, ISBN 0-521-63503-9, OCLC 436413336.
Goldrei, Derek (1996), Classic Set Theory, London: Chapman and Hall, p. 3, ISBN 0-412-60610-07.
Nielsen, Michael A; Chuang, Isaac L (2000), Quantum Computation and Quantum Information, New York: Cambridge University Press, p. 62, ISBN 0-521-63503-9, OCLC 436413338.
Berman, Kenneth A; Paul, Jerome L. (2005), Algorithms: Sequential, Parallel, and Distributed, Boston: Course Technology, p. 822, ISBN 0-534-42057-59.
Goldrei, Derek (1996), Classic Set Theory, London: Chapman and Hall, p. 5, ISBN 0-412-60610-010.
Nielsen, Michael A; Chuang, Isaac L (2000), Quantum Computation and Quantum Information, New York: Cambridge University Press, pp. 69–70, ISBN 0-521-63503-9, OCLC 4364133311.
Nielsen, Michael A; Chuang, Isaac L (2000), Quantum Computation and Quantum Information, New York: Cambridge University Press, pp. 71–72, ISBN 0-521-63503-9, OCLC 4364133312.
M. Benatia, A. Lazrik, and K. Sami, "Arabic mathematical symbols in Unicode (http://www.ucam.ac.ma/fssm/rydarab/doc/expose/unicodeme.pdf)", 27th Internationalization and Unicode Conference,
2005.
13.
External links
The complete set of mathematics Unicode characters (http://krestavilis.com/math.php)
Jeff Miller: Earliest Uses of Various Mathematical Symbols (http://jeff560.tripod.com/mathsym.html)
Numericana: Scientific Symbols and Icons (http://www.numericana.com/answer/symbol.htm)
GIF and PNG Images for Math Symbols (http://us.metamath.org/symbols/symbols.html)
Mathematical Symbols in Unicode (http://tlt.psu.edu/suggestions/international/bylanguage/math.html#browsers)
Using Greek and special characters from Symbol font in HTML (http://www.alanwood.net/demos/symbol.html)
Unicode Math Symbols (http://mathsymbols.net/) - a quick form for using unicode math symbols.
DeTeXify handwritten symbol recognition (http://detexify.kirelabs.org/classify.html) — doodle a symbol in the box, and the program will tell you what its name is
Handbook for Spoken Mathematics (http://web.efzg.hr/dok/MAT/vkojic/Larrys_speakeasy.pdf) — pronunciation guide to many commonly used symbols
Some Unicode charts of mathematical operators:
Index of Unicode symbols (http://www.unicode.org/charts/#symbols)
Range 2100–214F: Unicode Letterlike Symbols (http://www.unicode.org/charts/PDF/U2100.pdf)
Range 2190–21FF: Unicode Arrows (http://www.unicode.org/charts/PDF/U2190.pdf)
Range 2200–22FF: Unicode Mathematical Operators (http://www.unicode.org/charts/PDF/U2200.pdf)
Range 27C0–27EF: Unicode Miscellaneous Mathematical Symbols–A (http://www.unicode.org/charts/PDF/U27C0.pdf)
Range 2980–29FF: Unicode Miscellaneous Mathematical Symbols–B (http://www.unicode.org/charts/PDF/U2980.pdf)
Range 2A00–2AFF: Unicode Supplementary Mathematical Operators (http://www.unicode.org/charts/PDF/U2A00.pdf)
Some Unicode cross-references:
Short list of commonly used LaTeX symbols (http://www.artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols) and Comprehensive LaTeX Symbol List
(http://mirrors.med.harvard.edu/ctan/info/symbols/comprehensive/)
MathML Characters (http://www.robinlionheart.com/stds/html4/entities-mathml) - sorts out Unicode, HTML and MathML/TeX names on one page
Unicode values and MathML names (http://www.w3.org/TR/REC-MathML/chap6/bycodes.html)
Unicode values and Postscript names (http://svn.ghostscript.com/ghostscript/branches/gs-db/Resource/Decoding/Unicode) from the source code for Ghostscript
Retrieved from "https://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&oldid=730409871"
Categories: Mathematical notation Mathematics-related lists Mathematical symbols Mathematical tables Mathematical logic Lists of symbols
This page was last modified on 18 July 2016, at 21:19.
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C. Some List of Math Symbols
111
Appendix D
DISLAYING MATH EXPRESSIONS
112
Help:Displaying a formula
From Wikipedia, the free encyclopedia
"WP:MATH" and "WP:MATHS" redirect here. For the WikiProject on mathematics, see Wikipedia:WikiProject
Mathematics. For Wikipedia's mathematics style manual, see Wikipedia:Manual of Style/Mathematics. For the
mathematics reference desk, see Wikipedia:Reference desk/Mathematics.
MediaWiki renders mathematical equations using a combination of html markup and a variant of LaTeX.
The version of LaTeX used is a subset of AMS-LaTeX markup, a superset of LaTeX markup which is in turn a superset of TeX
markup, for mathematical formulae. Only a limited part of the full TeX language is supported; see below for details.[a]
By default SVG images with non-visible MathML are generated. The older PNG images can be set via user preferences.[b] On
some browsers like Firefox, it is possible to use MathML for display via extensions; see the main extension page at
mw:Extension:Math for details. Client side MathJax is no longer supported.
Contents
1 Basics
1.1 LaTeX commands
1.2 Special characters
1.3 Spaces
1.4 LaTeX environments
1.5 Rendering
1.5.1 Force-rerendering of formulas
2 TeX vs HTML
2.1 Pros of HTML
2.2 Pros of TeX
2.3 Using MathML
3 Formatting using TeX
3.1 Functions, symbols, special characters
3.1.1 Accents/diacritics
3.1.2 Standard numerical functions
3.1.3 Bounds
3.1.4 Projections
3.1.5 Differentials and derivatives
3.1.6 Letter-like symbols or constants
3.1.7 Modular arithmetic
3.1.8 Radicals
3.1.9 Operators
3.1.10 Sets
3.1.11 Relations
3.1.12 Geometric
3.1.13 Logic
3.1.14 Arrows
3.1.15 Special
3.1.16 Unsorted (new stuff)
3.2 Larger expressions
3.2.1 Subscripts, superscripts, integrals
3.3 Display attribute
3.3.1 Inline
3.3.1.1 Example
3.3.1.2 Technical implementation
3.3.2 Block
3.3.2.1 Example
3.3.2.2 Technical implementation
3.3.3 Not specified
3.3.3.1 Example
3.3.4 Fractions, matrices, multilines
3.3.5 Parenthesizing big expressions, brackets, bars
3.3.6 Equation numbering
3.4 Alphabets and typefaces
3.4.1 Mixed text faces
3.5 Color
3.6 Formatting issues
D. Dislaying Math Expressions
113
3.6.1 Spacing
3.6.2 Alignment with normal text flow
3.7 Commutative diagrams
3.7.1 Diagrams in TeX
3.7.2 Convert to SVG
3.7.3 Upload the file
3.7.4 Examples
3.8 Unimplemented elements and workarounds
3.8.1 \oiint and \oiiint
3.8.1.1 \oiint and \oiiint as PNG images
3.8.1.1.1 Examples
3.8.1.2 Oriented \oiint and \oiiint as PNG images
3.8.2 \overarc
3.8.3 \dddot
3.9 Syntax to avoid
3.9.1 Percentages
3.9.2 \textrm
3.9.3 Unicode characters
4 Chemistry
4.1 Molecular and Condensed formula
4.2 Bonds
4.3 Charges
4.4 Addition Compounds and Stoichiometric Numbers
4.5 (Italic) Math
4.6 Oxidation States
4.7 Greek characters
4.8 Isotopes
4.9 States
4.10 Precipitate
4.11 Reaction Arrows
4.12 Further Examples Using Ordinary LaTeX tags
5 Examples of implemented TeX formulas
5.1 Quadratic polynomial
5.2 Quadratic formula
5.3 Tall parentheses and fractions
5.4 Integrals
5.5 Matrices and determinants
5.6 Summation
5.7 Differential equation
5.8 Complex numbers
5.9 Limits
5.10 Integral equation
5.11 Example
5.12 Continuation and cases
5.13 Prefixed subscript
5.14 Fraction and small fraction
5.15 Area of a quadrilateral
5.16 Volume of a sphere-stand
5.17 Multiple equations
6 See also
7 References
7.1 Footnotes
7.2 Citations
8 External links
Basics
Math markup goes inside <math>...</math>. Chemistry markup goes inside <math chem>...</math chem> or
<ce>...</ce>. All these tags use TeX.
The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math
tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of
#if, etc. See m:Template:Demo of attempt to use parameters within TeX (backlinks edit (https://meta.wikimedia.org
/wiki/Template:Demo_of_attempt_to_use_parameters_within_TeX?action=edit)) for more information.
D. Dislaying Math Expressions
114
LaTeX commands
LaTeX commands are case-sensitive, and take one of the following two formats:
They start with a backslash \ and then have a name consisting of letters only. Command names are terminated by a
space, a number or any other "non-letter".
They consist of a backslash \ and exactly one non-letter.
Some commands need an argument, which has to be given between curly braces { } after the command name. Some
commands support optional parameters, which are added after the command name in square brackets []. The general syntax is:
\commandname[option1,option2,...]{argument1}{argument2}...
Special characters
The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the
fonts. If you enter them directly in your text, they will normally not render, but rather do things you did not intend.
# $ % ^ & _ { } ~ \
These characters can be entered by adding a prefix backslash or using special sequences:
\# \$ \% ^\wedge \& \_ \{ \} \sim \backslash
yielding
.
The backslash character \ can not be entered by adding another backslash in front of it (\\); this sequence is used for line
breaking. For introducing a backslash in math mode, you can use \backslash instead which gives .
The command \tilde produces a tilde which is placed over the next letter. For example, \tilde{a} gives . To produce just a
tilda character ~, use \tilde{} which gives , placing a ~ over an empty box. Alternatively \sim produces , a large centred ~
which may be more appropriate in some situations.
The command \hat produces a hat over the next character, for example \hat{o} produces . For a stretchable version use
\widehat{abc} giving . The wedge \wedge is normally used as a mathematical operator the sequence ^\wedge produces
the best equivalent to the ascii caret ^ character.
Spaces
"Whitespace" characters, such as blank or tab, are treated uniformly as "space" by LaTeX. Several consecutive whitespace
characters are treated as one "space". See below for commands that produces spaces of different size.
LaTeX environments
Environments
in LaTeX have a role that is quite similar to commands, but they usually have effect on a wider part of formula.
Their syntax is:
\begin{environmentname}
text to be influenced
\end{environmentname}
Environments supported by Wikipedia include matrix, align, etc. See below.
Rendering
By default, the PNG images are rendered black on white, with a transparent
background. On darker backgrounds, the characters may show white edges. To
remove these, match the PNG background color with the background color of the
page using \pagecolor. However, black text on a dark background is hard to read
and should be avoided altogether where possible.
The colors, as well as font sizes and types, are independent of browser settings or CSS. Font sizes and types will often deviate
from what HTML renders. Vertical alignment with the surrounding text can also be a problem; a work-around is described in
the "Alignment with normal text flow" section below. The css selector of the images is img.tex.
D. Dislaying Math Expressions
115
The alt text of the PNG images, which is displayed to visually impaired and other readers who cannot see the images, and is
also used when the text is selected and copied, defaults to the wikitext that produced the image, excluding the <math> and
</math>. You can override this by explicitly specifying an alt attribute for the math element. For example, <math
alt="Square root of pi">\sqrt{\pi}</math> generates an image whose alt text is "Square root of pi". This should not
be confused with the title attribute that produces popup text when the hovering over the PNG image, for example <math
title="pi">\pi</math> generates an image whose popup text is "pi".
Apart from function and operator names, as is customary in mathematics, variables and letters are in italics; digits are not. For
other text, (like variable labels) to avoid being rendered in italics like variables, use \text, \mbox, or \mathrm. You can also
define new function names using \operatorname{...}. For example, \text{abc} gives . \operatorname{...} provides
spacing before and after the operator name when appropriate, as when a\operatorname{\sn}b is rendered as (with
space to the left and right of "sn") and a\operatorname{\sn}(b+c) as (with space to the left and not to the right).
Latex does not have full support for Unicode characters and not all characters render. Most Latin characters with accents
render correctly. However some do not, in particular those that include multiple diacritics (e.g. with Latin letters used in
Vietnamese) or that cannot be precomposed into a single character (such as the uppercase Latin letter W with ring), or that use
other diacritics (like the ogonek or the double grave accent, used in Central European languages like Polish, or the horn
attached above some vowels in Vietnamese), or other modified letter forms (used in IPA notations, or African languages, or in
medieval texts), some digram ligatures (like IJ in Dutch), or Latin letters borrowed from Greek, or small capitals, as well as
superscripts and subscript letters. For example, \text{ð} or \mbox{ð}, and \text{þ} or \mbox{þ} (used in Icelandic) will give
errors.
Force-rerendering of formulas
MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the
page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables
action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral. To force the
rerendering of this formula you need to open the URL https://en.wikipedia.org/w/index.php?title=Integral&action=purge&
mathpurge=true . Afterwards you need to bypass your browser cache so that the new created images of the formulas are
actually downloaded. See also mw:Extension:Math#Purging pages that contain equations for more details.
TeX vs HTML
Main page: Wikipedia:Rendering math
Before using TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes
similar results can be achieved in HTML using Template:Math. See also Help:Special characters.
TeX syntax TeX rendering HTML syntax HTML rendering
\alpha {{math|''&alpha;''}} α
f(x) = x^2 {{math|''f''(''x'') {{=}} ''x''<sup>2</sup>}} f(x) = x2
\sqrt{2}{{math|{{radical|2}}}} √2
\sqrt{1-e^2}{{math|{{radical|1 &minus; ''e''<sup>2</sup>}}}} √1 − e2
The codes on the left produce the symbols on the right, but the latter can also be put directly in the wikitext, except for ‘=’.
D. Dislaying Math Expressions
116
HTML syntax Rendering
&alpha; &beta; &gamma; &delta; &epsilon; &zeta;
&eta; &theta; &iota; &kappa; &lambda; &mu; &nu;
&xi; &omicron; &pi; &rho; &sigma; &sigmaf;
&tau; &upsilon; &phi; &chi; &psi; &omega;
α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ σ ς
τ υ φ χ ψ ω
&Gamma; &Delta; &Theta; &Lambda; &Xi; &Pi;
&Sigma; &Phi; &Psi; &Omega;
Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω
&int; &sum; &prod; &radic; &minus; &plusmn; &infin;
&asymp; &prop; = &equiv; &ne; &le; &ge;
&times; &middot; &sdot; &divide; &part; &prime; &Prime;
&nabla; &permil; &deg; &there4; &empty;
∫ ∑ ∏ √ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× · ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ ∅
&isin; &notin; &cap; &cup; &sub; &sup; &sube; &supe;
&not; &and; &or; &exist; &forall;
&rArr; &hArr; &rarr; &harr; &uarr; &darr;
&alefsym; - &ndash; &mdash;
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑ ↓
ℵ - – —
The project has settled on using both HTML and TeX because each has advantages in some situations.
Pros of HTML
Formulas in HTML behave more like regular text. In-line HTML formulae always align properly with the rest of the
HTML text and, to some degree, can be copied-and-pasted (this is not a problem if TeX is rendered using MathJax, and
the alignment should not be a problem for PNG rendering once bug 32694 is fixed).
1.
The formula’s background and font size match the rest of HTML contents (this can be fixed on TeX formulas by using
the commands \pagecolor and \definecolor) and the appearance respects CSS and browser settings while the
typeface is conveniently altered to help you identify formulae.
2.
Pages using HTML code for formulae will load faster and they will create less clutter on your hard disk.3.
Formulae typeset with HTML code will be accessible to client-side script links (a.k.a. scriptlets).4.
The display of a formula entered using mathematical templates can be conveniently altered by modifying the templates
involved; this modification will affect all relevant formulae without any manual intervention.
5.
The HTML code, if entered diligently, will contain all semantic information to transform the equation back to TeX or
any other code as needed. It can even contain differences TeX does not normally catch, e.g. {{math|''i''}} for the
imaginary unit and {{math|<var>i</var>}} for an arbitrary index variable.
6.
Unlike generated bitmaps, HTML is not sensitive to dots per inch variances between viewing platforms.7.
Pros of TeX
TeX is semantically more precise than HTML.
In TeX, "x" means "mathematical variable " ", whereas in HTML "x" is generic and somewhat ambiguous.1.
On the other hand, if you encode the same formula as "{{math|<var>x</var>}}", you get the same visual result x
and no information is lost. This requires diligence and more typing that could make the formula harder to
understand as you type it. However, since there are far more readers than editors, this effort is worth considering if
no other rendering options are available (such as MathJax, which is available to logged-in users as a preferences
opt-in).
2.
1.
One consequence of point 1 is that TeX code can be transformed into HTML, but not vice versa.[1] This means that on
the server side we can always transform a formula, based on its complexity and location within the text, user
preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the
benefits of TeX. It is true that the current situation is not ideal, but that is not a good reason to drop information or
contents. It is more a reason to help improve the situation.
2.
Another consequence of point 1 is that TeX can be converted to MathML (e.g. by MathJax) for browsers which support
it, thus keeping its semantics and allowing the rendering to be better suited for the reader’s graphic device.
3.
TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers. It is easier
to persuade them to contribute if they can write in TeX.
4.
TeX has been specifically designed for typesetting formulae, so input is easier and more natural if you are accustomed to
it, and output is more aesthetically pleasing if you focus on a single formula rather than on the whole containing page.
5.
Once a formula is done correctly in TeX, it will render reliably, whereas the success of HTML formulae is somewhat
dependent on browsers or versions of browsers. Another aspect of this dependency is fonts: the serif font used for
rendering formulae is browser-dependent and it may be missing some important glyphs. While the browser is generally
capable to substitute a matching glyph from a different font family, it need not be the case for combined glyphs (compare
6.
D. Dislaying Math Expressions
117
"a
̅" and " a
̅").
When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or
that HTML entity. The burden of these decisions is put on the software. This does not hold for HTML formulae, which
can easily end up being rendered wrongly or differently from the editor’s intentions on a different browser.[2]
7.
TeX formulae, by default, render larger and are usually more readable than HTML formulae and are not dependent on
client-side browser resources, such as fonts, and so the results are more reliably WYSIWYG.
8.
While TeX does not assist you in finding HTML codes or Unicode values (which you can obtain by viewing the HTML
source in your browser), copying and pasting from a TeX PNG image in Wikipedia into simple text will return the
LaTeX source.
9.
^ Unless your wikitext follows the style of point 1.2
^ The entity support problem is not limited to mathematical formulae though; it can be easily solved by using the corresponding characters
instead of entities, as the character repertoire links do, except for cases where the corresponding glyphs are visually indiscernible (e.g.
&ndash; for ‘–’ and &minus; for ‘−’).
In some cases it may be the best choice to use neither TeX nor the HTML substitutes, but instead the simple ASCII symbols of
a standard keyboard (see hereafter, for an example).
Using MathML
The default MathML/SVG renderer option, selectable through My Preferences - Appearance - Math generate hidden MathML
code. This code can be used by screen readers and other assistive technology. To actually display the MathML in Firefox the
(https://addons.mozilla.org/en-US/firefox/addon/native-mathml/) extension and the MathML fonts
(https://developer.mozilla.org/en-US/docs/Mozilla/MathML_Project/Fonts) must be installed. Details on using MathML in
other systems can be found at mw:Extension:Math.
Formatting using TeX
Functions, symbols, special characters
D. Dislaying Math Expressions
118
Accents/diacritics
\dot{a}, \ddot{a}, \acute{a}, \grave{a}
\check{a}, \breve{a}, \tilde{a}, \bar{a}
\hat{a}, \widehat{a}, \vec{a}
Standard numerical functions
\exp_a b = a^b, \exp b = e^b, 10^m
\ln c, \lg d = \log e, \log_{10} f
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f
\arcsin h, \arccos i, \arctan j
\sinh k, \cosh l, \tanh m, \coth n
\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m,
\operatorname{coth}\,n
\operatorname{argsh}\,o, \operatorname{argch}\,p,
\operatorname{argth}\,q
\sgn r, \left\vert s \right\vert
\min(x,y), \max(x,y)
Bounds
\min x, \max y, \inf s, \sup t
\lim u, \liminf v, \limsup w
\dim p, \deg q, \det m, \ker\phi
Projections
\Pr j, \hom l, \lVert z \rVert, \arg z
Differentials and derivatives
dt, \operatorname{d}\!t, \partial t, \nabla\psi
dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx},
{\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial
x_1\partial x_2}y
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y
Letter-like symbols or constants
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS
Modular arithmetic
s_k \equiv 0 \pmod{m}
a\,\bmod\,b
\gcd(m, n), \operatorname{lcm}(m, n)
\mid, \nmid, \shortmid, \nshortmid
Radicals
D. Dislaying Math Expressions
119
For a little more semantics on these symbols, see the brief TeX Cookbook (http://www.math.upenn.edu/tex-stuff
/cookbook.pdf).
Larger expressions
Subscripts, superscripts, integrals
D. Dislaying Math Expressions
120
Feature Syntax How it looks rendered
Superscript a^2
Subscript a_2
Grouping 10^{30} a^{2+2}
a_{i,j} b_{f'}
Combining sub & super without and with
horizontal separation
x_2^3
{x_2}^3
Super super 10^{10^{8}}
Preceding and/or additional sub & super \sideset{_1^2}{_3^4}\prod_a^b
{}_1^2\!\Omega_3^4
Stacking
\overset{\alpha}{\omega}
\underset{\alpha}{\omega}
\overset{\alpha}{\underset{\gamma}{\omega}}
\stackrel{\alpha}{\omega}
Derivatives x', y'', f', f''
x^\prime, y^{\prime\prime}
Derivative dots \dot{x}, \ddot{x}
Underlines, overlines, vectors
\hat a \ \bar b \ \vec c
\overrightarrow{a b}\ \overleftarrow{c d}
\ \widehat{d e f}
\overline{g h i}\ \underline{j k l}
Arc (workaround) \overset{\frown} {AB}
Arrows A \xleftarrow{n+\mu-1} B
\xrightarrow[T]{n\pm i-1} C
Overbraces \overbrace{ 1+2+\cdots+100 }^{5050}
Underbraces \underbrace{ a+b+\cdots+z }_{26}
Sum \sum_{k=1}^N k^2
Sum (force \textstyle)\textstyle \sum_{k=1}^N k^2
Sum in a fraction (default \textstyle)\frac{\sum_{k=1}^N k^2}{a}
Sum in a fraction (force \displaystyle)\frac{\displaystyle \sum_{k=1}^N k^2}{a}
Sum in a fraction (alternative limits style) \frac{\sum\limits^{^N}_{k=1} k^2}{a}
Product \prod_{i=1}^N x_i
Product (force \textstyle)\textstyle \prod_{i=1}^N x_i
Coproduct \coprod_{i=1}^N x_i
Coproduct (force \textstyle)\textstyle \coprod_{i=1}^N x_i
D. Dislaying Math Expressions
121
This screenshot shows the formula
E = mc2 being edited using
VisualEditor. The visual editor shows
a button that allows to choose one of
three offered modes to display a
formula.
Limit \lim_{n \to \infty}x_n
Limit (force \textstyle)\textstyle \lim_{n \to \infty}x_n
Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (alternative limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
Integral (force \textstyle)\textstyle \int\limits_{-N}^{N} e^x\, dx
Integral (force \textstyle, alternative limits
style) \textstyle \int_{-N}^{N} e^x\, dx
Double integral \iint\limits_D \, dx\,dy
Triple integral \iiint\limits_E \, dx\,dy\,dz
Quadruple integral \iiiint\limits_F \, dx\,dy\,dz\,dt
Line or path integral \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Closed line or path integral \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy
Intersections \bigcap_{i=_1}^n E_i
Unions \bigcup_{i=_1}^n E_i
Display attribute
The <math> tag can take a display attribute with possible values of inline and block.
Inline
If the value of the display attribute is inline, the contents will be rendered in inline
mode; i.e., there will be no new paragraph for the equation and the operators will be
rendered to consume only a small amount of vertical space.
Example
The sum converges to 2.
The next line-width is not disturbed by large operators.
The code for the math example reads:
<math display="inline">\sum_{i=0}^\infty 2^{-i}</math>
Technical implementation
Technically the command \textstyle will be added to the user input before the tex command is passed to the renderer. The result
will be displayed without further formatting by outputting the image or MathMLelement to the page.
Block
In block-style the equation is rendered in its own paragraph and the operators are rendered consuming less horizontal space.
Example
D. Dislaying Math Expressions
122
The equation
It was entered as
<math display="block">\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 </math>
Technical implementation
Technically it will add the command \displaystyle will be added to the user input, if the user input does not contain the string
\displaystyle or \align before the tex command is passed to the renderer. The result will be displayed in a new paragraph.
Therefore, the style of the MathImage is altered i.e. the style attribute "display:block;margin:auto" is added. For MathML it is
ensured that display=inline is replaced by display block which produces a new paragraph
Not specified
If nothing is specified the current behavior is preserved. That means all equations are rendered in display style but not using a
new paragraph.
Example
The sum converges to 2.
The next line-width is disturbed by large operators.
The code for the math example reads:
<math>\sum_{i=0}^\infty 2^{-i}</math>
The equation
It was entered as
<math>\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 </math>
Fractions, matrices, multilines
D. Dislaying Math Expressions
123
Feature Syntax How it looks rendered
Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5
Small fractions (force
\textstyle)\tfrac{2}{4} = 0.5
Large (normal) fractions (force
\displaystyle)
\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c
+ \dfrac{2}{d + \dfrac{2}{4}}} = a
Large (nested) fractions \cfrac{2}{c + \cfrac{2}{d +
\cfrac{2}{4}}} = a
Cancellations in fractions \cfrac{x}{1 + \cfrac{\cancel{y}}
{\cancel{y}}} = \cfrac{x}{2}
Binomial coefficients \binom{n}{k}
Small binomial coefficients
(force \textstyle)\tbinom{n}{k}
Large (normal) binomial
coefficients (force
\displaystyle)
\dbinom{n}{k}
Matrices
\begin{matrix}
x & y \\
z & v
\end{matrix}
\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
\begin{bmatrix}
0 &\cdots & 0 \\
\vdots &\ddots &\vdots \\
0 &\cdots & 0
\end{bmatrix}
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix}\bigr)
D. Dislaying Math Expressions
124
Case distinctions
f(n) =
\begin{cases}
n/2, &\text{if }n\text{ is even}\\
3n+1, &\text{if }n\text{ is odd}
\end{cases}
Multiline equations
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
Multiline equations (must define
number of columns used ({lcl}))
(should not be used unless needed)
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
Multiline equations (more)
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
Breaking up a long expression
so that it wraps when necessary,
at the expense of destroying
correct spacing
f(x) =
\sum_{n=0}^\infty a_n x^n =
a_0+a_1x+a_2x^2+\cdots
Simultaneous equations
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
Arrays
\begin{array}{|c|c|c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
Parenthesizing big expressions, brackets, bars
Feature Syntax How it looks rendered
Bad ( \frac{1}{2} )
Good \left ( \frac{1}{2}\right )
You can use various delimiters with \left and \right:
D. Dislaying Math Expressions
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Feature Syntax How it looks rendered
Parentheses \left ( \frac{a}{b}\right )
Brackets \left [ \frac{a}{b}\right ] \quad
\left \lbrack \frac{a}{b}\right \rbrack
Braces \left \{ \frac{a}{b}\right \} \quad
\left \lbrace \frac{a}{b}\right \rbrace
Angle brackets \left \langle \frac{a}{b}\right \rangle
Bars and double bars \left | \frac{a}{b}\right \vert \quad
\left \Vert \frac{c}{d}\right \|
Floor and ceiling functions: \left \lfloor \frac{a}{b}\right \rfloor \quad
\left \lceil \frac{c}{d}\right \rceil
Slashes and backslashes \left / \frac{a}{b}\right \backslash
Up, down, and up-down arrows
\left \uparrow \frac{a}{b}\right \downarrow
\quad
\left \Uparrow \frac{a}{b}\right \Downarrow
\quad
\left \updownarrow \frac{a}{b}\right
\Updownarrow
Delimiters can be mixed,
as long as \left and \right match
\left [ 0,1 \right )
\left \langle \psi \right |
Use \left. and \right. if you
do not want a delimiter to appear \left . \frac{A}{B}\right \} \to X
Size of the delimiters (add "l" or "r" to
indicate the side for proper spacing)
( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr]
\biggr] \Bigr] \bigr] ]
\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots
\Biggr\rangle \biggr\rangle \Bigr\rangle
\bigr\rangle \rangle
\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg|
\bigg| \Big| \big| |
\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor
\Biggl\lfloor \dots
\Biggr\rceil \biggr\rceil \Bigr\rceil
\bigr\rceil \ceil
\uparrow \big\uparrow \Big\uparrow
\bigg\uparrow \Bigg\uparrow \dots
\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow
\big\Downarrow \Downarrow
\updownarrow \big\updownarrow \Big\updownarrow
\bigg\updownarrow \Bigg\updownarrow \dots
\Bigg\Updownarrow \bigg\Updownarrow
\Big\Updownarrow \big\Updownarrow \Updownarrow
/ \big/ \Big/ \bigg/ \Bigg/ \dots
\Bigg\backslash \bigg\backslash \Big\backslash
\big\backslash \backslash
Equation numbering
The templates {{NumBlk}} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be
used to refer to a numbered equation from surrounding text. For example, the following syntax:
{{NumBlk|:|<math>x^2 + y^2 + z^2 = 1</math>|{{EquationRef|1}}}}
produces the following result (note the equation number in the right margin):
(1)
Later on, the text can refer to this equation by its number using syntax like this:
D. Dislaying Math Expressions
126
As seen in equation ({{EquationNote|1}}), blah blah blah...
The result looks like this:
As seen in equation (1), blah blah blah...
Note that the equation number produced by {{
EquationNote}} is a link that the user can click to go immediately to the cited
equation.
Alphabets and typefaces
See also: Wikipedia:LaTeX symbols § Fonts
Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others,
such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.
D. Dislaying Math Expressions
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Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta
\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho
\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta
\iota \kappa \lambda \mu \nu \xi \pi \rho
\sigma \tau \upsilon \phi \chi \psi \omega
\varepsilon \digamma \varkappa \varpi
\varrho \varsigma \vartheta \varphi
Hebrew symbols
\aleph \beth \gimel \daleth
Blackboard bold/scripts
\mathbb{ABCDEFGHI}
\mathbb{JKLMNOPQR}
\mathbb{STUVWXYZ}
Boldface
\mathbf{ABCDEFGHI}
\mathbf{JKLMNOPQR}
\mathbf{STUVWXYZ}
\mathbf{abcdefghijklm}
\mathbf{nopqrstuvwxyz}
\mathbf{0123456789}
Boldface (Greek)
\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta}
\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho}
\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega}
\boldsymbol{\varepsilon\digamma\varkappa\varpi}
\boldsymbol{\varrho\varsigma\vartheta\varphi}
Italics (default for Latin alphabet)
\mathit{0123456789}
Greek italics (default for lowercase Greek)
\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
Roman typeface
\mathrm{ABCDEFGHI}
\mathrm{JKLMNOPQR}
\mathrm{STUVWXYZ}
\mathrm{abcdefghijklm}
\mathrm{nopqrstuvwxyz}
\mathrm{0123456789}
Sans serif
\mathsf{ABCDEFGHI}
\mathsf{JKLMNOPQR}
\mathsf{STUVWXYZ}
D. Dislaying Math Expressions
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\mathsf{abcdefghijklm}
\mathsf{nopqrstuvwxyz}
\mathsf{0123456789}
Sans serif Greek (capital only)
\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}
\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}
Calligraphy/script
\mathcal{ABCDEFGHI}
\mathcal{JKLMNOPQR}
\mathcal{STUVWXYZ}
Fraktur typeface
\mathfrak{ABCDEFGHI}
\mathfrak{JKLMNOPQR}
\mathfrak{STUVWXYZ}
\mathfrak{abcdefghijklm}
\mathfrak{nopqrstuvwxyz}
\mathfrak{0123456789}
Small scriptstyle text
{\scriptstyle\text{abcdefghijklm}}
Mixed text faces
Feature Syntax How it looks rendered
Italicised characters (spaces are ignored) x y z
Non-italicised characters \text{x y z}
Mixed italics (bad) \text{if} n \text{is even}
Mixed italics (good) \text{if }n\text{ is even}
Mixed italics (alternative: ~ or "\ " forces a space) \text{if}~n\ \text{is even}
Color
Equations can use color with the \color command. For example,
{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}
x_{1,2}=\frac{{\color{Blue}-b}\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}2a }
There are several alternate notations styles
{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1} works with both texvc and MathJax
\color{Blue}x^2\color{Black}+\color{Orange}2x\color{Black}-\color{LimeGreen}1 works with both texvc and
MathJax
\color{Blue}{x^2}+\color{Orange}{2x}-\color{LimeGreen}{1} only works with MathJax
Some color names are predeclared according to the following table, you can use them directly for the rendering of formulas (or
for declaring the intended color of the page background).
D. Dislaying Math Expressions
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Colors supported
Note that color should not be used as the
only way to identify something, because it will become meaningless on black-
and-white media or for color-blind people. See Wikipedia:Manual of Style (accessibility)#Color.
Latex does not have a command for setting the background color. The most effective of setting a background color is by setting
a CSS styling rules for a table cell
{| class="wikitable" align="center"
| style="background: gray;" | <math>\pagecolor{Gray}x^2</math>
| style="background: Goldenrod;" | <math>\pagecolor{Goldenrod}y^3</math>
|}
Rendered as
The \pagecolor{Goldenrod} command is necessary for the Texvc renderer to use the correct anti-aliasing around the edges of
the semi-transparent images. Without the command a default (white) background color is used — below are shown the results
displayed on non-white background.
{| class="wikitable" align="center"
| style="background: gray;" | <math>x^2</math>
| style="background: Goldenrod;" | <math>y^3</math>
|}
Custom colours can be defined using
\definecolor{myorange}{rgb}{1,0.65,0.4}\color{myorange}e^{i \pi}\color{Black} + 1 = 0
Formatting issues
Spacing
Note that TeX handles most spacing automatically, but you may sometimes want manual control.
D. Dislaying Math Expressions
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A sample commutative diagram,
created in the manner described
Feature Syntax How it looks rendered
double quad space a \qquad b
quad space a \quad b
text space a\ b
text space without PNG conversion a \mbox{ } b
large space a\;b
medium space a\<b[not supported]
small space a\,b
tiny space (use for multiplication of factors) ab
tiny space (syntax space ignored) a b
no space (use for multi-letter variables) \mathit{ab}
small negative space a\!b
Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):
0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots
This can be remedied by putting a pair of braces { } around the whole expression:
{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}
Alignment with normal text flow
Because of the default CSS
img.tex {vertical-align:middle; }
an inline expression like should look good.
If you need to align it otherwise, use <math style="vertical-align:-100%;">...</math> and play with the
vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.
Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of
this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.
Commutative diagrams
To make a commutative diagram, there are three steps:
write the diagram in TeX1.
convert to SVG2.
upload the file to Wikimedia Commons3.
Diagrams in TeX
Xy-pic (http://www.tug.org/applications/Xy-pic/) (online manual (http://tex.loria.fr
/graph-pack/doc-xypic/xyguide-html/xyguide-html.html)) is the most powerful and
general-purpose diagram package in TeX. Diagrams created using it can be found at
Commons: Category:Xy-pic diagrams.
Simpler packages include:
AMS's amscd (http://www.dante.de/CTAN//help/Catalogue/entries/amscd.html)
Paul Taylor's diagrams (http://www.ctan.org/tex-archive/macros/generic/diagrams/taylor/)
François Borceux Diagrams (http://www.ctan.org/tex-archive/help/Catalogue/entries/borceux.html)
The following is a template for Xy-pic, together with a hack to increase the margins in dvips, so that the diagram is not
truncated by over-eager cropping (suggested in TUGboat: TUGboat, Volume 17 1996, No. 3 (http://www.tug.org/TUGboat
/Articles/tb17-3/tb52rahtz.pdf)):
\documentclass{amsart}
D. Dislaying Math Expressions
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\usepackage[all, ps, dvips]{xy}% Loading the XY-Pic package
% Using postscript driver for smoother curves
\usepackage{color}% For invisible frame
\begin{document}
\thispagestyle{empty}% No page numbers
\SelectTips{eu}{} % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt}% Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin
\xymatrix{
%%% Diagram goes here %%%
}
$$}}} % end math, end frame
\end{document}
Convert to SVG
Once you have produced your diagram in LaTeX (or TeX), you can convert it to an SVG file using the following sequence of
commands:
pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
rm tmp.pdf
The pdfcrop (http://pdfcrop.sourceforge.net) and pdf2svg (http://www.cityinthesky.co.uk/opensource/pdf2svg) utilities are
needed for this procedure. You can alternatively use pdf2svg (http://www.pdftron.com/pdf2svg/) from PDFTron for the last
step.
If you do not have pdfTeX (which is unlikely) you can use the following commands to replace the first step (TeX → PDF):
latex file.tex
dvipdfm file.dvi
In general, you will not be able to get anywhere with diagrams without TeX and Ghostscript, and the inkscape program is a
useful tool for creating or modifying your diagrams by hand. There is also a utility pstoedit which supports direct conversion
from Postscript files to many vector graphics formats, but it requires a non-free plugin to convert to SVG, and regardless of the
format, this editor has not been successful in using it to convert diagrams with diagonal arrows from TeX-created files.
These programs are:
a working TeX distribution, such as TeX Live
Ghostscript
pstoedit
Inkscape
Upload the file
See also: commons:Commons:First steps/Upload form
See also: Help:Contents/Images and media
As the diagram is your own work, upload it to Wikimedia Commons, so that all projects (notably, all languages) can use it
without having to copy it to their language's Wiki. (If you've previously uploaded a file to somewhere other than Commons, to
Commons.)
Check size
Before uploading, check that the default size of the image is neither too large nor too small by opening in an SVG
application and viewing at default size (100% scaling), otherwise adjust the -y option to dvips.
Name
Make sure the file has a meaningful name.
Upload
Login to Wikimedia Commons, then upload the file (http://commons.wikimedia.org/w/index.php?title=Special:Upload&
uselang=ownwork); for the Summary, give a brief description.
Now go to the
image page and add a description, including the source code, using this template:
{{Information
|description =
{{en|1= Description [[:en:Link to WP page|topic]]
}}
|source = {{own}}, created as per:
[[:en:Help:Displaying a formula#Commutative diagrams]];
source code below.
|date = The Creation Date, like 1999-12-31
|author = [[User:YourUserName|Your Real Name]]
D. Dislaying Math Expressions
132
|permission = {{self|PD-self (or other license)
|author = [[User:YourUserName|Your Real Name]]}}
}}
==TeX source==
<source lang=latex>
% TeX source here
</source>
[[Category:Commutative diagrams]]
[[Category:Xy-pic diagrams]]
[[Category:Images with LaTeX source code]]
Source code
Include the source code in the image page, in the Source section of the {{Information}} template, so that the diagram
can be edited in future.
Include the complete .tex file, not just the fragment, so future editors do not need to reconstruct a compilable file.
You may optionally make the source code section collapsible, using the {{cot}}/{{cob}} templates.
(Don't include it in the Summary section, which is just supposed to be a summary.)
License
The most common license for commutative diagrams is PD-self; some use PD-ineligible, especially for simple
diagrams, or other licenses. Please do not use the GFDL (http://www.gnu.org/copyleft/fdl.html), as it requires the entire
text of the GFDL to be attached to any document that uses the diagram.
Description
If possible, link to a Wikipedia page relevant to the diagram. (The 1= is necessary if you use nest templates within the
description, and harmless otherwise.)
Category
Include [[Category:Commutative diagrams]], so that it appears in commons:Category:Commutative diagrams. There
are also subcategories, which you may choose to use.
Include image
Now include the image on the original page via [[File:Diagram.svg]]
Examples
A sample conforming diagram is commons:Image:PSU-PU.svg.
Unimplemented elements and workarounds
\oiint and \oiiint
Elements which are not yet implemented are \oiint, namely a two-fold integral \iint ( ) with a circular curve through the
centre of the two integrals, and similarly \oiiint, a circular curve through three integrals. In contrast, \oint ( ) exists for the
single dimension (integration over a curved line within a plane or any space with higher dimension).
These elements appear in many contexts: \oiint denotes a surface integral over the closed 2d boundary of a 3d region (which
occurs in much of 3d vector calculus and physical applications – like Maxwell's equations), likewise \oiiint denotes
integration over the closed 3d boundary (surface volume) of a 4d region, and they would be strong candidates for the next TeX
version. As such there are a lot of workarounds in the present version.
\oiint and \oiiint using currently implemented symbols
\oiint looks like:
, which uses \iint along with \subset and \supset (overdrawn after
backspacing):
\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot
\mathrm{d}\mathbf A
, which uses \int twice (with some backward kerning) along with \bigcirc
(also overdrawn after backpacing) to produce a more consistent circle:
\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;
\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A
\oiiint (should also be preferably more tightly kerned) looks more or less like:
D. Dislaying Math Expressions
133
which uses three \int symbols (with more backward kerning) with \subset
and \supset (overdrawn after backspacing):
\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!
\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A
, which uses three \int symbols (with more backward kerning) along with
\bigcirc (also overdrawn after backspacing):
\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!
\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A
However, since no standardisation exists as yet, any workaround like this (which uses many \! symbols for backspacing)
should be avoided, if possible. See below for a possibility using PNG image enforcement.
Note that
\iint (the double integral) and \iiint (the triple integral) are still not kerned as they should preferably be, and are
currently rendered as if they were successive \int symbols ; this is not a major problem for reading the formulas, even if the
integral symbols before the last one do not have bounds, so it's best to avoid backspacing "hacks" as they may be inconsistent
with a possible future better implementation of integrals symbols (with more precisely computed kerning positions).
\oiint and \oiiint as PNG images
These symbols are available as PNG images which are also integrated into two templates, {{oiint}} and {{oiiint}}, which take
care of the formatting around the symbols.
The templates have three parameters:
preintegral
the text or formula immediately before the integral
intsubscpt
the subscript below the integral
integrand
the text or formula immediately after the integral
Examples
Stokes' theorem: {{oiint | intsubscpt = <math>{\scriptstyle S}</math> | integrand=<math>( \nabla
\times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S}\bold{F}\cdot {\rm
d}\boldsymbol{\ell} </math> }}
Ampère's law + correction: {{oiint | preintegral=<math>\oint_C \bold{B}\cdot {\rm d}\boldsymbol{\ell}
= \mu_0 </math> | intsubscpt = <math>{\scriptstyle S}</math> | integrand = <math>\left ( \bold{J} +
\epsilon_0\frac{\partial \bold{E}}{\partial t}\right ) \cdot {\rm d}\bold{S}</math> }}
Continuity of 4-momentum flux (in general relativity):[1]{{oiiint | preintegral=<math>\bold{P} = </math> |
intsubscpt = <math>{\scriptstyle \partial \Omega}</math> | integrand = <math>\bold{T}\cdot {\rm
d}^3\boldsymbol{\Sigma} = 0</math> }}
Oriented \oiint and \oiiint as PNG images
Some variants of \oiint and \oiiint have arrows on them to indicate the sense of integration, such as a line integral around a
closed curve in the clockwise sense, and higher dimensional analogues. These are not implemented in TeX on Wikipedia
either, although the template {{intorient}} is available - see link for details.
\overarc
\overarc is not yet implemented to display the arc notation. However, there exists a workaround: use \overset{\frown}{AB},
which gives
D. Dislaying Math Expressions
134
\dddot
\dddot is not implemented in the TexVC renderer but does work in MathJax. For a workaround use \overset{...}{x}, which
gives .
Syntax to avoid
The texvc processor accepts some non-standard syntax. These should be avoided as the MathJax based renderers do not
support these syntax.
Percentages
Texvc accepts % for representing percentages. This causes an error with MathJax and should be replaced with \% in all
renderers.
\textrm
In texvc spaces need to be represented inside the \textrm environment using \, \ and normal spaces are ignored i.e.
\textrm{A\,B C} would render as A BC. In mathjax \textrm is an alias for \text which is renders its argument as normal text,
hence \textrm{A\,B C} renders as A\,B C. To ensure compatibility between versions alway use the \text environment:
\text{A B C}.
Unicode characters
Non-ASCII Unicode characters like
π work in MathML, and MathJax but not in texvc so should be avoided.
Chemistry
There are three ways to render chemical sum formulae as used in chemical equations:
<math chem>...</math>
<ce>...</ce>
{{chem}}
<ce>X</ce> is short for <math chem>\ce{X}</math>
(where X is a chemical sum formula)
Technically, <math chem>...</math> is a math tag with the extension mhchem enabled, according to the MathJax
documentation (http://mathjax.readthedocs.org/en/latest/tex.html#mhchem).
Note, that the commands
\cee and \cf are disabled, because they are marked as deprecated in the mhchem LaTeX package
documentation (http://www.ctan.org/pkg/mhchem).
Please note that there are still major issues (https://phabricator.wikimedia.org/T140217) with mhchem support in MediaWiki.
Molecular and Condensed formula
mhchem {{chem}} Equivalent
HTML
Markup Renders as
<ce>H2O</ce>
<ce>Sb2O3</ce>
<ce>(NH4)2S</ce>
Bonds
D. Dislaying Math Expressions
135
mhchem
Equivalent
{{chem}}
and
HTML
Markup Renders as
<ce>C6H5-CHO</ce>
<ce>A-B=C{\equiv}D</ce>
Charges
mhchem {{chem}} Equivalent
HTML
Markup Renders as
<ce>H+</ce>
<ce>NO3-</ce>
<ce>CrO4^2-</ce>
<ce>AgCl2-</ce>
<ce>[AgCl2]-</ce>
<ce>Y^{99}+</ce>
<ce>Y^{99+}</ce>
Addition Compounds and Stoichiometric Numbers
mhchem {{chem}}
Markup Renders as
<ce>MgSO4.7H2O</ce>
<ce>KCr(SO4)2*12H2O</ce>
<ce>{CaSO4.1/2H2O} + 1\!1/2H2O -> CaSO4.2H2O</ce>
<ce>{25/2O2} + C8H18 -> {8CO2} + 9H2O</ce>
(Italic) Math
D. Dislaying Math Expressions
136
mhchem
Markup <ce>{C_\mathit{x}H_\mathit{y}} + \mathit{z}O2 -> {\mathit{x}CO2} + \frac{\mathit{y}}{2}H2O</ce>
Renders
as
{{chem}}
Markup {{chem|C|''x''|H|''y''}} + ''z''{{chem|O|2}} &rarr; ''x''{{chem|C|O|2}} + {{frac|''y''|2}}
{{chem|H|2|O}}
Renders
as
CxHy + zO2 → xCO2 + y⁄2H2O
Oxidation States
mhchem
Markup <ce>Fe^{II}Fe^{III}2O4</ce>
Renders
as
{{chem}} with
<sup>...</sup>
Markup {{chem|Fe|<sup>II</sup>|Fe|<sup>III</sup>|2|O|4}}
Renders
as
FeIIFeIII2O4
Greek characters
mhchem
Equivalent
{{chem}}
and
HTML
Markup Renders as
<ce>\mu-Cl</ce>
<ce>[Fe(\eta^5-C5H5)2]</ce>
Isotopes
mhchem
Equivalent
{{chem}}
and
HTML
Markup Renders as
<ce>^{227}_{90}Th+</ce>
<ce>^0_{-1}n-</ce>
States
States Subscripting is not IUPAC recommendation.
D. Dislaying Math Expressions
137
mhchem {{chem}}
Markup Renders as
<ce>H2_{(aq)}</ce>
<ce>CO3^{2-}{(aq)}</ce>
Precipitate
mhchem
Markup <ce>{Ba^2+} + SO4^{2-} -> BaSO4 v</ce>
Renders
as
{{chem}}
Markup {{chem|Ba|2+}} + {{chem|S|O|4|2-}} &rarr; {{chem|Ba|S|O|4}}&darr;
Renders
as
Ba2+ + SO2−
4 → BaSO4↓
Equivalent HTML
Markup Ba<sup>2+</sup> + SO<sub>4</sub><sup>2-</sup>&rarr; BaSO<sub>4</sub>&darr;
Renders
as
Ba2+ + SO42- → BaSO4↓
Reaction Arrows
Markup Renders as
<ce>A ->[x] B</ce>
<ce>A ->[\text{text
above}][\text{text
below}] B</ce>
<ce>A ->[\ce{+H2O}]
B</ce>
Comparison of arrow symbols
Markup Renders as
<math>\rightarrow</math>
<math>\rightleftarrows</math>
<math>\rightleftharpoons</math>
<math>\leftrightarrow</math>
<math>\longrightarrow</math>
<ce>-></ce>
<ce><=></ce>
D. Dislaying Math Expressions
138
<math>\longleftrightarrow</math>
<ce><-></ce>
Further Examples Using Ordinary LaTeX tags
<math chem>\begin{align}
\ce{\overbrace{2Fe3O4}^{magnetite} + {1/2O2} ->}\ &{\color{Brown}\ce{\overbrace{3(\lambda-Fe2O3)}^{maghemite}}}\\
\ce{\underbrace{2Fe3O4}_{magnetite} + {1/2O2} ->}\ &{\color{Red}\ce{\underbrace{3(\alpha-Fe2O3)}_{hematite}}}
\end{align}</math>
To align the equations or color them, use <math chem> and \ce.
Examples of implemented TeX formulas
Quadratic polynomial
Markup <math>ax^2 + bx + c = 0</math>
Renders as
Quadratic formula
Markup <math>x={-b\pm\sqrt{b^2-4ac}\over 2a}</math>
Renders as
Tall parentheses and fractions
Markup <math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x}\right)</math>
Renders as
Markup <math>S_{\text{new}} = S_{\text{old}} - \frac{\left( 5-T \right) ^2} {2}</math>
Renders as
Integrals
Markup <math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>
Renders as
Markup <math>\int_e^{\infty}\frac 1{t(\ln t)^2}dt={\frac{-1}{\ln t}\,\Bigg\vert\,}_e^\infty=1</math>
Renders as
Matrices and determinants
Markup <math>\det(\mathsf{A}-\lambda\mathsf{I}) = 0</math>
Renders as
D. Dislaying Math Expressions
139
Summation
Markup <math>\sum_{i=0}^{n-1} i</math>
Renders as
Markup <math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}</math>
Renders as
Differential equation
Markup <math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>
Renders as
Complex numbers
Markup <math>|\bar{z}| = |z|,
|(\bar{z})^n| = |z|^n,
\arg(z^n) = n \arg(z)</math>
Renders as
Limits
Markup <math>\lim_{z\to z_0} f(z)=f(z_0)</math>
Renders as
Integral equation
Markup <math>\phi_n(\kappa) =
\frac{1}{4\pi^2\kappa^2}\int_0^\infty
\frac{\sin(\kappa R)}{\kappa R}
\frac{\partial}{\partial R}
\left [ R^2\frac{\partial D_n(R)}{\partial R}\right ] \,dR</math>
Renders as
Example
Markup <math>\phi_n(\kappa) =
0.033C_n^2\kappa^{-11/3},\quad
\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>
Renders as
Continuation and cases
Markup <math>
f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
D. Dislaying Math Expressions
140
1 - x^2 &\text{otherwise}
\end{cases}
</math>
Renders as
Prefixed subscript
Markup <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
= \sum_{n=0}^\infty
\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
\frac{z^n}{n!}</math>
Renders as
Fraction and small fraction
Markup <math>\frac{a}{b}\ \tfrac{a}{b}</math>
Renders as
Area of a quadrilateral
Markup <math>S=dD\,\sin\alpha\!</math>
Renders as
Volume of a sphere-stand
Markup <math> V = \frac 16 \pi h \left [ 3 \left ( r_1^2 + r_2^2 \right ) + h^2 \right ] </math>
Renders as
Multiple equations
Markup <math>\begin{align}
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
\end{align}</math>
Renders as
See also
Typesetting of mathematical formulae
Help:Score (a tag for tablatures, "sheet music") and Help:Musical symbols
Table of mathematical symbols
Wikipedia:Rendering math
mw:Extension:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
commons:Category:Images which should use TeX
References
Footnotes
D. Dislaying Math Expressions
141
Wikibooks has a book on
the topic of: LaTeX
Although, in all cases mentioned, TeX is generated by compilation, and not by an interpreter program, there is one essential difference
between, e.g., Knuth's TeX or Lamport's LaTeX and the present implementation: whereas in the first two cases the compiler typically
generates an all-in-one printable output, which has the quality of a whole book with all chapters, sections and subsections, and where
no line is "special", in the present case one has, typically, a mixture of TeX images (more precisely: PNG images) for the equations,
embedded into usual text, and with short TeX elements usually replaced by HTML parts. As a consequence, in many cases
TeX-elements, e.g. vector symbols, "stick out" below (or above) the text line. This "sticking out" is not the case in the above-
mentioned original products, and the HTML-substitutes for small TeX additions to the text are often insufficient in quality for many
readers. In spite of these shortcomings, the present product characterized by "many embedded PNG-images" should be preferred for
small texts, where the equations do not dominate.
a.
This can cause difficulty with setting the baseline as vertical alignment with the surrounding text can also be a problem (see bug
32694)
b.
Citations
J. A. Wheeler; C. Misner; K. S. Thorne (1973). Gravitation (2nd ed.). W. H. Freeman & Co. ISBN 0-7167-0344-0.1.
External links
A LaTeX tutorial (http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/)
LaTex online editor (http://www.codecogs.com/latex/eqneditor.php)
Doob, Michael, A Gentle Introduction to TeX: A Manual for Self-study (PDF). A
paper introducing TeX — see page 39 onwards for a good introduction to the maths side of things.
Oetiker, Tobias; Partl, Hubert; Hyna, Irene; Schlegl, Elisabeth (December 13, 2009), The Not So Short Introduction to
LaTeX 2ε(PDF) (4.27 ed.). A paper introducing LaTeX — skip to page 49 for the math section. See page 63 for a
complete reference list of symbols included in LaTeX and AMS-LaTeX.
The Comprehensive LaTeX Symbol List (http://tug.ctan.org/tex-archive/info/symbols/comprehensive/symbols-letter.pdf)
—symbols not found here may be documented there.
Long list of many symbols (http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-a4.pdf)
short list of common symbols (http://amath.colorado.edu/documentation/LaTeX/Symbols.pdf)
The esint package for closed double integrals (http://milde.users.sourceforge.net/LUCR/Math/mathpackages/esint-
symbols.pdf)
The esint package for closed double integrals (http://mirror.ox.ac.uk/sites/ctan.org/macros/latex/contrib/esint/esint.pdf)
cancel package homepage (http://www.ctan.org/pkg/cancel) and PDF documentation (http://mirrors.ctan.org/macros
/latex/contrib/cancel/cancel.pdf)
AMS-LaTeX guide (http://www.ams.org/tex/amslatex.html).
A set of public domain fixed-size math symbol bitmaps (http://us.metamath.org/symbols/symbols.html).
List of mathematical symbols with their Unicode characters and their LaTeX commands
(http://milde.users.sourceforge.net/LUCR/Math/unimathsymbols.xhtml)
MathML: A product of the W3C Math working group (http://www.w3.org/Math/), is a low-level specification for
describing mathematics as a basis for machine to machine communication.
Wikipedia help pages
Visit the Teahouse if you are a new editor looking for interactive help, or the Help desk for an interactive Q & A forum.
Noticeboards (?) · FAQs (?) · Reference desks (?) · The Missing Manual (?) · Directories (?)
About Wikipedia
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Avoiding common mistakes · Etiquette (community expectations) · Learning the ropes · Instructional material ·
Simplified Manual of Style · Simplified rule-set ("Ignore all rules" · "The rules are principles") · Style-tips ·
Tip of the day · Job Center · Your first article (article wizard) · Vandalism
Getting started
Wikipedia intro · Wikipedia tutorial · The Wikipedia Adventure · Newcomers' training ·
New contributors' help page · Manual of Style intro · Graphics tutorials · Picture tutorial (Uploading intro) ·
IRC (live chat) tutorial · Navigating intro · Policies intro · Referencing intro · Tables intro · Talk pages intro ·
VisualEditor user guide
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Email confirmation · Find sources · Files · Footnotes · Image deletion · Infoboxes · Linking (link color) ·
Logging in · Merging · Namespaces · Page name · Redirect · Renaming pages · Passwords · Reverting ·
Talk pages (archiving) · URL · User contributions · User page design center
D. Dislaying Math Expressions
142
Coding wiki markup
Wiki markup (cheatsheet) · Barcharts · Calculations · Characters · Citation templates · Columns · HTML · Lists ·
Magic words (introduction) · Music symbols · Sections · Sounds · Tables (introduction) · Templates
(documentation · messages (cleanup messages) ) · Transclusion · Visual files · Wiki tools
Directories Abbreviations · Departments · Editor's index · Essays · FAQs · Glossary · Guidelines · Help menu ·
Manual of Style · Policies · Shortcuts · Tips
Wikipedia technical help
Get personal technical help at the Teahouse, Help desk, Village pump (technical), talk pages or IRC.
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Mobile access · Printing · Keyboard shortcuts · Editing · Edit toolbar (CharInsert) · Edit conflict ·
VisualEditor (User guide) · Create a page · Page history · Reverting · Page name (Introduction) ·
User access levels · Editnotice · IRC (Tutorial)
Special page related
Special page help · Searching (Advanced search) · Logging in (Reset passwords) · Notifications/Echo (FAQ) ·
Moving a page (Fix cut-and-paste moves) · Watching pages · User contributions · Emailing users ·
Random pages · Logs · What links here · Related changes · Recent changes · Pending changes · Page Curation
· Linksearch · Page import · Edit filter
Wiki markup
Wiki markup main page (Cheatsheet) · Colours use · Columns · Line-break handling · Lists · Magic words
(For beginners · Conditional expressions · Switch parser function · Time function) · Redirects ·
Sections and TOCs · Tables (Introduction · Basics · Conditional tables · Sorting · Collapsing ·
Advanced table formatting)
Links and diffs
URLs · Links · Permanent link · Interwikimedia links · Interlanguage links · Link color · Pipe trick ·
Colon trick · Magic links · Diffs (Simplest diff guide · Simple diff and link guide ·
Complete diff and link guide)
Media files: images,
videos and sounds
Media help · Options to hide an image · Uploading images (Introduction) · Files (Creation and usage ·
Moving files to Commons) · Visual file markup · Images (Preparing images for upload · Picture tutorial ·
Extended image syntax) · Gallery tag · Graphics tutorials (Basic bitmap image editing ·
How to improve image quality) · Graphics Lab resources · Sound file markup · SVG help
Other graphics
Family trees · Graphs and charts (How to create · To scale charts · Barcharts) · Math formula (Math symbols
· Rendering math · LaTeX symbols) · Musical scores (Musical symbols) · Timeline (EasyTimeline syntax) ·
WikiHiero syntax
Templates
and Lua modules
Templates · Template messages · Citation templates · Transclusion (Labeled section) · Substitution ·
Advanced template coding · Template limits · Template sandbox and test cases · Template documentation ·
Purge · Lua help · Lua project (To do · Resources) · Guide to Scribbling
Namespaces
Main/Article · Talk namespaces (Archiving) · User (User page design) · Project/Wikipedia · File · MediaWiki
(Bug reports and feature requests) · Template · Help · Category · Portal · Book · Draft · Education Program ·
TimedText · Module/Lua · Topic/Flow · Special · Media
HTML and CSS HTML in wikitext · Markup validation · Span tags · Cascading Style Sheets · Catalogue of CSS classes ·
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Techniques) · IRC Scripts · User styles · Tools (Navigation shortcuts · Browser tools · Alternative browsing ·
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Relevant navigation Help pages (Administrators) · Templates · Referencing (Citation metadata) · Accessibility · Bots · User scripts
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D. Dislaying Math Expressions
143
Appendix E
IEEE EDITORIAL STYLE MANUAL
144
IEEE EDITORIAL STYLE MANUAL
IEEE Periodicals
Transactions/Journals Department
445 Hoes Lane
Piscataway, NJ 08854 USA
V8 10-30-2014
© 2014 IEEE
E. IEEE Editorial Style Manual
145
1
TABLE OF CONTENTS
I. Introduction 3
A. Purpose of Manual 3
B. IEEE Transactions Editing Philosophy 3
C. Different Models of Editing 3
D. Preprinting 3
E. Rapid Posting 4
F. Continuous Pagination 4
Print Collections
Index of Contents
Blanks and Announcements
G. Article Numbering 4
H. Public Access 4
I. Open Access 4
J. Creative Commons Attribution 5
II. Editing Principles 6
A. Editing the Parts of a Paper 6
Paper Title
Byline and Membership Citation
IEEE Membership Grades
Invited Paper Line
Running Heads
Copyright Lines
Open Access
1) OAPA; 2) CC BY
First Footnote
B. Editing the Body of a Paper 13
Abstract
Index Terms
Nomenclature
Text Section Headings
Introduction
Text Equations
Appendix
Acknowledgment
References
Text Citation of Figures and Tables
Republished graphics
Biographies
Squibs
D. Other Text to Edit 19
Footnotes
Lists in Text
Note Added in Proof
E. Other Types of Papers 20
Editorials
Brief Papers
Short Papers, Correspondence, and
Communications
Comments and Replies
Corrections
Book Reviews
Obituaries/In Memoriam
F. Editing Style for Transactions 22
Acronyms
Spelling
Trademarks
Plurals
Hyphenation Rules
The En, Em, or Two-Em Dash
Grammar
Contractions
Capitalization
Math
Equation Numbers
Displayed Equations
Typical Problems
G. General Layout Rules 26
III. Grammar and Usage in Transactions 27
A. Rules of Grammar 27
B. Words Often Confused 27
IV. Editing Mathematics 29
A. The Language of Math 29
B. In-Line Equations and Expressions 29
C. Break/Alignment Rules 30
D. Exceptions and Oddities 30
E. Headings for Theorems , proofs , and
Postulates 31
F. Text Equations 31
G. Reminders 31
H. Short references List of Italics , Roman , and
Small Capitals 32
I. Functions and Operators Always Set in Roman
Font 32
J. Glossary 33
K. The Greek Alphabet 33
V. Editing References 34
A. Citing References 34
B. Style 34
Periodicals
Books
Reports
Handbooks
Published Conference Proceedings
Papers Presented at Conferences
Patents
Theses (M.S.) and Dissertations (Ph.D.)
Unpublished
Standards
C. On-Line Sources 38
Books, Monographs
Periodicals
Papers Presented at Conferences
Reports and Handbooks
U.S. Government Documents
Patents
Manuals/Software
E. IEEE Editorial Style Manual
146
IEEE EDITORIAL STYLE MANUAL
2
D. Common Abbreviations of Words in
References 40
E. IEEE Transactions, Journals, and Letters
Abbreviations 43
F. IEEE Magazines Abbreviations 48
VI. Appendix 49
Some Common Acronyms and Abbreviations 49
E. IEEE Editorial Style Manual
147
E. IEEE Editorial Style Manual
148
IEEE EDITORIAL STYLE MANUAL
3
I. INTRODUCTION
A. Purpose of Manual
This style manual provides general editing guidelines for IEEE Transactions, Journals, and Letters. For guidance
in grammar and usage notincluded in this manual, please consult The Chicago Manual of Style, published by the
University of Chicago Press.
B. IEEE Transactions Editing Philosophy
The IEEE’s responsibility in editing papers for the Transactions is not to make any determination on or do any
editing of the technical content of the papers we work with, but is instead to render the work as readable,
grammatically correct, and as consistent with IEEE style as possible.
Since we are concerned with the IEEE house style, the author’s style of writing is not changed. A mechanical
edit to correct or question grammatical errors is done, obvious inconsistencies or omissions, spelling, and
punctuation are fixed. Since we work with highly technical text, extensive formatting of mathematical material is
also done.
Some manuscripts require closer editing than others. Some papers, for example, are from authors unfamiliar with
the English language. Authors with questions or requiring assistance with the English language may visit
http://www.ieee.org/publications_standards/publications/authors/authors_journals.html. Often, an IEEE Staff Editor
must determine how to correct a grammatical error or in decide what can be safely changed or corrected without
altering the author’s original meaning. Because of the highly technical nature of the material we deal with, and
because of our often limited understanding of that material, it is especially important that Staff Editors do not risk
making any unnecessary changes or any that may affect the author’s meaning.
Sometimes there are cases where it is simply not possible to decipher an author’s meaning or to find a way to
correct a sentence. In these cases, a judgment is made either to query the author on the proof about the passage in
question, to directly contact the author, or in rare cases, to work with the Transactions Editor or Guest Editor to
clarify the material.
C. Different Models of Editing
There are several different models of editing.
• Fully edited articles: These papers are edited and follow the IEEE Transactions/Journal style.
• Moderately edited articles: These articles are minimally edited. The abstract, first footnote, figure captions, and
biographies are edited to style. The references are checked for accuracy and completion.
Excludes:
– Editing text for grammar, punctuation, spelling or style
Includes Editing of:
– Abstracts
– Bios
– Callouts & art captions
Ensures accuracy of:
– Article metadata
– Automated spell check
– Reference validation
Also includes:
– Author proofs & alterations
D. Preprinting (Pre-edit Rapid Posting)
Preprinting is a term used to define the process of posting an author-submitted PDF of his/her manuscript online on
the IEEEXplore site. This is done within a day or two of receipt at the IEEE. The author is required to include a
signed copyright form with their submission package. If the form is not provided, the paper cannot be preprinted. On
Xplore, it appears under “Early Access.” This version of the paper has been accepted for publication by IEEE, but
E. IEEE Editorial Style Manual
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IEEE EDITORIAL STYLE MANUAL
4
has not yet been edited and may not have been assigned to a print issue. A paper that has been preprinted is
considered published.
E. Rapid Posting (Post-edit Rapid Posting)
Rapid Posting is a term used to define the process of posting the author-approved edited version online. This is done
within 3 weeks of receipt at the IEEE for a fully edited article, and within 2 weeks of receipt for a moderately edited
article (see section I-C for explanation). The running head will contain only the publication title. The page numbers
would contain generic numbers (e.g., 1 – 10). On IEEEXplore, the article appears under “Early Access” till it is
assigned to an issue. Once the article is assigned to a print issue, the article is paginated, and the running head is
“opened up” and will contain the volume, issue, month , and year.
F. Continuous Pagination
In a continuously paginated journal, each individual article goes through the entire workflow process, is assigned an
issue, real-time page numbers, and finally posted to Xplore at the issue level. These articles may already be either
pre-printed or rapid posted, not both. Note: Once the paginated article is on Xplore, no changes to the content or
page layout may occur.
The running head should not indicate a month till the very end of the process. (Note to staff: The <proddate> tags
for “first publication and current version…” are suppressed till author review, and unsupressed prior to final posting
to Xplore.)
• Print Collections — In addition, several journals have Print Collections. A print collection is a literal
collection of online issues collected into one print edition. For this reason, additional concerns must be
taken into considering when paginating. Each online issue will contain an Index of Contents listing of the
papers in the issue. Due to postal requirements, in a print collection, a blank page MUST precede the Index
of Contents in subsequent issues. The first article must begin on a verso page. Therefore, if the last page of
one print collection ends on an even number (left-hand side), TWO blank pages must be left in order to
start the next issue on the right-hand side.
• In Print Collections, the front cover will contain information reflecting the pages on which the Index of
Contents will appear in each issue. Staff may refer to the “Table of Contents (ToC)” section for more
information.
• Some publications may also choose to include a graphic on the front cover. Staff may refer to the ToC
section for more detail.
G. Article Numbering
Article numbers are applied under the continuous pagination model. The articles are assigned article numbers and
are final prior to being posted to Xplore in the appropriate issue in which they are to appear . In the 7-digit article
number, the first two digits within the subject category, the following three digits are the sequence number (for the
year), and the last two are the page count. Example: 5701712
H. Public Access
If the government agency that funded this paper requires that the paper be deposited in an institutional repository in
order to be made publicly available (there is not a consistent policy among government agencies), the author should
comply with the requirement and submit the paper. We will send the author the paper as accepted for publication, in
PDF format through the Author Gateway, once the paper has been finalized. This is the version the author should
submit to the institutional repository. IEEE requires that the paper not be deposited before 12 months from the date
of publication of the paper, unless the agency policy is different.
I. Open Access
Open access (OA) means unrestricted online access to peer-reviewed scholarly research. There are two ways to
make an article openly available: 1) through author self-archiving in an OA repository, also known as 'green' OA, or
2) through publishing in an open access journal, known as 'gold' OA.
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IEEE EDITORIAL STYLE MANUAL
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With green OA, authors publish in any journal and then self-archive a version of the article for gratis public use on
the author’s personal web site, on a server operated by the author’s employer, or on a server operated by an
approved not-for-profit third party. IEEE allows its authors to follow mandates of agencies that fund the author’s
research by posting accepted versions of their articles in the agencies’ publicly accessible repositories.
With gold OA, authors publish in Open Access journals, which provide immediate, free access to all of their
articles, usually on the publisher's website. ("Hybrid" gold OA journals are subscription journals that provide gold
open access only for those individual articles for which their authors (or their author's institution or funder) pay an
article processing charge.
J. Creative Commons Attribution (CC BY)
Some funding agencies require that authors use specific publication licenses in place of a traditional copyright
transfer if a portion of their grants are to be used to pay article processing charges (APCs). Two such funding
agencies are the Wellcome Trust and the Research Councils of the United Kingdom (RCUK), both of which require
authors to use the CC BY license. In addition, some authors whose work has not been supported by such funding
agencies also want to use the CC BY license. In either case, these authors should explicitly declare their interest in
having their papers published under a CC BY license to IEEE staff editors upon submitting their manuscripts.
Interested authors may also e-mail a request to copyrights@ieee.org. The e-mail should declare the author(s) interest
in submitting their manuscripts under a CC BY license and should also provide basic information about the
manuscript (e.g., author names, article title and IEEE publication title to which the manuscript is being submitted).
Authors who need to satisfy their funding agency’s specific requirement(s) should also identify the specific agency.
The IEEE IPR Office will respond with an acceptance letter indicating that the use of the CC BY license has been
approved.
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II. EDITING PRINCIPLES
The sections of a paper should generally be edited in the following order:
1) Title Page (including paper title, byline, membership, first footnote including Digital Object Identifier (DOI)
information, running head, and copyright line)
2) Abstract, must be one paragraph, and no more than 250 words. A minimum of 150 words are suggested, but not
mandatory.
3) Index Terms
4) Nomenclature (optional)
5) Introduction
6) Body of Paper
7) Conclusion
8) Appendix(es)
9) Acknowledgment
10) References
11) Figure and Table Captions
12) Photos and Biographies
A. Editing the Parts of a Paper
Paper Title
In the paper title, capitalize the first letter of the first and last word and all nouns, pronouns, adjectives, verbs,
adverbs, and subordinating conjunctions (If, Because, That, Which). Capitalize abbreviations that are otherwise
lower case (i.e., use DC, not dc or Dc) except for unit abbreviations and acronyms. Articles (a, an, the), coordinating
conjunctions (and, but, for, or, nor), and most short prepositions are lower case unless they are the first or last word.
Prepositions of more than three letters (Before, Through, With, Versus, Among, Under, Between, Without.) should be
capitalized. Example:
• Nonlinear Gain Coefficients in Semiconductor Lasers: Effects of Carrier Heating
• Self-Pulsation in an InGaN Laser
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Part I: Theory and Experiment
Byline and Membership Citation
Check authors’ names against biographies and editorial correspondence (compare to IEEE Membership
Directory listing if necessary). Use the longest and most complete name given in either the biography or byline. Use
the same information in both places. Always defer to the author’s wishes if changes are made in the proof stage.
Nicknames are not allowed in the byline, but may be included in the biography. Examples:
C.-Y. Chen, Member, IEEE, K. S. Snyder, Jr., Fellow, IEEE,
and J. Fortunato, III, Senior Member, IEEE
Mohammed Z. Ali, Member, IEEE, and Murat Torlak, Fellow, IEEE
Check the manuscript byline and biographies to see if IEEE membership information has been provided by the
author. If so, verify the information in the IEEE Membership Directory and enter it into the byline and into the
biography.
IEEE Membership Grades
Student Member, Graduate Student Member, Associate Member, Member, Senior Member, Fellow, Life
Associate Member, Life Member, Life Senior Member, and Life Fellow. The highest grades other than Affiliate
Members are listed in the byline. All grades are listed in the biography. Life Members carry the highest previous
grade in their byline.
NOTE: Affiliate Members are not considered members for the purposes of the byline and biography. An
affiliate of an IEEE Society is not an IEEE member, but rather an individual who has been admitted by a
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Society with the special rights and privileges of that particular organization within the IEEE. In general, an
affiliate must have attained stature in a related scientific and technical field, comparable to that for IEEE
membership.
Invited Paper
If the EIC notes that a paper is an Invited Paper either directly on the hard copy, on the table of contents, or
elsewhere, use an Invited Paper line between the byline and the text of the paper. Insert a 12-pt. space between the
byline and the words “(Invited Paper).” Also be sure to include the Invited Paper line directly after the title on the
table of contents. Example in a byline:
Shadow Codes and Weight Enumerators
Steven T. Dougherty, Fellow, IEEE
(Invited Paper)
Example in a table of contents:
Shadow Codes and Weight Enumerators (Invited Paper) ...................S. T. Dougherty 24
Running Heads
Transactions contain two types of running heads: issue and author. Running heads appear in 7-pt. capitals.
Issue Running Heads appear on all left-hand (verso) pages of full length papers, on all first pages of full length
papers, and on both left and right pages of all other types of papers. Issue running heads consist of the full name of
the Transactions, volume number, issue number, month, and year. Note that the volume number of a Transactions
increases by one at the start of every calendar year. The format used is as follows:
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 23, NO. 3, MARCH 2014
Author Running Heads appear on all right-hand (recto) pages of full length papers (except the first page of
papers). The author running heads are written by Staff Editors and should appear on the author’s proof. Guidelines
for writing author running heads are as follows.
• Use only the most important words; it should be the gist of the title.
• For a very long title, try to find the critical phrase or phrases.
• Frequently, it is possible to eliminate adjectives completely.
• If units of measure, chemical compounds, mathematical terms, etc., must be included in the running head,
stet the use of lower case as determined by IEEE style.
• Use 7-pt. caps for all author names, e.g., SMITH, DIBENEDETTO, MCLEAN
• Do not include Jr., Sr., III, etc., in running heads.
• Do not exceed one line.
The format used for author running heads is as follows:
For one author:
SPINA: MODELING OF HIGHLY EFFICIENT GRATING FEEDBACK
For two authors:
BONIFAS AND RICCARDELLA: DYNAMICS OF AlGaAs SEMICONDUCTOR LASERS
MACGREGOR AND GROVER: ROUTING OF TRANSPORT NETWORK DEMANDS
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I
Note: Parts, e.g., part I, is written only as “I” in the running head, preceded by an emdash. The subtitle is not
included.
For three or more authors: ANDERSEN et al.: DYNAMICAL MODEL OF DC WAVEGUIDE LASERS
Copyright Lines
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Authors of non-OA articles must sign and return the IEEE Copyright Form before their paper is published (either
online or in print). A paper is considered published on the date it appears on IEEEXplore (this includes pre-prints,
rapid posts). The section of the form signed determines the type of copyright line used.
There are several different types of copyright lines used in Transactions papers.
The IEEE copyright line is by far the most commonly used line. The IEEE copyright line Copyright Clearance
Center Code (or CCC code) is used at all times whenever the “A” section of the IEEE copyright form has been
signed by the author. The author’s signature on the “A” section of the IEEE copyright form and use of the IEEE
copyright line indicate IEEE ownership of the paper’s copyright.
The following is a sample IEEE copyright line from the IEEE JOURNAL OF QUANTUM ELECTRONICS:
0018-9197 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
The first two sets of four numbers (separated by an hyphen) in the line are the ISSN code for the Transactions
(also found on the front cover of the printed book). (Note: the price information was omitted in 2013. This appeared
before the copyright symbol representing the amount the IEEE charges per copy when permission is granted to use
IEEE copyrighted material.) Last on the line is a circled copyright symbol followed by the full year of publication
and the identifier “IEEE.”
Other types of lines may be used when certain conditions are met.
The U.S. Government copyright line is used when the “B” section of the copyright form is signed and all the
authors of a paper are U.S. government employees and prepared the paper as part of their job. The U.S. Government
line reads:
U.S. Government work not protected by U.S. copyright.
NOTE: This copyright line ends with a period.
The EU copyright line is used when all authors are employed by one or more European Union organizations.
The following is a sample EU copyright line from the IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY:
1051-8223 © 2014 EU
The Crown Copyright line is used when the “C” section of the copyright form is signed and all the authors of a
paper are employees of the British or British Commonwealth governments. The Crown Copyright line is similar to
the IEEE copyright line, except that the “IEEE” at the end of the line is replaced with “British Crown Copyright” or
“Canadian Crown Copyright” as follows:
The following sample copyright lines are from the IEEE JOURNAL OF DISPLAY TECHNOLOGY:
1551-319X © 2014 British Crown Copyright
1551-319X © 2013 Canadian Crown Copyright
Rapid posted/pre-printed papers: If you are posting papers in 2013 for a print issue in 2014, please note the
year in the copyright line MUST be the year of online publication. Also, note the copyright line (year) information
will NOT change when the article is printed in 2014.
Note this applies to all models of publication, rapid post, preprint, and continuous (e.g., JSEN, JQE, LPT).
That is, rapid-posted , preprinted, or continuously paginated articles that posted to IEEEXplore in 2013,
but will be printed in 2014, should carry a copyright year of 2013.
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Open Access
http://www.ieee.org/publications_standards/publications/rights/oapa.pdf
Q: Do authors need to sign an IEEE copyright transfer form for an OA article?
Not in every case. The standard document for an author to authorize publication of an article supported by an article
processing charge (APC) is the IEEE Open Access Publishing Agreement (OAPA). This form transfers copyright to
IEEE, while assuring that IEEE will make the article freely available to all visitors to IEEE Xplore. The OAPA gives
IEEE full authority to resolve any complaints of abuse (such as plagiarism) of the authors' content.
IEEE will make exceptions for authors who have special requirements from their funding agencies to publish their
OA articles with a Creative Commons Attribution (CC BY) license. Two such funding agencies are the Wellcome
Trust and the Research Councils of the United Kingdom (RCUK), both of which require authors to use the CC BY
license. IEEE will accept use of the CC BY license in these cases. Authors with a funding requirement to use the CC
BY license should not sign the OACF, but instead should request a CC BY license.
Q: What if the authors choose both OAPA and are also US Government employees? Which copyright form do they
sign?
ANS: Section (2) of the OAPA copyright form.
How do an author obtain the Creative Commons Attribution (CC BY) license?
Authors who choose to submit their manuscripts under a CC BY license, or whose research has been supported by
any funding agency and are required to submit their manuscripts under a CC BY license, will need to provide a letter
or e-mail to the editorial staff or the IEEE Intellectual Property Rights Office, in which they must clearly state their
interest in submitting their manuscript under a CC BY license. The letter must also provide basic information about
the manuscript (e.g., author names, article title, and IEEE publication title to which the manuscript is being
submitted). Authors will receive an acceptance letter indicating that the CC BY license has been approved.
Authors who submit a manuscript and opt for a CC BY license are required to accept the Terms & Conditions of
IEEE in order for their paper to be published and posted in IEEE Xplore. Authors who choose to submit under a CC
BY license will be subject to the publishing policies and procedures of IEEE.
The IEEE Open Access Publishing Agreement (OAPA)
With the OA publication model comes a new IEEE Open Access Publishing Agreement, which is available for
immediate use. The agreement serves four important purposes:
1. An explicit promise is made to OA authors that IEEE will present their work with free access to all users.
2. OA authors are assured that they are free to post the final, published version of their articles on their personal
Web sites, their employers' sites, or their funding agency's sites.
3. The OAPA gives IEEE sufficient legal rights to resolve any complaints of abuse (such as infringement and
plagiarism) of the authors’ content.
4. The OAPA allows users to copy the work, as well as to translate it or to reuse it for text/data mining, as long as
the usage is for non-commercial purposes.
IEEE authors who want to submit their manuscripts under an OA license are encouraged to use the IEEE OAPA.
Open Access copyright lines
OAPA:
1949-3029 © 2013 IEEE. Translations and content mining are permitted for academic research only. Personal use is
also permitted, but republication/redistribution requires IEEE permission. See
http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
U.S. Government + OAPA
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U.S. Government work not protected by U.S. copyright.
CCBY License:
This work is licensed under a Creative Commons Attribution 3.0 License. For more information,
see http://creativecommons.org/licenses/by/3.0/
First Footnote
The first footnote (or the author affiliation paragraph) is made up of three paragraphs. This footnote is not
numbered. All other footnotes in the paper are numbered consecutively. Do not use asterisks or daggers.
An example follows:
Manuscript received April 27, 2012; revised September 18, 2012; accepted July 25, 2013. Date of publication August 15, 2013; date of
current version September 09, 2013. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS
UEFISCDI, under Project PN-II-ID-PCE-2011-3-0566.
The authors are with the National Institute for Lasers, Plasma and Radiation Physics, Plasma Physics and Nuclear Fusion Laboratory,
077125 Bucharest-Magurele, Romania (e-mail: florin.gherendi@infim.ro; mnistor@infim.ro; mandache@infim.ro).
Color versions of one or more of the figures are available online at http:// ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JDT.2013.2278036
The first paragraph of the first footnote contains the received and (possibly) revised dates, followed by the accepted
date of the paper. When a paper has more than one revised date, list all the dates given. Effective June 2008, it also
contains the two additional online published dates. The first date identifies the date of publication, i.e., when the
“single article” version is posted on Xplore (either preprint or rapid post—ePub date); the second date identifies
when the “final, paginated” version (date of current version—predicted online date) is posted on Xplore.
China-affiliated authors may request the name of the corresponding author to be listed in the first footnote. This is
added in italics at the very end of the first paragraph. See examples of various footnotes below.
Manuscript received May 2, 2011; revised September 9, 2011; accepted October 12, 2011. Date of publication November 29, 2011; date of
current version March 7, 2012. This work was supported by the National Basic Research Program (973 program) of China under Grant
2012CB619302 and Grant 2011CB301903, by the National High Technology Research and Development Program (863 program) of China under
Grant 2011AA03105, and by the Innovative Doctoral Student Training Program in Sun Yat-sen University. (Corresponding authors: Jessie Y. C.
Chen; Shiyuan Fan.)
Manuscript received April 27, 2012; revised September 18, 2012; accepted July 25, 2013. Date of current version September 09, 2013.
This work was supported by the UEFISCSU under Grant PN-II 65/01.10.2007 and Grant PN-II 331/01.10.2007. The associate editor coordinating
the review of this manuscript and approving it for publication was Prof. Vesa Valimaki. (Corresponding author: Jun Ming.)
Equally contributed authors: In some case, the authors may request credit be given to specific auhors who have
contributed equally to the work. This is added in italics at the very end of the first paragraph before the
corresponding author . See examples of various footnotes below.
Manuscript received May 2, 2011; revised September 9, 2011; accepted October 12, 2011. Date of publication November 29, 2011; date of
current version March 7, 2012. This work was supported by the National Basic Research Program (973 program) of China under Grant
2012CB619302 and Grant 2011CB301903, by the National High Technology Research and Development Program (863 program) of China under
Grant 2011AA03105, and by the Innovative Doctoral Student Training Program in Sun Yat-sen University. (Shanjin Fan and Shiyuan Fan
contributed equally to this work.) (Corresponding authors: Jessie Y. C. Chen; Shiyuan Fan.)
Examples (Traditional - articles not preprinted or rapid posted):
Manuscript received April 27, 2012; revised September 18, 2012; accepted July 25, 2013. Date of current version September 09, 2013.
This work was supported by the UEFISCSU under Grant PN-II 65/01.10.2007 and Grant PN-II 331/01.10.2007. The associate editor coordinating
the review of this manuscript and approving it for publication was Prof. Vesa Valimaki. (Corresponding author: J. Ming.)
Manuscript received June 10, 2014; revised July 29, 2014; accepted July 31, 2014. Date of publication August 29, 2014; date of current verson
October 2, 2014.
Note: There is only one final date. The “published” date here is acquired from IDAMS data.
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Examples (print collections (continuous)----articles published online (continuously) with pagination, e.g., LPT,
JQE:
Manuscript received April 27, 2012; revised September 18, 2012; accepted July 25, 2013. Date of publication August 15, 2013; date of current
version September 09, 2013. (Corresponding author: J. Ming.)
Examples (preprinted or rapid posted articles):
Manuscript received November 07, 2013; revised January 20, 2014; accepted February 09, 2014. Date of publication March 11, 2014; date of
current version April 29, 2014.
Manuscript received December 14, 2006; revised November 8, 2007 and February 8, 2008; accepted February 20, 2008. Date of publication
June 8, 2008; date of current version January 29, 2009.
Manuscript received June 10, 2014; revised July 29, 2014; accepted July 31, 2014. Date of publication August 29, 2014; date of current verson
October 2, 2014.
Manuscript received February 22, 2009; accepted March 3, 2009. Date of publication June 8, 2009; date of current version August 29, 2009.
Manuscript received January 15, 2013; revised April 10, 2013; accepted April 29, 2013. Manuscript received in final form on May 20, 2013.
Date of publication September 8, 2013; date of current version January 18, 2014.
In some Transactions, the Volunteer Associate Editor who processed the paper is listed next in the first paragraph,
and this is referred to as a “recommended line.” See specific Transactions for placement and wording. Some
examples are:
Manuscript received February 5, 2007; revised March 29, 2007; accepted March 29, 2007. Date of publication June 8, 2007; date of current
version January 18, 2008. Paper recommended by Associate Editor Thomas Lynch.
Manuscript received February 5, 2007; revised March 29, 2007. Date of publication June 8, 2007; date of current version January 18, 2008. This
paper was recommended by Associate Editor T. Lynch.
Manuscript received July 4, 2007; revised September 4, 2007. Date of publication June 8, 2007; date of current version July 18, 2008. This work
was supported by the UEFISCSU under Grant PN-II 65/01.10.2007 and Grant PN-II 331/01.10.2007. The associate editor coordinating the
review of this manuscript and approving it for publication was Prof. Vesa Valimaki. (Corresponding author: J. Ming.)
All financial support for the work in the paper is listed next in the first paragraph and not in the
Acknowledgment at the end of the paper. Examples of financial support acknowledgment are:
1) This work was supported by the National Science Foundation under Grant 90210 and Grant ECS-12345.
2) This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under
Contract 12345 and Contract 702589 and in part by the National Science Foundation.
3) This work was supported by grants from the Muscular Dystrophy Association of America and the Swedish
Medical Research Council.
4) If an author/organization requests specific wording, e.g., by National Institutes of Health (NIH), use language
provided.
If support was given to a specific author, the following wording is used:
The work of C. T. Walsh was supported by the National Institutes of Health.
Information of full or partial prior presentation of a paper at a conference may be included in the first paragraph
of the first footnote. It may not be necessary, however, to cite prior presentation of a paper at a conference if the
paper is appearing in a special issue made up exclusively of papers presented at the conference.
If a paper is a thesis or part of a thesis or dissertation, this should be so noted in the last sentence of the first
paragraph of the footnote.
Below is a sample of a first paragraph of the first footnote:
Manuscript received January 15, 2008; revised April 10, 2008; accepted April 29, 2008. Manuscript received in final form on May 20, 2008.
Date of publication September 8, 2008; date of current version January 18, 2009. This work was supported in part by the National Science
Foundation under Grant GK-716, by the Joint Services Electronics Program under Contract AF-AFOSR-128-94/95, and by the Adolph C. and
Mary Sprague Miller Institute for Basic Research in Science. This paper was presented in part at the Fourth (or 4th) Annual Allerton Conference
on Circuit and System Theory, University of Illinois, Urbana, IL, October 1995.
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The second paragraph of the first footnote is made up of the authors’ affiliations, and the corresponding author’s
email address. There are instances when several authors may want their email addresses included. E-mail addresses
are separated by semicolons. Examples are shown below.
.
For one author or if all authors have the same, or more than one affiliation:
The author is with the Department of Electrical Engineering, Rutgers University, Piscataway, NJ 08854 USA, and also with Bellcore,
Morristown, NJ 07960 USA (e-mail: author@ieee.org).
The author(s) is (are) with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139
USA (e-mail: corresponding-author@ieee.org).
K. Gong is with the Tsinghua National Laboratory, Beijing 10084, China, and also with Tianjin University, Tianjin, 300725, China (e-mail:
gongk@tsinghua.edu.cn).
The authors are with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA 02139 USA
(e-mail: firstauthor@mit.edu; IamNext@mit.org; thirdauthor@ieee.org).
Two or more authors: For two or more authors with different affiliations, use separate sentences and paragraphs
for each, using all initials with a surname. Group the authors with the same affiliation together; list the affiliations
according to the order of the first author listed in the byline for each location. Email addresses are separated by
semicolons. Examples:
L. P. Li is with the Department of Electrical Engineering and the Electronics Research Laboratory, University of California at Berkeley,
Berkeley, CA 94720 USA.
T. Ikeda and H. Ishikawa are with Fujitsu Laboratories Ltd., Atsugi, Kanagawa 243-01, Japan (e-mail:correspondingauthor@ieee.org).
The authors are with Fujitsu Laboratories Ltd., Atsugi, Kanagawa 243-01, Japan, and also with the Department of Electrical Engineering and the
Electronics Research Laboratory, University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: corresponding-author@ieee.org).
If an author had one affiliation at the time the paper was written and a new one at the time of publication, list the
information as follows:
The author was with the Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12181
USA. He is now with the Institute for Microstructural Sciences, National Research Council, Ottawa, ON K1A 0R6, Canada.
If an author is on leave from his current position, list the information as follows:
The author is with the Faculty of Information Sciences and Engineering, University of Canberra, Canberra, A.C.T. 2616, Australia, on leave
from the Department of Electronic Engineering, Zhengzhou University, Zhengzhou, China.
Additional Examples:
Retired author:
L. A. Tepper, retired, was with the Applied Research Laboratory, Bellcore, Morristown, NJ 07851 USA. He resides in Laguna Niguel, CA
92677 USA (e-mail: retiredauthor@yahoo.com).
Deceased author:
P. Dorigo, deceased, was with the Progetto di Intelligenza Artificiale e Robotica, Dipartimento di Elettronica e Informazione, Politecnico di
Milano, 20133 Milano, Italy.
Consultant:
P. Leff Jr. was with the Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908 USA. He resides in
Charlottesville, VA 22908 USA.
Additional Notes:
• Do not include street addresses of employers. For domestic authors, use official U.S. Postal Service
abbreviations for states and include U.S. zip codes, and country. Use Canadian Province and international
codes as listed in this manual. Also include international cities, countries, and zip codes.
• List department or subdivision first, then company or school. Write out the words “Company” and
“Corporation.” Abbreviate “Inc.” and “Ltd.” (One exception to this is Texas Instruments Incorporated.)
• At the request of some societies, most Transactions include e-mail addresses in the affiliation. The standard
usage of e-mail addresses is to list the address at the end of the affiliation line for that particular author.
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E-mail listing for one author:
R. A. Morgan is with the Department of Information Technology, Honeywell Corporation, Bloomington, MN 55420 USA (e-mail:
r.morgan@empire.honeywell.com
E-mail listing for more than one author:
H. Saidi and P. S. Min are with the Department of Electrical Engineering, Washington University, St. Louis, MO 63130 USA (e-mail:
saidi@rgit.wustl.edu; psm@ee.wustl.edu).
• In a book review, to avoid confusion with the author of a book, when listing the affiliation of the reviewer of
a book, do not use “The author is with …”; instead, list the reviewer’s affiliation (“The reviewer is with …”).
• Except in rare cases (e.g., IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING to indicate the corresponding
author), asterisks or daggers are not acceptable means of referencing a footnote in IEEE Transactions.
•
The third or final paragraph of the first footnote contains the Digital Object Identifier (DOI). (The DOI system m
was conceived by the Association of American Publishers (AAP) in partnership with the Corporation for National
Research Initiatives and is now administered by the International DOI Foundation. Essentially, the DOI system is a
scheme for Web page redirection by a central manager.) In January 2004, the IEEE adopted the use of the Digital
Object Identifier system to provide unique identification of documents and facilitate on-line publication. The
purpose of the DOI is to describe the structure and assignment of an identification code for publication items
(articles) within publication types (journals and books).
The DOI consists of the following:
• 10.1109 identifies IEEE Publication;
• the calendar year of the date of assignment;
• a number unique to the publication item within the publication type.
An example of the DOI as it appears in the first footnote is as follows:
Digital Object Identifier 10.1109/JQE.2004.834561
The DOI is the last line of the author affiliation paragraph.
NOTE: It is very important that this number appear correctly in print. It will be a permanent means of
identifying the document. If the printed DOI number does not match the database assigned DOI number, errors
will result when linking the electronic version of the document.
C. Editing the Body of the Paper
Abstract
Every published paper must contain an Abstract; request one immediately from the EIC and/or author if it is not
provided with the manuscript. Abstracts appear in text in 8-point boldface type per Transactions specs. All variables
should appear lightface italic; numbers and units will remain bold. Abstracts should be a single paragraph. By
nature, Abstracts shall not contain numbered mathematical equations nor numbered references. Numbered reference
citations are not allowed. If a citation is made, reword the sentence to exclude citation numbers.
In order for an abstract to be effective when displayed in IEEE Xplore® as well as through indexing services
such as Compendex, INSPEC, Medline, ProQuest, and Web of Science, it must be an accurate, stand-alone
reflection of the contents of the article.
The abstract must be a concise yet comprehensive reflection of what is in your article. In particular:
• The abstract must be self-contained, without abbreviations, footnotes, or references. It should be a
microcosm of the full article.
• The abstract must be between 150-250 words. Be sure that you adhere to these limits; otherwise, you will
need to edit your abstract accordingly.
• The abstract must be written as one paragraph, and should not contain displayed mathematical equations or
tabular material.
• The abstract should include three or four different keywords or phrases, as this will help readers to find it. It
is important to avoid over-repetition of such phrases as this can result in a page being rejected by search
engines.
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• Ensure that your abstract reads well and is grammatically correct.
Index Terms
All papers must contain Index Terms. These are keywords provided by the authors. Request them if they are not
provided. Index Terms appear in bold type in the same style as the Abstract, in alphabetical order, and as a final
paragraph of the Abstract section. Separate Abstract and Index Terms by a 6-pt. space. Capitalize the first word of
the Index Terms list; lower case the rest unless capitalized in text. Include the definition of an acronym followed by
the acronym in parentheses. Example:
Index Terms—Abstraction, computer-aided system engineering (CASE),
conceptual schema, data model, entity type hierarchy, ISO reference model, layered
architecture meta model, reverse engineering.
Note to Practitioners
This is formatted in the same style as Abstracts. It follows the Abstract and is separated by a line space.
There may be more than one paragraph. The text appears in boldface and in 8-point type. Example:
Note to Practitioners—Abstraction, computer-aided system engineering (CASE), conceptual schema, data model,
entity type hierarchy, ISO reference model, layered architectural meta model, reverse engineering.
Note Added in Proof: This added information is usually inserted at the end of the Conclusion section of the paper or in
whatever section contains the last paragraph of the main body of the paper. (See p. 18.)
Nomenclature
Nomenclature lists (lists of symbols and definitions) generally follow the Abstract and Index Terms and precede
the Introduction. This type of list is characterized by the following.
1) The Nomenclature heading is a primary heading without a Roman numeral.
2) The first column of the list is flush left.
3) The second column is aligned on the left.
4) There is one em space from the longest item on the left side to the right side.
5) The first letter on the right-hand side is capitalized.
6) Each item ends with a period.
7) Do not use “is” or “the” at the beginning of items.
8) Do not use equality symbols between the left and right sides.
Equations in an item should be handled as follows.
1) When the equation is at the beginning of an item, align the equal sign with the right-hand side capitals, end
the equation with a period, begin the definition with a capital, and end with a period.
2) When the equation is at the end of an item, end the definition with a comma, follow with an equal sign and
the rest of the equation, then end with a period.
NOMENCLATURE
SPQ
Strictly proper pole constraints.
M
Minimal weighted sensitivity.
P(s)
Physical feedback.
W
Weighting.
Q
= P – 1. Improper function.
S, l
Signal density, = P, M.
NOTE: Acronyms defined in a Nomenclature list do not need to be defined again in the text. If the section
headings are made up of only previously defined acronyms, we should continue to add the acronym in parentheses
next the the definition, as it becomes unreadable otherwise.
Text Section Headings
Standard specifications have been established for Transactions text section headings. There are four levels of
section headings with established specs: primary (section), secondary (subsect1), tertiary (subsect2), and quaternary
(subsect3) heads.
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Enumeration of section headings is desirable, but is not required. Follow the author’s preference. However, the
choice must be consistent throughout the paper. That is, if an author enumerates some but not all section headings,
the remaining headings in the paper should be labeled so that all headings and all levels of section headings in the
paper are enumerated.
Author enumeration notation that is not in IEEE style should be changed to IEEE style. For example, if an author
labels primary headings with capital letters, they should be changed to Roman numerals to match IEEE style. The
remaining style rules for each level of section heading as listed below should also be followed.
Primary headings (section) are enumerated by Roman numerals, centered above text, and set in 10-pt. and 8-pt.
caps. Note that Introduction, Conclusion, and Acknowledgment are Singular heads. Example:
I. INTRODUCTION
Secondary headings (subsect1) are enumerated by capital letters followed by periods (“A.,” “B.,” etc.), flush left,
italic, upper and lower case. Example:
A. Formal Frameworks
Tertiary headings (subsect2) are enumerated by Arabic numerals followed by parentheses. They are indented
one em, run into the text in their sections, italic, upper and lower case, and followed by a colon. Example:
1) Sophisticated Local Control: Sophisticated local control is applied when …
Quaternary headings (subsect3) are identical to tertiary headings, except that they are indented two ems instead
of one em, lower case letters are used as labels, and only the first letter of the heading is capitalized. Example:
a) Communication policies: Policies developed to improve communication …
Reference and Acknowledgment headings are unlike all other section headings in text. They are never
enumerated. They are simply primary headings without labels, regardless of whether the other headings in the
papers are enumerated. Example:
REFERENCES
ACKNOWLEDGMENT (note spelling here)
Appendix headings are a special case. The primary heading(s) in the Appendix or Appendixes (note spelling of
plural) are set according to the usual style, except that there is flexibility in the enumeration of the heading. The
author may use Roman numerals as heading numbers (Appendix I) or letters (Appendix A). Either is acceptable. The
Appendix is not preceded by a Roman numeral. Follow the rules given earlier for labeling subsidiary heads. Note
that if there is only one Appendix in the paper, leave the Appendix unnumbered and unnamed as is. (Appendix
subheads should also not be enumerated in this case.) Examples:
APPENDIX
APPENDIX I
PROOF OF THEOREM
APPENDIX A
PROOF OF THEOREM
Headings for Theorems, Proofs, and Postulates: Some papers do not conform to an outline style for theorems
and proofs that is easily transformed into the normal heading sequence. The preferred style is to set the head giving
the theorem number as a tertiary heading (no Arabic numeral preceding) and the proof head as a quaternary head.
This rule also applies to Lemmas, Hypotheses, Propositions, Definitions, Conditions, etc.
In-text references to text sections are written: “in Section II” or “in Section II-A” or “in Section II-A1.”
Capitalize the word “Section.” Do not use the word “Subsection”; use “Section” and write out the complete citation.
Introduction
Initial Cap or Drop Cap: In full length papers and/or editorials (but not in short papers), the first letter of the
Introduction is set as an initial cap, two lines deep (drop cap). After the cap, the next 8–12 characters (1–2 words)
are capitalized. (Do not break up hyphenated words into cap and lower case sections—extend the caps if necessary.)
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If it is not possible to use the first word or character of the Introduction as an initial cap (i.e., if the paper begins with
a quotation mark), try rewriting the sentence and query the author. See Section II-A of this guide for type specs of
the initial cap.
Text Equations
Consecutive Numbering: Equations within a paper are numbered consecutively from the beginning of the paper
to the end. There are some Transactions in which an author’s own numbering system such as numbering by section,
e.g., (1.1), (1.2.1), (A1), is permitted.
Appendix Equations: Continued consecutive numbering of equations is best in the Appendix, but if an author
starts equation numbering over with (A1), (A2), etc., for Appendix equations, it is permissible to leave the copy as
is. Hyphens and Periods: Hyphens and periods are accepted, if consistent in paper, e.g., (1a), (1.1), (1-1). This
should be done consistently throughout the paper.
Appendix
Refer to the Appendix in text as “given in the Appendix.” Note that the plural of Appendix is Appendixes. Also
note that all figures and tables in the Appendixes must be labeled in consecutive order with the other figures in the
paper. Never start a separate numbering system or group of numbers for the figures or tables in the Appendix
section.
Acknowledgment
The placement of the Acknowledgment appears after the final text of the paper, just before the References and
after any Appendix(es). The spelling of the heading for the Acknowledgment section is always singular, with no “e”
between the “g” and the “m.” As noted previously in the Text Headings section, the Acknowledgment head is a
primary heading. Do not enumerate the Acknowledgment heading.
When citing names within the Acknowledgment, use first initials only, not full names. Drop Mr., Mrs., or Miss
(list first initial and last name only). For Dr. or Prof., use the Dr. or Prof. title with each name separately; do not use
plural Drs. or Profs. with lists of names.
All acknowledgments of financial support must be removed from the Acknowledgment section and placed in the
first footnote/author affiliation.
Any acknowledgments of permission to publish and disclaimers to the content of the work made to/by the
author’s employer may be added as an Acknowledgment section.
Rewrite the Acknowledgment section to be read in the third person. Rewrite it even if the paper is given in the
first person.
References
A few guidelines related to the editing of references are summarized here. See Section V of this manual for a
more complete discussion of reference style.
The numbering of references is employed by citing one reference per number. Every reference in a Transactions
reference list should be a separate number entry. Use of one reference number to designate a group of references is
not preferred, and is discouraged. If the author-supplied reference list is unnumbered, the Staff Editor must provide
numbers, or if the list contains multiple references, these should be separated and renumbered by the Staff Editor. If
numbering or renumbering is necessary, then in-text references to the reference list must be checked and
renumbered by the Staff Editor.
Footnotes or other words and phrases that are part of the reference format do not belong on the reference list.
These full footnotes or extraneous phrases must always be removed from the list, changed into text or footnotes on
the appropriate page, and the references renumbered (renumber reference citation in text as well). Even the words
“For example” should not introduce references in the actual list, but should instead be included in parentheses in text
(or in a footnote), followed by the reference number, i.e., “For example, see [5].”
Do not say “in reference [1] …”; rather, the text should be edited to read simply, “in [1] …” The author’s name
should not be included in a text reference with a number (i.e., “In Smith [1]”) and should be changed to “in [1]”
except in such cases where the author’s name is integral to the understanding of the sentence (e.g., “Smith [1]
reduced calculated time …”). Reference dates should not be used as reference identifiers and should be deleted in
text except in rare cases where the date is somehow relevant to the paper’s subject.
Sometimes an author will refer to a specific figure of a reference or to a specific page or equation from a
reference. To avoid confusion, rewrite phrases such as “in Fig. 2 of reference [1]” to the IEEE cross-reference
notation “in [1, Fig. 2].” Similarly, rewrite phrases such as “in equation (8) of reference [1]” to be [1, eq. (8)]. Other
phrases may be rewritten as [1, Sec. IV], [1, Th. 4.2], or [1, Ch. 3].
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If an author lists the same reference more than once on the reference list, giving a new reference number for each
page or part of the same source that is cited, these separate references should all be made into one reference and the
separate citations of pages, equations, etc., should be made in text using the notation explained in the previous
paragraph.
If a reference author’s name is mentioned in text, check its spelling against the reference list.
Text Citation of Figures and Tables
All first citations of figures and tables in the paper must be in numerical order. If a figure is not mentioned or if
the first text mentions are not in order, call or query the author and/or renumber the figures where necessary.
Citations to figures in text always carry the abbreviation “Fig.” followed by the figure number. The abbreviation is
used even when it begins a sentence.
Figures: If labeled, parts of figures (callouts) should be 8-pt. lower case Roman letters within parentheses.
Whenever possible, all caption parts shown on the figure must be removed and keyed along with the caption.
The general style for captions is such that each caption number should be cited with the abbreviation “Fig.” and
the number, followed by a period, an em space, and then the text of the caption. The first word of the caption should
always be capitalized, regardless of any style that may be chosen to list caption parts (a), (b), etc., if included. In
general, do not use A, An, or The at the beginning of a figure or table caption. Example:
Fig. 1. Theoretical measured values of n.
There are several acceptable styles for listing the parts of the figure in the caption. Be consistent within each
paper, but otherwise use whichever style is most convenient for the figure. Regardless of which caption notation is
used, the citation of (a), (b), etc., should always appear before the corresponding caption part. Examples:
Fig. 1. Intercomplex crosstalk characteristics. (a) Electrode transmission.
(b) Interelectrode crosstalk.
Fig. 2. (a) Variation of effective mode index with time. (b) Step-index
change.
Fig. 3. Output resistance as a function of channel doping for 1-m-long gate.
(a) InGaAs and (b) InP JFETs with pinchoff voltage as a parameter.
Fig. 4. (a) and (b) Plain and side views, respectively, of the experimental
setup used to measure the effective diffraction loss which can be achieved
using the feedback technique.
Do not use:
Fig. 1. (a) Electrode transmission. (b) Interelectrode crosstalk.
If a figure after reduction will run more than one 21-pica column in width, the caption should be flush left on 43
picas.
If parts of a figure after reduction will run the length of more than one page, the full descriptive part of the
caption should be cited with the first part of the figure followed by the corresponding caption for the part. On the
subsequent pages, the word (Continued.) will be placed under the carryover parts of the figure followed by a repeat
of the full descriptive part of the caption and the corresponding caption for the carryover parts.
Captions for Landscape/broadside figures: The text should appear below the figures and facing outward at all
times. Example:
Fig. 6. True and estimated spectra for a real data sequence. (a) True
spectrum.
Fig. 6. (Continued..) True and estimated spectra for a real data sequence. (b)
Estimated with the periodogram.
Tables: The general style for table captions is such that each caption number should be centered above the table
with the label TABLE (set in 8-pt. caps) and the enumeration given in Roman numerals. The descriptive text of the
caption should be centered directly below the table number caption and is set in 8-pt. and 6-pt. caps. The captions
are usually centered on 21 picas, unless the table will be wider than one column width, in which case the table
caption should be centered on 43 picas.
The descriptive text of the table caption does not contain a period at the end of the caption, although punctuation
may be necessary within the caption itself. In general, table captions should be set as an inverted pyramid.
As in figures, labeled parts of tables should be 8-pt. lower case Roman letters within parentheses. The style for
listing the parts of a table in the caption and in text depends on whichever style is most convenient for the table. The
most acceptable style is to follow the conventions for callouts of figures. Example:
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TABLE I
PARAMETER VALUES
TABLE II
OPTIMAL WAVELENGTH AS A FUNCTION OF POLARIZER ANGLE. (a) WAVELENGTH
FOR EXTERNAL CAVITY. (b) ESTIMATED WAVELENGTH FOR LASER DIODE
A single rule should be added above and below the table body. Use the hrule macro to create rules. The type
specs for the text of a table is 8-pt. TR for full length papers, brief papers, and short papers.
The same rules as in figures apply for listing table part labels (callouts).
Table footnotes should be 8-pt. type and should be placed below the bottom rule of the table.
Obtaining permission to reuse copyrighted material
1) Reusing IEEE graphics previously published in IEEE publications. Author should email IEEE
Intellectual property department at: copyrights@ieee.org. In mose cases, the only requirements
will be to give full credit to the original source and to obtain the author’s approval (as a courtesy
to the author). At the end of the caption, add the reference number of the papers from which the
graphics are being used.
2) Reusing graphics previously published in non-IEEE publications. Author must have obtained
permission to republish from copyright holder (in most cases, this is the publishing house (not
the author of the paper). The wording is provided by the author (usually supplied by the
publishing house itself). This text is added at the end of the caption.
Photos and Biographies
IEEE Transactions author biographies are generally divided into three paragraphs. However, if appropriate
information for each paragraph is not provided by the author, the biography may be only one or two paragraphs.
The author’s photograph is sized at 6 picas wide by 7.5 picas deep and is surrounded by the biography.
The biography begins with the author’s full name and IEEE membership history as listed in the IEEE
Membership Directory. The author’s name appears in boldface type and must match the byline. A nickname may
appear within parentheses, e.g., Sung-Mo (Steve) Kang, but not in the byline. The format for listing the IEEE
membership history is to list each grade of membership attained followed by an apostrophe and the year it was
attained, with each year and grade combination separated from the others by an en dash. Note that if an author
attains the same membership grade in more than one year, list only the first year that it was reached. Check the
current membership listed with the biography against the byline.
Abbreviations for IEEE membership grades are: S (Student Member), A (Associate Member), M (Member), SM
(Senior Member), F (Fellow), LA (Life Associate Member), LM (Life Member), LSM (Life Senior Member), and
LF (Life Fellow). Note that A stands for Associate, not Affiliate, Member. Affiliate memberships are not listed
in the byline or biography membership history.
Delete all references to IEEE membership from the text of the biography.
First Paragraph: If provided by the author, the first paragraph may contain a place and/or date of birth (list
place, then date). Next, the author’s educational background is listed. When listing degrees earned, the biography
should state “[S]he received the Ph.D. degree from …” (not “[S]he received [her] his Ph.D. degree from …”).
Always add the word degree after a degree title if it is not included. Include the years degrees were received. If the
author was educated overseas, the names of the degrees earned may not be familiar. Abbreviations for some
common international and domestic degrees are:
Dipl.Ing., Diplom-Physiker, Dr. Ing., Dr. Phil., Dr. Eng., B.S., S.B., B.Sc.(Hons.), B.E.E., B.S.E., M.Eng.,
M.Sc.(tech.), M.S.E.E., M.S.E., Civilingenir, Lic.es Sci., Lic.es Lett.
Add the locations of universities and colleges the first time they are mentioned if not included (refer to the
University website for location). For U.S. state-named universities, repeat the state name in the location, and
included the country (e.g., University of Colorado, Boulder, CO, USA); but for city-named universities, repeat the
name of the city when giving the location (e.g., University of Chicago, Chicago, IL, USA). For universities outside
the U.S., give locations with the name of the city (postal abbreviations of Canadian Provinces, if used) and the
country the first time.
Use lower case for the author’s major field of study.
Second Paragraph: The second paragraph of the biography should list military and work experience, including
summer and fellowship jobs and consultant positions. Job titles are capitalized. The current job must have a location;
previous positions may be listed without one (retain if given). Do not abbreviate city names, Company, Laboratory,
or Department. Use standard names for all countries. If there is space, information the author provides about
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previous publications may be included at the end of this paragraph. Edit out long lists of published books or articles.
Instead use the sentence s(he) “is the author of several books and many published articles.” The format for listing
publishers of an author’s books within the biography is: Title of the Book (publisher name, year) similar to a
reference. List author affiliations with non-IEEE journals. The author often notes current and sometimes previous
research interests. If space is available, these may be retained; otherwise, edit out the prior interests and leave in the
current. Any homepage of the author may be listed in the biography only.
Do not repeat the author’s name in the second paragraph; use “he” or “she.”
Third Paragraph: The third paragraph begins with the author’s title and last name (e.g., Dr. Smith, Prof. Jones,
Mr. Kajor, Ms. Hunter). It lists the author’s memberships in professional societies other than the IEEE and his or her
status as a Professional Engineer if given. Finally, list awards and work for IEEE committees and publications,
affiliation with other professional societies, and symposia.
Personal notes such as hobbies should be deleted from the biography. Examples:
Michael C. Author, Jr. (S’87–A’89–SM’90–F’93) was born in New York, NY, USA, on March 2, 1969. He received the B.S. degree in
applied mathematics from the University of Michigan, Ann Arbor, MI, USA, in 1989, the M.S. degree in mathematical physics from Stanford
University, Stanford, CA, in 1991, and the Ph.D. degree in electrical engineering from the Massachusetts Institute of Technology, Cambridge,
MA, USA, in 1995.
From 1993 to 1995, he was with the Raytheon Corporation, Bedford, MA, USA. From 1995 to 1996, he was with the General Electric Space
Laboratory, Valley Forge, PA, USA. During 1996–1997, he was a Fulbright Lecturer at the University of Madrid, Madrid, Spain. He is currently
an Associate Professor of Electrical Engineering at the University of Maryland, College Park, MD, USA. His research has been concerned with
reentry plasma effects and microwave diagnostics of plasmas.
Dr. Author, Jr. is a Registered Professional Engineer in the State of Pennsylvania.
Katsunari Okamoto was born in Hiroshima Prefecture, Japan, on October 19, 1949. He received the B.S. degree from Rutgers University,
New Brunswick, NJ, in 1979 and the M.S. degree from Monmouth University, Long Branch, NJ, USA, in 1984
He was a Postdoctoral Fellow at the University of Tokyo in 1978. He joined the Ibaraki Electrical Communication Laboratory, N.T.T.,
Ibaraki-ken, Japan, in 1979, where he was engaged in research on the optimum waveguide structure of optical fibers. At present, he is a Member
of Technical Staff at Bellcore, Red Bank, NJ, USA.
Dr. Okamoto is a member of the Institute of Electronics and Communication Engineers of Japan.
NOTE: If no photograph is available or the journal does not require them, the biography is set 8/9×21 picas.
Squibs
If no biography or photograph is available, a squib is used. The phrase is run at 8/9 ×21 picas, flush left. Example:
James A. Author, (S’87–A’89–SM’90–F’93) photograph and biography not available at the time of publication.
D. Other Text to Edit
Footnotes
Footnotes should be numbered in consecutive order throughout the text. In full length, brief, and short papers,
they are 8/9 TR ×21. Each footnote should be a new paragraph. The footnote numbers are superscripts in text and in
the actual footnotes. In text, place the superscript footnote numbers after punctuation such as periods, commas, and
parentheses, quotation marks, but generally before dashes, colons, and semicolons in a compound sentence. The
footnotes should be placed at the bottom of the text column in which they are cited.
Lists in Text
There are three types of lists in text: run-in lists, displayed lists, and where lists. The ordering of labeling for all
lists is 1), 2), 3) followed by a), b), c), and then i), ii), iii). All are Roman; note single parenthesis. The order of
indentation is 1 em, 2 ems, 3 ems.
Run-In Lists: Lists that run in with text must be grammatically correct. They must also be introduced by a colon,
separated by semicolons, and have parallel construction. Example:
The carrier–phonon interaction matrices are given by: 1) polar optical phonons; 2) deformation potential
optical phonons; and 3) piezoelectric acoustic phonons.
Displayed Lists: Lists that are displayed may be either incomplete sentence items or full sentence items.
Incomplete sentence items contain a few items, are very short, are grammatically parallel, and are handled in two
ways. If the items are not mentioned in the text or are less than three items, run in as shown in the example for run-
in lists. If, however, the items are mentioned later in text, introduce the item with a colon, number the items, begin
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the entry with a lower case letter, and set block paragraph style. Use semicolons between items and a period at the
end of the list. Example:
This operating scenario provides all of the contributors necessary to configure a resonant power distribution
system:
1) the implementation of capacitor power factor correction on the power line;
2) the presence of nonlinear load;
3) the tuning of the power line by the load adjustments to a frequency present in the nonlinear generator.
Incomplete sentence items that are mentioned in text may also be formatted as shown in the example for full
sentence items.
Full sentence items may be introduced by “that” or other words taking object and are rewritten to end with a
period. If the items are introduced by a sentence ending with a colon, change the colon to a period. Number all
items, start each entry with a capital letter, and end with a period. Example:
The synthesis is performed in three major steps.
1) Geometry is generated for the selected module variants.
2) Shape variants using different fold counts for resistors are generated for each module.
3) Routing and postprocessing complete the final layout.
Where Lists: Where lists define variables in the equations preceding the list. They are characterized by
incomplete sentences and follow the same rules as Nomenclature lists, with the following exceptions.
1) There is no primary heading.
2) The left-hand side is indented one em space.
3) The first letter on the right-hand side is lower case.
4) Each item ends with a semicolon (except for the last item, which ends with a period).
5) The lists are at least three items long; if fewer than three items, the list is generally run in paragraph form.
Follow author preference for run-in or displayed lists. Example:
where
S
υ
∆
);
t(cos
φ
ω
′
+
′
∆=
S
V
S
V∆
amplitude of supply voltage flicker;
ω
′
angular frequency of supply voltage flicker;
fS
V
supply voltage amplitude;
ω
supply angular frequency.
Note the alignment of the equal sign with the right-hand side.
Lists having mixed items (start with an incomplete item, then have a full sentence explanation) are treated as a
full sentence item list.
Note Added in Proof
An author may wish to add a brief note in the proof stage, citing results obtained after acceptance of the paper or
mentioning additional references that have come to the author’s attention since acceptance. This added information
is usually inserted at the end of the Conclusion section of the paper or in whatever section contains the last
paragraph of the main body of the paper. As long as the note is not a major change to the paper or more than a few
lines long, the addition generally does not require further review procedures. Use the tertiary heading “Note Added
in Proof:” (run into text), but set in boldface italic with no enumeration and an em space indent. Example:
Note Added in Proof:
E. Other Types of Papers
Editorials
This category of papers includes the various types of introductory papers, such as Editorials, Guest Editorials,
Forewords, Introductions, and Editorial Announcements that appear at the beginning of issues as non-technical
introductory material. A discussion of the papers in an editorial should follow the order of the table of contents. The
editorial may contain illustrations, citations, and references. Follow general rules for editing. An acknowledgment
does not contain a heading. If a heading is required, set as a separate section and follow the primary heading specs
without enumeration. Note: In the Editorial, the Acknowledgment does not need to be in third person.
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Procedures and style for Editorials include the following.
General Specs: Type specs are the same as for full length papers. The initial cap remains the same. The title of
the Editorial is set in 24 pt. as in a full length paper title. There is no Abstract. There is a rule above the DOI.
NOTE: Editorials generally do not carry a section heading above the title. Center the word “Editorial” in
24-pt. type above the title.
Byline: Note that the byline for the Editorial does NOT appear below the title as it does in a full length paper.
The name of the author of the Editorial or Foreword (usually the Editor or Guest Editor) (called “signature”) appears
at the end of the Editorial, 6 pts. below the end of text, in 10-pt. and 8-pt. caps. Stack and align the name or names
with an identifier such as “Guest Editor” which should appear in italics next to the name. The affiliation should
appear as a “list” under each name. The right edge of the longest of these aligned lines should then be flush right at
the end of the last column of text. Example:
M. K. SAIN, Guest Editor
Department of Electrical Engineering
University of Illinois
Urbana, IL 60617 USA
Biographies and Photos: Biographies and photographs that appear with Editorials are set differently from
regular biographies and photos in the Transactions. They are, for example, not 8/9 type, but are the same type size as
the text of the Editorial (normally 10/12). In addition, Editorial biographies are: first 13 lines ×32, rest at 43 picas.
The photos are reduced to 9 1/2 ×12 picas.
Copyright Line: Run a copyright line for the Editorial, even if no copyright form is submitted by the Editor.
Brief Papers
Brief papers are set up like full length papers, except that the paper title is set in 16-pt. TR, centered on 43
picas. These papers do contain Abstracts and also take the initial cap. The byline includes the membership
grade. See Section I-B. They do not contain biographies and photographs of the authors. Footnotes,
references, and figure/table captions are 8/9 TR. The papers carry issue running heads on both left and right
pages.
Short Papers, Correspondence, and Communications
Short papers are set up like full-length papers, except that usually they are 9/11 type and their titles and bylines
are smaller type and run across only one column. Usually, short paper titles are 10/12 bold with bylines 9-pt. upper
and lower case. These papers do contain Abstracts, but do not take the initial cap. The membership grade is not
included in the byline. Author biographies and photos are not included. Footnotes, captions, references are 8/9 type.
Comments and Replies
Comments are generally in response to a previously published paper. The Comments and Author(s) Reply are
short papers published together in that the “Reply” is in response to the Comments. These short items may appear
without Abstracts. A special format applies for Comments and Author(s) Reply. Begin the first sentence with “In the
above paper [1], ...” Reference [1] is the commented paper’s citation, will appear as Reference [1] in the References
section. Include a copyright line for Comments and Replies even if no new forms are required from the author(s).
Some publications refer to these articles as Discussions and Closures.
Index Terms are optional.
Example of the Comments:
Title: Comments on “Harmonics: The Effects on Power Quality and Transformers”
Byline: Keith H. Sueker
Footnote:
Manuscript received July 15, 1995.
The author is with the School of Engineering, Vanderbilt University, Nashville, TN 37235 USA (e-mail: k.sueker@ieee.org)..
Digital Object Identifier 10.1109/JQE.2006.12345
NOTE: The footnote here relates back to the original paper being commented upon. The title is not repeated.
Example of the Reply:
Title: Authors’ Reply
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Byline: Robert D. Henderson and Patrick J. Rose
Footnote:
Manuscript received October 3, 2009; accepted October 5, 2009. Date of publication November 2, 2009; date of current version November
25, 2009.
The authors are with RDH Consultants, Inc., Charlotte, NC 28241 USA.
Digital Object Identifier 10.1109/JQE.2006.12348
Corrections/Errata
The format for a Corrections is basically the same as for the Comments, except that a Corrections does not carry
a Reply. Run a copyright line with a Corrections even if no new forms are received from the author(s). Corrections
that has been generated in-house may be labeled “Erratum,” and should also follow the standard format, although
the byline may be omitted because the IEEE Transactions/Journals Department assumes authorship of the
Corrections. Note: The plural form of the word is used in the title, even if there may be only one correction.
Example of a “Corrections” article:
Title: Corrections to “On the Exact Realization of LOG-Domain Elliptic Filters Using the Signal Flow
Graph Approach”
Byline: Costas Psychalinos and Spiridon Vlassis
Footnote:
Manuscript received May 1, 2003.
The authors are with the Physics Department, Electronics Laboratory, Aristotle University
of Thessaloniki, GR-54124 Thessaloniki, Greece (e-mail: cpsychal@physics.auth.gr; svals@skiathos.physics.auth.gr).
Digital Object Identifier 10.1109/TCSII.2003.814788
Example of Errata:
Title: Erratum
Byline: There is no byline for an erratum, as this is created if the department (staff/vendor) is responsible for
the error.
Footnote:
Manuscript received January 20, 2004.
Digital Object Identifier 10.1109/TVLSI.2004.830244
Book Reviews
Some publications carry Book Reviews. The type specs of the text are the same as for a short paper or
correspondence; however, the title runs additional information about the book that is being reviewed. The title is
separated from the book’s author by an em dash. Included in parentheses is the city of publication, publisher, date of
publication, the total number of pages of the book, and the price. Outside of the parentheses is the reviewer’s name
in italics. Some Transactions carry a short biography of the reviewer under the title. Book Reviews appear in the
table of contents with a listing for both the author of the book and the reviewer. Example:
Title and Byline:
The Analysis and Design of Pneumatic Systems—B. L. Andersen. (New York: Wiley, 1987, 302 pp., $65.00.)
Reviewed by J. L. Shearer.
First Footnote:
The reviewer is with the College of Engineering, Idaho State University, Pocatello, ID 83209 USA. Digital Identifier 0090-
6778/TNN.2005.828433.
Table of Contents:
The Analysis and Design of Pneumatic Systems—B. L. Andersen .......Reviewed by J. L. Shearer 123
Obituaries/In Memoriam
Obituaries are usually run as the first page of an issue, like an Editorial. They are set up with the same specs as
Editorials. Obituaries normally are formatted as one column, at 36 picas width. They may carry a photo of the
person being memorialized, usually the same size as in Editorials (9-1/2 ×12 picas). The name appears above the
photograph in 12-pts., boldface. The photograph is generally centered above the text. The years of birth and death
are generally cited at the bottom of the photo in 12-pts., boldface type in parentheses. The obituary is normally set as
one column, across a 36-pica width.
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F. Editing Style for Transactions
The following provides a summary of the most important style distinctions to be made in the final copy editing
of a Transactions paper.
Acronyms
Define acronyms the first time they appear in the Abstract as well as the first time they appear in the body of the
paper, written out first as part of the sentence, followed by the acronym in parentheses. Widely used or familiar
terms should be defined (see Section VIII-F of this manual for some terms that must be defined the first time they
are used in text). Acronyms do not need to be defined in the text if mentioned in the Nomenclature. Coined plurals
or plurals of acronyms do not take the apostrophe as per Chicago Manual of Style. Example: FET (singular); FETs
(plural).
Indefinite articles are assigned to abbreviations to fit the sound of the first letter: an FCC regulation; a BRI.
Spelling
Obviously, in reading and editing a paper, misspellings and typographical errors are top priority for correction.
Note that IEEE Transactions use the first spellings indicated in our first reference, the most current edition of
Webster’s New Collegiate Dictionary.
British Spellings and Terminology: Change all British spellings to American spellings. In particular, watch for
“our” endings in words like “behaviour” (change to “behavior”) and “re” endings in words like “centre” (change to
“center”). Also watch for the use of “s” rather than “z” in words like “polarisation” (change to “polarization”). See
“Common Hyphenations and Misspellings” in Section VIII-E.
Trademarks
The trademark symbol, ™ and ® are no longer used. Capitalize the first letter in the trademark name only.
Follow the author’s notation. The symbols ™ and ®, which often accompany registered trademark names on
product packaging and in advertisements, need not be used in running text.
Plurals
Plurals of units of measure take the “s.” For example, the plural form of 3 mil is 3 mils; 3 bits/s instead of 3 bit/s.
The plural of calendar years do not take the apostrophe before the “s.” For example, the plural form of 1990 is
1990s.
Hyphenation Rules
For hyphenation and spelling guidelines, IEEE style follows: 1) the list of preferred spellings and hyphenated words;
2) the guidelines discussed in the Grammar and Usage in Transactions section of this guide; and 3) the first version
of the spelling given in Webster’s Tenth New Collegiate Dictionary. Do not hyphenate most compound modifiers if
they occur after the noun being modified, even if hyphenating them before the noun. "Except for cooperate and
coordinate, use a hyphen if the prefix ends in a vowel and the word that follows begins with the same vowel."
Example:
The plan was well prepared. The man was little known. The woman was better qualified. His boat was 42
feet long. He has a 42-feet-long boat. T was the data period of the 40-Gb/s data signal. The 160-GHz MLLD
was a diode in which a 40-nm-long saturable absorber was located.
Follow the author’s preference if the result is consistent and clear. The most important hyphenation guideline is
to be certain that the hyphenation for a particular word or group of adjectives is consistent within a particular paper.
The En, Em, or Two-Em Dash
The en dash represents the words “to,” “through,” or “and.” Use it between page numbers, reference numbers,
figure citations, academic years, proper nouns, names, a range of values, or for opposites. Examples are: pp. 10–15,
1984–1990, Jones–Smith theorem, input–output, voltage–current curve, analog–digital converter, 10–20 cm. Also,
use the en dash in chemical abbreviations such as Ni–Al–Si. When using the en dash to represent a range, if the
word “from” occurs, the word “to” must be used rather than an en dash (ranges from 5 to 50 times).
The em dash is used in ordinary writing to mark a suspension of the sense. It is also used like parentheses, to
mark a subordinate thought within a sentence.
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Grammar
Check closely for lapses of clarity, subject/verb agreement, and parallel clause construction. See samples below
and a more detailed discussion in the Grammar and Usage in Transactions section of this guide.
Number:
A number of samples were taken …
A number N expressing the relation x/y is chosen …
Data:
The data were collected … (always plural)
Series:
A series of tests was run … (always singular with “a”)
Some, All, Half:
Some (all, half) of it is …
Some of them are …
Quantity:
Three volts was applied …
Four grams was added …
Contractions
Contractions such as “don’t” and “can’t” are not used in technical text. Change to “do not” and “cannot.”
Note: “don’t care,” “best-case,” and “worst-case” are allowed and used often in journals like TCAD.
Capitalization
In general, discourage capitalization in text except where absolutely necessary. For example, only proper names
attached to the names of laws, principles, theorems, etc., get capitalized (Boyle’s law, Newton’s first law, etc.).
Computer commands are in computer tags and remain small caps; most computer languages (Cobol, Java, LISP,
PERL, etc.) are upper and lower case. In text, the names of IEEE publications are 10-pt. and 8-pt. caps:
TRANSACTIONS, IEEE SPECTRUM, PROCEEDINGS OF THE IEEE.
Math
Some brief guidelines for editing math are explained here. For further discussion, see Section IV of this guide.
1) Variables are set italic; vectors are usually boldface italic (if distinguished by the author).
2) Remove commas around variables in text.
3) If not included by the author, always add a zero before decimals, but do not add after (e.g., 0.25).
4) Stet the use of the author’s parentheses and brackets (i.e., [0,1) may be correct).
5) Spell out units used in text without quantities (e.g., “where the noise is given in decibels”). For units
appearing with quantities, use the standard abbreviations listed in Section VIII-G.
6) Numbers and units used as compound adjectives may be hyphenated only if needed for clarity: 10-kV
voltage, 5-in-thick glass. Do not insert a hyphen when they are not used as adjectives: a current of 2 A, a line
4 in long, a length of 3.05 mm.
7) Use thin spaces instead of commas between numbers in tens or hundreds of thousands (e.g., 62 000, 100 000,
but 4000).
8) Always change µ to µm, “micron” to “micrometer,” “submicron” to submicrometer.” Always change cycle
per second to hertz (Hz); cycle per second may not appear as cycle, cps, c/s, csec. See “Table of Units and
Quantity Symbols” in Section VIII-G.
9) In text, break down (shill) multiline (built-up) fractions so they can be placed on one line. Sometimes
parentheses may need to be added to distinguish between expressions, especially when a minus appears [e.g.,
cb a
−
becomes )( c ba −],
4k dc +
−
becomes
[ ]
4)(kd)(c +−
.
10) In exponential expressions [e.g.,
e
xyzkjwt- )(
], there are sometimes long and complicated superscripts. These
may be brought down on line with the substitution of “exp” for “e” and the addition of square brackets (e.g.,
exp[–(jwt)xyzk]).
11) Distinguish between lower case italic “ell” or “oh” versus one and zero.
12) Always use numerals for numbers written with units. Otherwise, spell out numbers below 11, and use
numerals for others unless they begin a sentence or are combined in a phrase (gives 7 to 13 times more).
13) Use zeroth, first, nth, (k + 1)th, not 1st, 2nd, (k + 1)st, etc.
14) Use the word “equation” at the start of a sentence, but in text, just use the number [e.g., in (1)].
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15) Use the $ symbol versus “dollars” in sums of money.
16) The slash (/) is acceptable in place of the word “per” when it lends to the clarity of the sentence. For
example: “the ratio of 16 samples/s to 35 samples/s as compared to …”
Ellipses: In mathematics an author may use dots (ellipses) to show continuation in an expression (e.g., x2, ...,
x16). The type of mathematical expression will determine whether the ellipses points are set on the baseline or
centered. If commas or operational signs are present, they are placed after each term and after the three ellipses
points (almost all expressions will use three points). If operational signs are used, the ellipses are centered on the
operator. When commas are used the ellipses are on the baseline. Example:
x1, x2, …, xn not x1, x2 … xn
x1 + x2 + … + xn not x1 + x2 + … xn
y = 0, 1, 2, … not y = 0, 1, 2 …
x1x2 … an not x1x2 … an
Conditions: In displayed equations, there should be a comma or parentheses and a two-em space between the
main expression and the condition following it. Example:
m y yn x
y n yn x
n yn x
-
,,3,
.-3if,
3
2-
42-
2-
==
==
=∀=
NOTE: There is no comma before a for all “
∀
” symbol.
Compound Units: Compound units should be separated by a multidot (e.g., 4 V · s), but leave the slash if the
author uses it since this has a different meaning (for instance, 6 V/s means volts per second). It is also possible to
use a negative power to put a unit in the denominator: cm/s2 = cm · s–2. Parentheses may be used to clarify a unit:
g/(cm · s) or g · cm–1 · s–1.
Use of Periods and Commas: Equations which conclude a sentence should end with a period. The only time
punctuation is used to lead into an equation is when the lead-in text is a complete sentence. Example:
where we had the following:
x = Y + Z.
or where, i.e.,
x = Y + Z.
Commas appearing at the ends of equations are deleted unless they are critical to the punctuation of the sentence
containing the equation.
Equation Numbers
Check that equation numbering is consecutive, that it appears flush right on line with the last line of an equation,
that there are no repeats or missing numbers, and that a correct numbering style has been used.
Displayed Equations
Material in displayed equations is automatically italic unless otherwise indicated by the author. Some simple
general rules apply. All variables are italic. Function names and abbreviations are Roman, as are units, unit
abbreviations, complete words, and abbreviations of words. Superscripts and subscripts follow this same formula:
when they are variables, they are italic; when they are abbreviations of words (such as “in” and “out” for input and
output), they are Roman. Single-letter superscripts and subscripts may be italic even if they are abbreviations, unless
this leads to inconsistency between italic and Roman characters for similar types of subscripts.
Typical Problems
Which does the author mean: zero or “oh”? one or “ell”? subscript variable or on line? A general guideline to
help resolve these questions before querying the author is to read carefully through the paper—does the author
mention “O” for output or use a series of numbers like 0, 1, 2,?—and look through the illustrations—does Vs appear
in the figures or is it Vs? This may provide clues.
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G. General Layout Rules
1) Normal page depth for a Transactions is 60 picas (called even).
2) Pages may run one line long (61 picas) or short (59 picas), but facing pages (left and right) must be the same
depth.
3) Transactions papers are set in a two-column format. Each column is 21 picas wide, with a 1-pica space
between the two columns, giving a total page width of 43 picas.
4) Specifics of type area spacing are approximately 18 pts. between text and footnotes or figures and text, 6 pts.
above and below equations and lists, 12 pts. above primary heads, at least 6 pts. above secondary heads, and
3 picas between biographies.
5) Figures and tables are placed at the tops of columns as close to their first mention as possible, but preferably
after the mention.
6) Figures and tables progress vertically, not horizontally, on pages.
7) Footnotes must appear at the bottom of the column where they are first mentioned.
8) There must be at least two or three lines of text under a head at the bottom of a column.
9) Never leave widows at the tops of columns when breaking text. (A “widow” is any single last line of a
paragraph, even if it is of full column width.) The exceptions are when widows are used to introduce
equations or when they are in the Reference section.
10) Avoid breaking multiline equations so that one line appears at the bottom of a column and the others at the
top of the next column.
11) The starting page number is determined by checking the previous issue—it is the next page number after the
last page of the preceding issue, including any fillers. Issues beginning a new calendar year always start with
page 1.
12) Obituaries/In Memoriam(s) are articles formatted on 36-pica width.
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III. GRAMMAR AND USAGE IN TRANSACTIONS
A. Rules of Grammar
The principles of style given below aim to concentrate on fundamentals of modern usage. Particular emphasis is
given to the rules most commonly violated.
1) Form the possessive singular of nouns by adding’s (Avogadro’s theorem).
2) In a series of three or more terms, use a comma immediately before the coordinating conjunction
(usually and, or, or nor).
3) Enclose parenthetic expressions between commas. (Improvement, as shown in Fig. 1, is attained by the
addition of the cogeneration.).
4) Use the semicolon, not the comma, to separate two complete sentences which form a compound sentence.
5) Use a colon after an independent clause to introduce a list.
6) Punctuation always goes inside quotation marks, except for the colon and semicolon. Use single quotation
marks around quotes within quotes. Quotes may be used around a new or special usage of a term the first time
only, but use of quotes in this manner should be kept to a minimum.
7) Do not use double parentheses in text expressions, but keep them in math. For example, (see (10)) should
become [see (10)].
8) All acronyms and numerical plurals do not use apostrophes, i.e., FETs, 1980s.
9) Compound nouns made from a one-syllable verb and a short adverb are one word when found that way in
the dictionary (setup, takeoff, breakup). Compound nouns are likely to be two words, without a hyphen, or one
word (bandwidth, bypass, flowchart, phase shift, sideband, standing wave). Compound nouns of more than two
words can be hyphenated.
10) A pair of words, modifying a third word separately, does not get a hyphen (a tall water tower, a hot metal
cylinder). If the first word modifies the second, and the pair together modify the third, there is a hyphen between
the pair (a high-frequency signal, a second-order equation). The exception to this is the adverb ending in “ly,”
which needs no hyphen to join it to the next word.
11) A hyphen is not used after the comparative or the superlative (a higher order equation, a worst case value,
nearest neighbor method). Do not hyphenate chemical compounds (sodium chloride crystals). Alloys and
mixtures take the en dash (Ni–Co, He–Ne laser).
12) Do not use commas between adjectives (a planar equiangular spiral antenna).
13) Do not hyphenate predicate adjectives (… is well known, …is second order).
14) Compound verbs are generally hyphenated (arc-weld, freeze-dry). Keep the hyphen when using the participles
of such verbs as adjectives (freeze-dried, arc-welded). However, verbs with up, out, down, off, on, etc., do not
have a hyphen, although the nouns formed from them may be hyphenated or one word (Verb: set up, break down,
read out; Noun: setup, breakdown, readout).
B. Words Often Confused
Affect: to change or modify (verb).
Effect: result (noun); cause (verb).
Alternate: a substitute.
Alternative: a matter of choice.
Among: involves more than two things.
Between: involves more than two things, but considers each individually.
Compare to: point out resemblances between different objects.
Compare with: point out differences between same objects.
Compose: a set composed of members.
Comprise: a set comprising members; members comprising a set.
Farther: distance.
Further: quantity.
Fewer: modifies plural nouns specifying countable units, e.g., fewer tubes.
Less: modifies singular mass nouns and singular abstract nouns, e.g., less air.
Imply: something suggested though not expressed.
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Infer: something deduced from evidence.
Number: a large number of people.
Amount: a large amount of water.
Principal: chief, main, most important (adjective).
Principle: a rule (noun).
Precede: come before.
Proceed: continue, advance.
That: (defining, restrictive).
Which: (nondefining, nonrestrictive)
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IV. EDITING MATHEMATICS
A. The Language of Math
When editing technical publications it is important to remember that the mathematics often carries as much if not
more meaning than the body of text itself. Therefore, it is critical that the grammar of an equation be taken into account
when editing.
Most equations should read like a sentence. They should contain a noun and a verb and often contain adjectives,
prepositional phrases, conjunctions, and conditions. Equations also contain punctuation. When math occurs along with
text it shares the grammatical characteristics of the text. A displayed expression may be a main or subordinate clause,
an expression in apposition, a direct object, an item in a list, or the object of a preposition. Use comma at end of
introductory sentences after: i.e., e.g., “Hence” or “That is.” Use a colon after words such as “following” or “as
follows.” There should be no punctuation after forms of the verb to be, or between a verb and its object or a preposition
and its object. IEEE style dictates that the only punctuation used at the end of an equation is a period. There is,
however, other punctuation permitted in the equation itself and between an equation and its condition. This interior
punctuation contains mathematical meaning and must not be changed.
Some examples of interior punctuation are as follows.
Mathematical Ellipses:
I = 1, 2, 3, … , n
NOTE: Only three dots are used and they are enclosed by commas and are on the baseline.
Matrix:
)1(
37.192.127.601.110.162.1 46.114.288.580.844.197.1 36.352.250.942.107.165.4
012110
012010
014110
Eopt
−−−−
−−−−
=++−+−+
++−+−+
++−−−+
EEEEEE EEEEEE EEEEEE
C
NOTE: There is a centered operator, equation number, and period.
Parenthetic Statement:
v(t) = u (t), t = 1, 2,…, m.
NOTE: There is a 2em space after the comma and before the condition t = 1, 2,…, m. Multiple conditions should
be separated with a semicolon, with a comma at the end of the equation, a 2em space, and the condition aligned on
the operator.
B. In-Line Equations and Expressions
An inline equation is an equation within text or part of a paragraph. It is not displayed.
Rule 1: Equations appearing in text should be broken after a verb or an operator, meaning, if at all possible, the verb
or operator should remain on the top line of text.
Rule 2: Fractions should not appear stacked in line.
xy
xy )6(
α
+
should be written as
)()6( xyxy
α
+
.
Rule 3: Collective signs should not appear with limits to top and bottom, but to the side instead.
∑
∞=
=
i
i0
should be written as
∑
∞=
=
i
i0
.
Rule 4: Use Roman function exp instead of e followed by a lengthy superscript.
ezxyxyzx +−+ )2()( 2
α
should be written
as exp[(zx2 + y) (α – 2yx) + zx].
Rule 5 (optional): Avoid square roots (radical signs) having long bars.
)(
α
+x
should be rewritten as (x + α)½.
C. Break/Alignment Rules
Rule 1: Break equations at verbs and align on same when possible for a displayed equation.
A = (5α + x) + (10y + β)2
≥ (5x – α + y + x2)
≡ B2
E. IEEE Editorial Style Manual
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Appendix F
IEEE CITATION REFERENCE
176
IEEE Citation Reference
IEEE Publications uses Webster’s College Dictionary, 4th Edition. For guidance on grammar and usage not included
in this manual, please consult The Chicago Manual of Style, published by the University of Chicago Press.
Citiation standards in this reference are provided for:
Books
Conference Technical Articles
Periodicals
Handbooks
References
Reports
Books
Basic Format:
[1] J. K. Author, “Title of chapter in the book,” in Title of His Published Book, xth ed. City of Publisher, Country if not
USA: Abbrev. of Publisher, year, ch. x, sec. x, pp. xxx–xxx.
Examples:
[1] B. Klaus and P. Horn, Robot Vision. Cambridge, MA: MIT Press, 1986.
[2] L. Stein, “Random patterns,” in Computers and You, J. S. Brake, Ed. New York: Wiley, 1994, pp. 55-70.
[3] R. L. Myer, “Parametric oscillators and nonlinear materials,” in Nonlinear Optics, vol. 4, P. G. Harper and B. S.
Wherret, Eds. San Francisco, CA: Academic, 1977, pp. 47-160.
[4] M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions (Applied Mathematics Series 55).
Washington, DC: NBS, 1964, pp. 32-33.
[5] E. F. Moore, “Gedanken-experiments on sequential machines,” in Automata Studies (Ann. of Mathematical
Studies, no. 1), C. E. Shannon and J. McCarthy, Eds. Princeton, NJ: Princeton Univ. Press, 1965, pp. 129-153.
[6] Westinghouse Electric Corporation (Staff of Technology and Science, Aerospace Div.), Integrated Electronic
Systems. Englewood Cliffs, NJ: Prentice-Hall, 1970.
[7] M. Gorkii, “Optimal design,” Dokl. Akad. Nauk SSSR, vol. 12, pp. 111-122, 1961 (Transl.: in L. Pontryagin, Ed.,
The Mathematical Theory of Optimal Processes. New York: Interscience, 1962, ch. 2, sec. 3, pp. 127-135).
[8] G. O. Young, “Synthetic structure of industrial plastics,” in Plastics, vol. 3, Polymers of Hexadromicon, J. Peters,
Ed., 2nd ed. New York: McGraw-Hill, 1964, pp. 15-64.
[1] Name of Manual/Handbook, x ed., Abbrev. Name of Co., City of Co., Abbrev. State, year, pp. xx-xx.
Examples:
[1] Transmission Systems for Communications, 3rd ed., Western Electric Co., Winston-Salem, NC, 1985, pp. 44–60.
[2] Motorola Semiconductor Data Manual, Motorola Semiconductor Products Inc., Phoenix, AZ, 1989.
[3] RCA Receiving Tube Manual, Radio Corp. of America, Electronic Components and Devices, Harrison, NJ, Tech.
Ser. RC-23, 1992.
NOTE: Use et al. when three or more names are given.
O nline S ources
Patents, S tandards, Unpublished Theses,
page 1 of 7
rev. Sept 09 D. Graffox
Basic Format:
Handbooks
F. IEEE Citation Reference
177
Reports
The general form for citing technical reports is to place the name and location of the company or institution after the
author and title and to give the report number and date at the end of the reference.
Basic Format:
[1] J. K. Author, “Title of report,” Abbrev. Name of Co., City of Co., Abbrev. State, Rep. xxx, year.
Examples:
[1] E. E. Reber absorption in the earth’s atmosphere,” Aerospace Corp., Los
Angeles, CA, Tech. Rep. TR-0200 (4230-46)-3, Nov. 1988.
[2] J. H. Davis and J. R. Cogdell, “Calibration program for the 16-foot antenna,” Elect. Eng. Res. Lab., Univ. Texas,
Austin, Tech. Memo. NGL-006-69-3, Nov. 15, 1987.
[3] R. E. Haskell and C. T. Case, “Transient signal propagation in lossless isotropic plasmas,” USAF Cambridge Res.
Labs., Cambridge, MA, Rep. ARCRL-66-234 (II), 1994, vol. 2.
[4] M. A. Brusberg and E. N. Clark, “Installation, operation, and data evaluation of an oblique-incidence ionosphere
sounder system,” in “Radio Propagation Characteristics of the Washington-Honolulu Path,” Stanford Res. Inst.,
Stanford, CA, Contract NOBSR-87615, Final Rep., Feb. 1995, vol. 1.
[5] P. Diament and W. L. Lupatkin, “V-line surface-wave radiation and scanning,” Dept. Elect. Eng.,
New York, Sci. Rep. 85, Aug. 1991.
Conference Technical Articles
The general form for citing technical articles published in conference proceedings is to list the author/s and title of
the paper, followed by the name (and location, if given) of the conference publication in italics using these standard
abbreviations.
When the word below appears in the
conference publication title, abbreviate to
Annals Ann.
Annual Annu.
Colloquium Colloq.
Conference Conf.
Congress Congr.
Convention Conv.
Digest Dig.
Exposition Expo.
International Int.
National Nat.
When the word below appears in the
conference publication title, abbreviate to
Proceedings Proc.
Record Rec.
Symposium Symp.
Technical Digest Tech. Dig.
Technical Paper Tech. Paper
First 1st
Second 2nd
Third 3rd
Fourth/nth ... 4th/nth...
Write out all the remaining words, but omit most articles and prepositions like “of the” and “on.” That is, Proceedings of
the 1996 Robotics and Automation Conference becomes Proc. 1996 Robotics and Automation Conf.
Basic Format:
[1] J. K. Author, “Title of paper,” in Unabbreviated Name of Conf., City of Conf., Abbrev. State (if given), year, pp.
xxx-xxx.
For an electronic conference article when there are no page numbers:
J. K. Author [two authors: J. K. Author and A. N. Writer ] [three or more authors: J. K. Author et al.],
“Title of Article,” in [Title of Conf. Record as ],
[copyright year] © [IEEE or applicable copyright holder of the Conference Record]. doi: [DOI number]
[1]
[1] J. K. Author, “Title of paper,” presented at the Unabbrev. Name of Conf., City of Conf., Abbrev. State, year.
For an unpublished papr presented at a conference:
it appears on the copyright page
page 2 of 7
rev. Sept 09 D. Graffox
Angeles, CA, Tech. Rep.
et al., “Oxygen
TR-0200 (4230-46)-3, Nov. 1988.
Columbia Univ.,
F. IEEE Citation Reference
178
paginated. The DOI for each IEEE conference article is assigned when the article is processed for inclusion in the IEEE Xplore
The basic guideline for citing online sources is to follow the standard citation for the source given previously and add
the Digital Object Identifier (DOI) at the end of the citation, or add the DOI in place of page numbers if the source is not
FTP
Basic Format:
[1] J. K. Author. (year). Title (edition) [Type of medium]. Available FTP: Directory: File:
Example:
[1] R. J. Vidmar. (1994). On the use of atmospheric plasmas as electromagnetic reflectors [Online]. Available FTP:
atmnext.usc.edu Directory: pub/etext/1994 File: atmosplasma.txt
WWW
Basic Format:
[1] J. K. Author. (year, month day). Title (edition) [Type of medium]. Available: http://www.(URL)
Example:
[1] J. Jones. (1991, May 10). Networks (2nd ed.) [Online]. Available: http://www.atm.com
E-Mail
Basic Format:
[1] J. K. Author. (year, month day). Title (edition) [Type of medium]. Available e-mail: Message:
Example:
[1] S. H. Gold. (1995, Oct. 10). Inter-Network Talk [Online]. Available e-mail: COMSERVE@RPIECS Message: Get
NETWORK TALK
Telnet
Basic Format:
O nline S ources
[1] J. K. Author. (year, month day). Title (edition) [Type of medium]. Available Telnet: Directory: File:
Example:
[1] V. Meligna. (1993, June 11). Periodic table of elements [Online]. Available Telnet: Library.CMU.edu Directory:
Libraries/Reference Works File: Periodic Table of Elements
The following sources are unique in that they are electronic only sources.
digital library and is included with the reference data of the article in Xplore. See The DOI System for more information about
the benefits of DOI referencing.
page 3 of 7
rev. Sept 09 D. Graffox
F. IEEE Citation Reference
179
Patents
Basic Format:
[1] J. K. Author, “Title of patent,” U.S. Patent x xxx xxx, Abbrev. Month, day, year.
Example:
[1] J. P. Wilkinson, “Nonlinear resonant circuit devices,” U.S. Patent 3 624 125, July 16, 1990.
NOTE: Use “issued date” if several dates are given.
Theses (M.S.) and Dissertations (Ph.D.)
Basic Format:
[1] J. K. Author, “Title of thesis,” M.S. thesis, Abbrev. Dept., Abbrev. Univ., City of Univ., Abbrev. State, year.
[2] J. K. Author, “Title of dissertation,” Ph.D. dissertation, Abbrev. Dept., Abbrev. Univ., City of Univ., Abbrev. State,
year.
Examples:
[1] J. O. Williams, “Narrow-band analyzer,” Ph.D. dissertation, Dept. Elect. Eng., Harvard Univ., Cambridge, MA,
1993.
[2] N. Kawasaki, “Parametric study of thermal and chemical nonequilibrium nozzle flow,” M.S. thesis, Dept. Electron.
Eng., Osaka Univ., Osaka, Japan, 1993.
[3] N. M. Amer, “The effects of homogeneous magnetic fields on developments of tribolium confusum,” Ph.D.
dissertation, Radiation Lab., Univ. California, Berkeley, Tech. Rep. 16854, 1995. *** The state abbreviation is
omitted if the name of the university includes the state name, i.e., “Univ. California, Berkeley.”***
[4]
C. Becle, These de doctoral d’etat, Univ. Grenoble, Grenoble, France, 1968.
Unpublished
These are the two most common types of unpublished references.
Basic Format :
[1] J. K. Author, private communication, Abbrev. Month, year.
[2] J. K. Author, “Title of paper,” unpublished.
Examples:
[1] A. Harrison, private communication, May 1995.
[2] B. Smith, “An approach to graphs of linear forms,” unpublished.
[3] A. Brahms, “Representation error for real numbers in binary computer arithmetic,” IEEE Computer Group
Repository, Paper R-67-85.
Standards
Basic Format:
[1] Title of Standard, Standard number, date.
Examples:
[1] IEEE Criteria for Class IE Electric Systems, IEEE Standard 308, 1969.
[2] Letter Symbols for Quantities, ANSI Standard Y10.5-1968.
Patents, S tandards, Theses, Unpublished
page 4 of 7
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F. IEEE Citation Reference
180
Periodicals
When referencing IEEE Transactions, the issue number should be deleted and month carried.
NOTE:
Basic Format:
[1] J. K. Author, “Name of paper,” Abbrev. Title of Periodical, vol. x, no. x, pp. xxx-xxx, Abbrev. Month, year.
Examples:
[1] R. E. Kalman, “New results in linear filtering and prediction theory,” J. Basic Eng., ser. D, vol. 83, pp. 95-108,
Mar. 1961.
[2]
[3]
[4]
[5]
[6]
Ye. V. Lavrova, “Geographic distribution of ionospheric disturbances in the F2 layer,” Tr. IZMIRAN, vol. 19, no.
29, pp. 31–43, 1961 (Transl.: E. R. Hope, Directorate of Scientific Information Services, Defence Research Board
of Canada, Rep. T384R, Apr. 1963).
E. P. Wigner, “On a modification of the Rayleigh–Schrodinger perturbation theory,” (in German), Math.
Naturwiss. Anz. Ungar. Akad. Wiss., vol. 53, p. 475, 1935.
E. H. Miller, “A note on reflector arrays,” IEEE Trans. Antennas Propag..., to be published.**
C. K. Kim, “Effect of gamma rays on plasma,” submitted for publication. **
W. Rafferty, “Ground antennas in NASA’s deep space telecommunications,” Proc. IEEE vol. 82, pp. 636-640,
May 1994.
** Always use this style when the paper has not yet been accepted or scheduled for publication. Do not use “to appear in.”
Abbreviations for IEEE Periodicals
Proceedings of the IEEE abbreviates to: Proc. IEEE
Proceedings of the IRE abbreviates to: Proc. IRE (until 1962)
IEEE Journals IEEE J. Comput. Aid. Des. IEEE J. Solid-State Circuits
IEEE J. Ocean. Eng. IEEE Sensors J.
IEEE J. Quantum Electron. IEEE Syst. J.
IEEE J. Sel. Areas Commun. IEEE Transl. J. Magn. Jpn.
IEEE J. Sel. Topics Signal Process. J. Lightw. Technol.
IEEE J. Sel. Topics. Quantum Electron. J. Microelectromech. Syst.
IEEE Letters IEEE Antennas Wireless Propag. Lett. IEEE Photonics Technol. Lett.
IEEE Commun. Lett. IEEE Power Electron. Lett. (until 2005)
IEEE Electron Device Lett. IEEE Signal Process. Lett.
IEEE Magazines
IEEE Aerosp. Electron. Syst. Mag. IEEE Ind. Appl. Mag.
IEEE Annals Hist. Comput. IEEE Instrum. Meas. Mag.
IEEE Antennas Propagat. Mag. IEEE Intell. Syst.
IEEE ASSP Mag. (1984–1990) IEEE Internet Comput.
IEEE Circuits Devices Mag. (1985–present) IEEE IT Prof.
IEEE Circuits Syst. Mag. (1979–1984) IEEE Micro
IEEE Commun. Mag. (1979–present) IEEE Microwave
IEEE Commun. Soc. Mag. (until 1978) IEEE Multimedia
IEEE Comput. Appl. Power IEEE Nanotechnol. Mag.
IEEE Comput. Graph. Appl. IEEE Network
IEEE Comput. Intell. Mag. IEEE Pers. Commun.
IEEE Comput. Sci. Eng. Mag. IEEE Potentials
IEEE Computer IEEE Power Eng. Rev.
IEEE Concurrency IEEE Robot. Automat. Mag.
IEEE Control. Syst. Mag. IEEE Signal Processing Mag. (1991–present)
IEEE Des. Test Comput. IEEE Softw.
IEEE Electr. Insul. Mag. IEEE Spectr.
IEEE Eng. Manag. Rev. IEEE Technol. Soc. Mag.
IEEE Eng. Med. Biol. Mag. IEEE Veh. Technol. Mag.
IEEE Expert (until 1997) Today’s Eng.
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F. IEEE Citation Reference
181
IEEE Transactions abbreviations
IEEE Adv. Packag. IEEE Trans. Ind. Electron.
IEEE/ACM Trans. Netw. IEEE Trans. Ind. Informat.
IEEE Human–Factors Electron. (until 1968) IEEE Trans. Inf. Forens. Security
IEEE Man–Mach. Syst. (until 1970) IEEE Trans. Inf. Technol. Biomed.
IEEE Trans. Acoust., Speech, Signal Process. (1975–1990) IEEE Trans. Inf. Theory
IEEE Trans. Aeronaut. Navig. Electron. IEEE Trans. Instrum.
IEEE Trans. Aerosp. IEEE Trans. Instrum. Meas.
IEEE Trans. Aerosp. Electron. Syst. IEEE Trans. Intell. Transp. Syst.
IEEE Trans. Aerosp. Navig. Electron. IEEE Trans. Knowl. Data Eng.
IEEE Trans. Airbone Electron. IEEE Trans. Magn.
IEEE Trans. Antennas Propag. IEEE Trans. Manuf. Technol. (1972–1977)
IEEE Trans. Appl. Supercond. IEEE Trans. Mechatron.
IEEE Trans. Audio Electroacoust. (until 1974) IEEE Trans. Med. Imag.
IEEE Trans. Autom. Control IEEE Trans. Microw. Guid. Wave Lett. (1987–1999)
IEEE Trans. Biomed. Circuits Syst. IEEE Trans. Microw. Theory Tech.
IEEE Trans. Biomed. Eng. IEEE Trans. Microw. Wireless Compon. Lett. (until 2004)
IEEE Trans. Broadcast. IEEE Trans. Mil. Electron.
IEEE Trans. Broadcast. Technol. IEEE Trans. Multimedia
IEEE Trans. Circuit Theory (until 1973) IEEE Trans. Nanotechnol.
IEEE Trans. Circuits Syst. (1974–1992) IEEE Trans. Neural Netw.
IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. (until 2003) IEEE Trans. Neural Syst. Rehabil. Eng.
IEEE Trans. Circuits Syst. I, Reg. Papers IEEE Trans. Nucl. Sci.
IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. (until
2003) IEEE Trans. Parallel Distrib. Syst.
IEEE Trans. Circuits Syst. II, Exp. Briefs IEEE Trans. Parts, Hybrids, Packag. Technol. (June 1971–
1977)
IEEE Trans. Circuits Syst. Video Technol. IEEE Trans. Parts, Mater. Packag.
IEEE Trans. Commun. IEEE Trans. Pattern Anal. Mach. Intell.
IEEE Trans. Commun. Technol. (until 1971) IEEE Trans. Plasma Sci.
IEEE Trans. Compon. Hybrids, Manuf. Technol. (1978—1993) IEEE Trans. Power App. Syst. (until 1985)
IEEE Trans. Compon. Packag. Manuf. Technol. A (1994–1998) IEEE Trans. Power Del.
IEEE Trans. Compon. Packag. Manuf. Technol. B (1994–1998) IEEE Trans. Power Electron.
IEEE Trans. Compon. Packag. Manuf. Technol. C (1996–1998) IEEE Trans. Power Syst.
IEEE Trans. Compon. Packag. Technol. IEEE Trans. Prof. Commun.
IEEE Trans. Comput. IEEE Trans. Rehabil. Eng. (until 2000)
IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. IEEE Trans. Reliab.
IEEE Trans. Consum. Electron. IEEE Trans. Robot. Autom.
IEEE Trans. Control Syst. Technol. IEEE Trans. Semicond. Manuf.
IEEE Trans. Dev. Mat. Rel. IEEE Trans. Signal Process.
IEEE Trans. Dielectr. Electr. Insul. IEEE Trans. Softw. Eng.
IEEE Trans. Edu. IEEE Trans. Sonics Ultrason. (until 1985)
IEEE Trans. Electromagn. Compat. IEEE Trans. Speech Audio Process.
IEEE Trans. Electron Devices IEEE Trans. Syst. Man Cybern. (1971–1995)
IEEE Trans. Electron. Packag. Manuf. IEEE Trans. Syst. Man Cybern. A., Syst. Humans
IEEE Trans. Energy Convers. IEEE Trans. Syst. Man Cybern. B, Cybern.
IEEE Trans. Eng. Manag. IEEE Trans. Syst. Man Cybern. C, Appl. Rev.
IEEE Trans. Evol. Comput. IEEE Trans. Ultrason. Eng.
IEEE Trans. Fuzzy Syst. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
IEEE Trans. Geosci. Electron. (1962–1979) IEEE Trans. Veh. Technol.
IEEE Trans. Geosci. Remote Sens. IEEE Trans. Very Large Scale Integr. (VLSI) Syst.
IEEE Trans. Image Process. IEEE Trans. Vis. Comput. Graphics
IEEE Trans. Ind. Appl. IEEE Trans. Wireless Commun.
page 6 of 7
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F. IEEE Citation Reference
182
References
References in Text:
References need not be cited in the text. When they are, they appear on the line, in square
the punctuation.
as shown by Brown [4], [5]; as mentioned earlier [2], [4]–[7], [9]; Smith [4] and Brown and Jones [5]; Wood et
al. [7]
NOTE: Use et al. when three or more names are given.
or as nouns:
as demonstrated in [3]; according to [4] and [6]–[9].
References Within a Reference:
Check the reference list for ibid. or op. cit. These refer to a previous reference and
reference section. In text, repeat the earlier reference number and renumber the reference
ibid. gives a new page number, or other information, use the following forms:
[3, Th. 1]; [3, Lemma 2]; [3, pp. 5-10]; [3, eq. (2)]; [3, Fig. 1]; [3, Appendix I]; [3, Sec. 4.5]; [3, Ch. 2, pp. 5-10];
[3, Algorithm 5].
NOTE: Editing of references may entail careful renumbering of references, as well as the citations in text.
Style
their own, hanging out beyond the body of the reference.
The reference numbers are on the line, enclosed in square brackets. In all references, the given name of the author or
editor is abbreviated to the initial only and precedes the last name. Use commas around Jr., Sr., and III in names. If there
Grammatically, they may be treated as if they were footnote numbers, e.g.,
are many names, use et al.
Note that
be kept, although it is normally deleted. Keep the day of the month when
include all information; please obtain and include relevant information. Do not
one reference with e ach number. If there is a URL included with the print reference, it can be included at the end of
brackets, inside
should be eliminated from the
section accordingly. If the
When the word below appears in the reference, abbreviate to
Acoustics Acoust.
Administration Admin.
Administrative Administ.
American Amer.
Analysis Anal.
Annals Ann.
Annual Annu.
Apparatus App.
Applications Applicat.
Applied Appl.
Association Assoc.
Automatic Automat.
Broadcasting Broadcast.
Business Bus.
Communications Commun.
Computer(s) Comput.
Congress Congr.
Convention Conv.
Correspondence Corresp.
Cybernetics Cybern.
Department Dept.
Development Develop.
Digest Dig.
Electrical Elect.
Electronic Electron.
Engineering Eng.
Ergonomics Ergonom.
Evolutionary Evol.
Foundation Found.
Geoscience Geosci.
Graphics Graph.
Industrial Ind.
Industry Ind.
Information Inform.
Institute Inst.
Intelligence Intell.
International Int.
Journal J.
Letter(s) Lett.
Machine Mach.
Magazine Mag.
Management Manage.
Managing Manag.
Mathematic(s) Math.
Philosophical Philosph.
Proceedings Proc.
Processing Process.
Production Prod.
Productivity Productiv.
Quarterly Quart.
Record Rec.
Reliability Rel.
Report Rep.
Royal Roy.
Science Sci.
Selected Select.
Society Soc.
Sociological Sociol.
Statistics Stat.
Studies Stud.
Supplement Suppl.
Symposium Symp.
Systems Syst.
Technical Tech.
Telecommunication Telecommun.
Transactions Trans.
Vehicular Veh.
Working Work.
Econ. Economic(s)
Education Educ.
Mathematical Math.
Mechanical Mech.
National Nat.
Newsletter Newslett.
Nuclear Nucl.
Occupation Occupat.
page 7 of 7
rev. Sept 09 D. Graffox
month is not available, the number may
referencing a patent. References may not
combine references. There must be only
w hen citing IEEE Transactions, if the
Reference numbers are set flush left and form a column of
the reference.
F. IEEE Citation Reference
183
Appendix G
IEEE PUBLICATION ABBREVIATIONS
184
pg 1 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE Abbreviations for Transactions, Journals,
Letters, and Magazines
NOTE: * denotes past acronyms/abbreviations of journals (used for pre-1988 publications).
List of IEEE Transactions, Journals, and Letters
Publication Acronym Reference Abbreviation
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS AES IEEE Trans. Aerosp. Electron. Syst.
ANE* IEEE Trans. Aeronaut. Navig. Electron.*
ANE* IEEE Trans. Aerosp. Navig. Electron.*
AS* IEEE Trans. Aerosp.*
MIL* IEEE Trans. Mil. Electron.*
AE* IEEE Trans. Airborne Electron.*
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION AP IEEE Trans. Antennas Propag.
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS LAWP IEEE Antennas Wireless Propag. Lett.
IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY ASC IEEE Trans. Appl. Supercond.
IEEE/ACM TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING ASLP IEEE/ACM Trans. Audio, Speech, Language Process.
IEEE TRANSACTIONS ON AUDIO, SPEECH, AND LANGUAGE PROCESSING ASL IEEE Trans. Audio, Speech, Language Process.
(2006–2013)
SAP* IEEE Speech Audio Process. (1993−2005)
IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC IEEE Trans. Autom. Control
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING ASE IEEE Trans. Autom. Sci. Eng. (from July 2004)
IEEE TRANSACTIONS ON AUTONOMOUS MENTAL DEVELOPMENT AMD IEEE Trans. Auton. Mental Develop.
IEEE TRANSACTIONS ON BIG DATA BD IEEE Trans. Big Data
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS BHI IEEE J. Biomed. Health Inform.
ITB IEEE Trans. Inf. Technol. Biomed. (1995–2012)
IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS BCAS IEEE Trans. Biomed. Circuits Syst.
IEEE REVIEWS IN BIOMEDICAL ENGINEERING RBME IEEE Rev. Biomed. Eng.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING BME IEEE Trans. Biomed. Eng.
BME* IEEE Trans. Bio Med. Eng.*
BME* IEEE Trans. Bio Med. Electron.*
PGME* IEEE Trans. Med. Electron.*
IEEE TRANSACTIONS ON BROADCASTING BC IEEE Trans. Broadcast.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS CSI IEEE Trans. Circuits Syst. I, Reg. Papers
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS CSII IEEE Trans. Circuits Syst. II, Exp. Briefs
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL CAS1* IEEE Trans. Circuits Syst. I, Fundam. Theory
THEORY AND APPLICATIONS Appl. (1993–2003)
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND CAS2* IEEE Trans. Circuits Syst. II, Analog Digit. Signal
DIGITAL SIGNAL PROCESSING Process.(1993–2003)
CAS* IEEE Trans. Circuits Syst.* (1974–1992)
CT* IEEE Trans. Circuit Theory* (until 1973)
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY CSVT IEEE Trans. Circuits Syst. Video Technol.
IEEE TRANSACTIONS ON CLOUD COMPUTING CC IEEE Trans. Cloud Comput.
IEEE TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING CCN IEEE Trans. Cogn. Commun. Netw.
IEEE TRANSACTIONS ON COMMUNICATIONS COM IEEE Trans. Commun.
COM* IEEE Trans. Commun. Technol.* (until 1971)
G. IEEE Publication Abbreviations
185
pg 2 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE COMMUNICATIONS LETTERS COMML IEEE Commun. Lett.
IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND CPMT IEEE Trans. Compon. Packag. Manuf. Technol.
MANUFACTURING TECHNOLOGY
CAPT IEEE Trans. Compon. Packag. Technol. (1999–2010)
CPMTA IEEE Trans. Compon., Packag.,Manuf. Technol. A
(1994–1998)
CHMT* IEEE Trans. Compon., Hybrids, Manuf. Technol.*
(1978–1993)
MFT* IEEE Trans. Manuf. Technol.* (1972–1977)
PHP* IEEE Trans. Parts, Hybrids, Packag.* (June 1971–1977)
PMP* IEEE Trans. Parts, Mater., Packag.* (1965−1971)
ADVP IEEE Trans. Adv. Packag. (1999–2010)
CPMTB IEEE Trans. Compon., Packag., Manuf. Technol. B
(1994–1998)
EPM IEEE Trans. Electron. Packag. Manuf. (1999−2010)
CPMTC IEEE Trans. Compon., Packag., Manuf. Technol. C
(1996–1998)
IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY CBB IEEE/ACM Trans. Comput. Biol. Bioinf.
AND BIOINFORMATICS
IEEE TRANSACTIONS ON COMPUTATIONAL INTELLIGENCE AND AI IN GAMES CIAIG IEEE Trans. Comput. Intell. AI in Games
IEEE TRANSACTIONS ON COMPUTATIONAL SOCIAL SYSTEMS CSS IEEE Trans. Comput. Social Syst.
IEEE TRANSACTIONS ON COMPUTERS C IEEE Trans. Comput.
IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CAD IEEE Trans. Comput.-Aided Design Integr. Circuits Syst.
CIRCUITS AND SYSTEMS
IEEE COMPUTER ARCHITECTURAL LETTERS CAL IEEE Comput. Archit. Lett.
IEEE TRANSACTIONS ON CONSUMER ELECTRONICS CE IEEE Trans. Consum. Electron.
BTR IEEE Trans. Broadcast. Telev. Receiv. (1963−1974)
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY CST IEEE Trans. Control Syst. Technol.
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS CNS IEEE Trans. Control Netw. Syst.
IEEE TRANSACTIONS ON CYBERNETICS CYB IEEE Trans. Cybern.
SMCB* IEEE Trans. Syst. Man, Cybern. B, Cybern. (1995–2012)
IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY DMR IEEE Trans. Device Mater. Rel.
IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION DEI IEEE Trans. Dielectr. Electr. Insul.
EI* IEEE Trans. Electr. Insul.* (through 1993)
IEEE/OSA JOURNAL OF DISPLAY TECHNOLOGY DT J. Display Technol.
IEEE TRANSACTIONS ON EDUCATION E IEEE Trans. Edu.
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY EMC IEEE Trans. Electromagn. Compat.
RFI* IEEE Trans. Radio Freq. Interference*
IEEE TRANSACTIONS ON ELECTRON DEVICES ED IEEE Trans. Electron Devices
IEEE JOURNAL OF ELECTRON DEVICES SOCIETY EDS IEEE J. Electron Devices Soc.
IEEE ELECTRON DEVICE LETTERS EDL IEEE Electron Device Lett.
IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING EPM IEEE Trans. Electron. Packag. Manuf. (1999−2010)
IEEE EMBEDDED SYSTEMS LETTERS ES IEEE Embedded Syst. Lett.
IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING ETC IEEE Trans. Emerg. Topics Comput.
IEEE TRANSACTIONS ON EMERGING AND SELECTED TOPICS IN ETCAS IEEE Trans. Emerg. Sel. Topics Circuits Syst.
CIRCUITS AND SYSTEMS
IEEE TRANSACTIONS ON EMERGING AND SELECTED TOPICS IN ESTPE IEEE Trans. Emerg. Sel. Topics Power Electron.
POWER ELECTRONICS
IEEE TRANSACTIONS ON ENERGY CONVERSION EC IEEE Trans. Energy Convers.
IEEE Abbreviations for Transactions, Journals, Letters, and Magazines (ctd.)
Publication Acronym Reference Abbreviation
G. IEEE Publication Abbreviations
186
pg 3 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT EM IEEE Trans. Eng. Manag.
IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION EVC IEEE Trans. Evol. Comput.
IEEE JOURNAL ON EXPLORATORY SOLID-STATE COMPUTATIONAL XCDC IEEE J. Explor. Solid-State Computat. Devices Circuits
DEVICES AND CIRCUITS
IEEE TRANSACTIONS ON FUZZY SYSTEMS FUZZ IEEE Trans. Fuzzy Syst.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING GRS IEEE Trans. Geosci. Remote Sens.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS GRSL IEEE Geosci. Remote Sens. Lett.
IEEE TRANSACTIONS ON HUMAN–MACHINE SYSTEMS HMS* IEEE Trans. Human–Mach. Syst.
SMCC* IEEE Trans. Syst., Man, Cybern. C, Appl. Rev.
(1995–2012)
SMC* IEEE Trans. Syst., Man, Cybern.* (1971–1995)
SSC* IEEE Trans. Syst. Sci. Cybern.* (through 1970)
IEEE TRANSACTIONS ON IMAGE PROCESSING IP IEEE Trans. Image Process.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS IE IEEE Trans. Ind. Electron.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS II IEEE Trans. Ind. Informat.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS IA IEEE Trans. Ind. Appl.
IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY IFS IEEE Trans. Inf. Forensics Security
IEEE TRANSACTIONS ON INFORMATION THEORY IT IEEE Trans. Inf. Theory
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT IM IEEE Trans. Instrum. Meas.
I, PGI* IEEE Trans. Instrum.*
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS ITS IEEE Trans. Intell. Transp. Syst.
IEEE INTERNET OF THINGS JOURNAL IoT IEEE Internet Things J.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING KDE IEEE Trans. Knowl. Data Eng.
IEEE LIFE SCIENCES LETTERS LS IEEE Life Sci. Lett.
IEEE/OSA JOURNAL OF LIGHTWAVE TECHNOLOGY LT J. Lightw. Technol.
IEEE TRANSACTIONS ON MAGNETICS MAG IEEE Trans. Magn.
IEEE MAGNETICS LETTERS MAGL IEEE Magn. Lett.
IEEE/ASME TRANSACTIONS ON MECHATRONICS MECH IEEE/ASME Trans. Mechatronics
IEEE TRANSACTIONS ON MEDICAL IMAGING MI IEEE Trans. Med. Imag.
IEEE JOURNAL OF MICROELECTROMECHANICAL SYSTEMS MEMS J. Microelectromech. Syst.
IEEE/ASME JOURNAL OF MICROELECTROMECHANICAL SYSTEMS MEMS J. Microelectromech. Syst. (1992–2013)
IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS MWCL IEEE Microw. Compon. Lett.
MGWL IEEE Microw. Guided Wave Lett. (1991−2000)
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES MTT IEEE Trans. Microw. Theory Techn.
IEEE TRANSACTIONS ON MOBILE COMPUTING MC IEEE Trans. Mobile Comput.
IEEE TRANSACTIONS ON MOLECULAR, BIOLOGICAL AND MBSC IEEE Trans. Mol. Biol. Multi-Scale Commun.
MULTI-SCALE COMMUNICATIONS
IEEE TRANSACTIONS ON MULTIMEDIA MM IEEE Trans. Multimedia
IEEE TRANSACTIONS ON MULTI-SCALE COMPUTING SYSTEMS MSCS IEEE Trans. Multi-Scale Comput. Syst.
IEEE TRANSACTIONS ON NANOBIOSCIENCE NB IEEE Trans. Nanobiosci.
IEEE TRANSACTIONS ON NANOTECHNOLOGY NANO IEEE Trans. Nanotechnol.
IEEE NANOTECHNOLOGY EXPRESS ENANO IEEE Nanotechnol. Express
IEEE/ACM TRANSACTIONS ON NETWORKING NET IEEE/ACM Trans. Netw.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS NNLS IEEE Trans. Neural Netw. Learn. Syst.
NN IEEE Trans. Neural Netw. (1990−2011)
IEEE TRANSACTIONS ON NUCLEAR SCIENCE NS IEEE Trans. Nucl. Sci.
IEEE Abbreviations for Transactions, Journals, Letters, and Magazines (ctd.)
Publication Acronym Reference Abbreviation
G. IEEE Publication Abbreviations
187
pg 4 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION NSRE IEEE Trans. Neural Syst. Rehabil. Eng.
ENGINEERING
RE* IEEE Trans. Rehabil. Eng.* (1993–2000)
IEEE JOURNAL OF OCEANIC ENGINEERING OE IEEE J. Ocean. Eng.
IEEE JOURNAL OF OPTICAL COMMUNICATIONS AND NETWORKING OCN IEEE J. Opt. Commun. Netw.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS PDS IEEE Trans. Parallel Distrib. Syst.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE PAMI IEEE Trans. Pattern Anal. Mach. Intell.
IEEE PHOTONICS TECHNOLOGY LETTERS PTL IEEE Photon. Technol. Lett.
IEEE PHOTONICS JOURNAL PJ IEEE Photon. J.
IEEE JOURNAL OF PHOTOVOLTAICS PHOT IEEE J. Photovolt.
IEEE TRANSACTIONS ON PLASMA SCIENCE PS IEEE Trans. Plasma Sci.
IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS PAS* IEEE Trans. Power App. Syst.* (through 1985)
IEEE TRANSACTIONS ON POWER DELIVERY PWRD IEEE Trans. Power Del.
IEEE TRANSACTIONS ON POWER ELECTRONICS PEL IEEE Trans. Power Electron.
IEEE POWER ELECTRONICS LETTERS LPEL IEEE Power Electron Lett. (2003-2005; abolished)
IEEE TRANSACTIONS ON POWER SYSTEMS PWRS IEEE Trans. Power Syst.
IEEE JOURNAL OF PRODUCT SAFETY ENGINEERING PSE IEEE J. Product Safety Eng.
IEEE POWER AND ENERGY TECHNOLOGY SYSTEMS JOURNAL PETS IEEE Power Energy Technol. Syst. J.
IEEE TRANSACTIONS ON PROFESSIONAL COMMUNICATION PC IEEE Trans. Prof. Commun.
IEEE JOURNAL OF QUANTUM ELECTRONICS QE IEEE J. Quantum Electron.
IEEE RFIC JOURNAL RFIC IEEE RFIC J.
IEEE RFID JOURNAL RFID IEEE RFID J.
IEEE TRANSACTIONS ON RELIABILITY R IEEE Trans. Rel.
IEEE TRANSACTIONS ON ROBOTICS RO IEEE Trans. Robot.
IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION RA* IEEE Trans. Robot. Autom. (1989–June 2004)
RA* IEEE J. Robot. Autom.* (1985–1988)
IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS STARS IEEE J. Sel. Topics Appl. Earth Observ. in Remote Sens.
IN REMOTE SENSING
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS SAC IEEE J. Sel. Areas Commun.
IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS STQE IEEE J. Sel. Topics Quantum Electron.
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING STSP IEEE J. Sel. Topics Signal Process.
IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING SM IEEE Trans. Semicond. Manuf.
IEEE SENSORS JOURNAL SEN IEEE Sensors J.
IEEE TRANSACTIONS ON SIGNAL PROCESSING SP IEEE Trans. Signal Process.
ASSP* IEEE Trans. Acoust., Speech, Signal Process. *
(1975–1990)
AU* IEEE Trans. Audio Electroacoust. (until 1974)
IEEE SIGNAL PROCESSING LETTERS SPL IEEE Signal Process. Lett.
IEEE TRANSACTIONS ON SMART GRID SG IEEE Trans. Smart Grid
IEEE TRANSACTIONS ON SUSTAINABLE ENERGY STE IEEE Trans. Sustain. Energy
IEEE SYSTEMS JOURNAL SJ IEEE Syst. J.
IEEE TRANSACTIONS ON SOFTWARE ENGINEERING SE IEEE Trans. Softw. Eng.
IEEE JOURNAL OF SOLID-STATE CIRCUITS SSC IEEE J. Solid-State Circuits
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS SMC IEEE Trans. Syst., Man, Cybern., Syst.
SMCA* IEEE Trans. Syst., Man, Cybern. A, Syst.,Humans
(1995-2012)
MMS* IEEE Trans. Man-Mach. Syst.* (through 1970)
HFE* Hum. Factors Electron.* (through 1968)
IEEE Abbreviations for Transactions, Journals, Letters, and Magazines (ctd.)
Publication Acronym Reference Abbreviation
G. IEEE Publication Abbreviations
188
pg 5 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE JOURNAL OF TRANSLATIONAL ENGINEERING IN HEALTH AND MEDICINE TEHM IEEE J. Transl. Eng. Health Med.
IEEE TRANSLATION JOURNAL ON MAGNETICS IN JAPAN TJMJ IEEE Transl. J. Magn. Jpn. (through 2010)
IEEE JOURNAL ON TECHNOLOGY IN COMPUTER AIDED DESIGN TCAD IEEE J. Technol. Computer Aided Des.
IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY THz IEEE Trans. THz Sci. Technol.
IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION IEEE Trans. Transport. Electrific.
IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND UFFC IEEE Trans. Ultrason., Ferroelect., Freq. Control
FREQUENCY CONTROL
SU* IEEE Trans. Sonics Ultrason.* (through 1985)
UE* IEEE Trans. Ultrason. Eng.*
PGUE* IEEE Trans. Ultrason. Eng.*
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY VT IEEE Trans. Veh. Technol.
VC* IEEE Trans. Veh. Commun.*
IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS VLSI IEEE Trans. Very Large Scale Integr. (VLSI) Syst.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS VCG IEEE Trans. Vis. Comput. Graphics
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS WC IEEE Trans. Wireless Commun.
PROCEEDINGS OF THE IEEE Proc. IEEE
Proc. IRE* (through 1962)
IEEE Abbreviations for Transactions, Journals, Letters, and Magazines (ctd.)
Publication Acronym Reference Abbreviation
G. IEEE Publication Abbreviations
189
pg 6 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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IEEE Aerospace and Electronics Systems Magazine IEEE Aerosp. Electron. Syst. Mag.
IEEE Annals of the History of Computing IEEE Ann. Hist. Comput.
IEEE Antennas and Propagation Magazine IEEE Antennas Propag. Mag.
IEEE ASSP Magazine (1984–1990) IEEE ASSP Mag.
IEEE Circuits and Systems Magazine IEEE Circuits Syst. Mag.
IEEE Circuits and Devices Magazine (1988–2006) IEEE Circuits Devices Mag.
IEEE Communications Society Magazine (through 1978) IEEE Commun. Soc. Mag.
IEEE Communications Magazine (1979–present) IEEE Commun. Mag.
IEEE Computational Intelligence Magazine IEEE Comput. Intell. Mag.
IEEE Computing in Science and Engineering Magazine IEEE Comput. Sci. Eng.
IEEE Computer Applications in Power IEEE Comput. Appl. Power
IEEE Computer Graphics and Applications Magazine IEEE Comput. Graph. Appl. Mag.
IEEE Concurrency IEEE Concurrency
IEEE Consumer Electronics Magazine IEEE Consum. Electron. Mag.
IEEE Control Systems Magazine IEEE Control Syst. Mag.
IEEE Design & Test IEEE Des. Test.
IEEE Des. Test. Comput.* (through 2012)
IEEE Electrical Insulation Magazine IEEE Elect. Insul. Mag.
IEEE Electomagnetic Compatibility Magazine IEEE Electrmagn. Compat.
IEEE Electrification Magazine IEEE Electrific. Mag.
IEEE ElectroTechnology Review IEEE ElectroTechnol. Rev.
IEEE Eng. Med. Biol. Mag. (1982−2009)
IEEE Engineering Management Review IEEE Eng. Manag. Rev.
IEEE Expert (through 1997) IEEE Expert
IEEE Geoscience and Remote Sensing Magazine IEEE Geosci. Remote Sens. Mag. (replaces Newsletter)
IEEE Industrial Electronics Magazine IEEE Ind. Electron. Mag.
IEEE Industry Applications Magazine IEEE Ind. Appl. Mag.
IEEE Instrumentation and Measurement Magazine IEEE Instrum. Meas. Mag.
IEEE Intelligent Systems (formerly IEEE Expert) IEEE Intell. Syst.
IEEE Intelligent Transportation Systems Magazine IEEE Intell. Transp. Syst. Mag.
IEEE Internet Computing Magazine IEEE Internet Comput.
IEEE IT Professional IEEE IT Prof.
IEEE Micro Magazine IEEE Micro
IEEE Microwave Magazine IEEE Microw. Mag.
IEEE MultiMedia IEEE Multimedia Mag.
IEEE Nanotechnology Magazine IEEE Nanotechnol. Mag.
IEEE Network IEEE Netw.
IEEE Personal Communications IEEE Pers. Commun.
IEEE Potentials IEEE Potentials
IEEE Power Electronics Magazine IEEE Power Electron. Mag.
IEEE Power and Energy Magazine IEEE Power Energy Mag.
IEEE Power Engineering Review IEEE Power Eng. Rev.
IEEE Pulse IEEE Pulse
IEEE Robotics and Automation Magazine IEEE Robot. Autom. Mag.
IEEE Signal Processing Magazine (1991–present) IEEE Signal Process. Mag.
List of IEEE Magazines
List of IEEE Magazines
Magazine Reference Abbreviation
G. IEEE Publication Abbreviations
190
pg 7 IEEE Abbreviations for Transactions, Journals, Letters, and Magazines ©2015 IEEE Transactions and Journals Department
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••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
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••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
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IEEE Solid-State Circuits Magazine IEEE Solid State Circuits Mag.
IEEE Security and Privacy IEEE Security Privacy
IEEE Software IEEE Softw.
IEEE Spectrum IEEE Spectr.
IEEE Technology and Society Magazine IEEE Technol. Soc. Mag.
IEEE Vehicular Technology Magazine IEEE Veh. Technol. Mag.
China Communications Magazine China Commun.
Communications Surveys and Tutorials Commun. Surveys Tuts.
Computer Magazine Computer
Internet Computing Internet Comput.
Pervasive Computing Pervasive Comput.
Today’s Engineer Today’s Engineer
Wireless Communications Wireless Commun.
List of IEEE Magazines
Magazine Reference Abbreviation
G. IEEE Publication Abbreviations
191
Appendix H
IEEE INDEX TERMS
192
2014 IEEE
Taxonomy
Version
1.0
Created by
The Institute
of Electrical
and
Electronics
Engineers
(IEEE)
H. IEEE Index Terms
193
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 2
IEEE Taxonomy: A Subset Hierarchical Display of IEEE Thesaurus Terms
The IEEE Taxonomy comprises the first three hierarchical 'levels' under each term-family (or
branch) that is formed from the top-most terms of the IEEE Thesaurus. In this document these
term-families are arranged alphabetically and denoted by boldface type. Each term family's
hierarchy goes to no more than three sublevels, denoted by indents (in groups of four dots)
preceding the next level terms. A term can appear in more than one hierarchical branch and
can appear more than once in any particular hierarchy. The 2014 IEEE Taxonomy is defined in
this way so that it is always a subset of the 2014 IEEE Thesaurus.
Aerospace and electronic systems
....Aerospace control
........Air traffic control
........Attitude control
........Ground support
....Aerospace engineering
........Aerospace biophysics
........Aerospace electronics
........Aerospace safety
............Air safety
........Aerospace simulation
........Aerospace testing
........Satellites
............Artificial satellites
............Earth Observing System
............Low earth orbit satellites
............Moon
............Space stations
........Space technology
............Space exploration
....Aerospace materials
........Aerospace components
....Aircraft manufacture
....Aircraft navigation
....Aircraft propulsion
........Propellers
....Command and control systems
....Electronic warfare
........Electronic countermeasures
........Jamming
........Radar countermeasures
....Military equipment
........Military aircraft
............Payloads
........Military satellites
........Weapons
............Guns
............Missiles
............Nuclear weapons
............Projectiles
....Radar
........Airborne radar
........Bistatic radar
........Doppler radar
........Ground penetrating radar
........Laser radar
........Meteorological radar
........Millimeter wave radar
........Multistatic radar
............MIMO radar
........Passive radar
........Radar applications
............Radar countermeasures
............Radar detection
............Radar imaging
............Radar measurements
............Radar polarimetry
............Radar remote sensing
............Radar tracking
........Radar clutter
........Radar cross-sections
........Radar equipment
........Radar theory
........Spaceborne radar
........Spread spectrum radar
........Synthetic aperture radar
............Inverse synthetic aperture radar
............Polarimetric synthetic aperture
radar
........Ultra wideband radar
....Sensor systems
........Gunshot detection systems
....Sonar
........Sonar applications
............Sonar detection
............Sonar measurements
........Sonar equipment
........Synthetic aperture sonar
....Telemetry
........Biomedical telemetry
H. IEEE Index Terms
194
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 3
Antennas and propagation
....Antennas
........Antenna accessories
........Antenna arrays
............Adaptive arrays
............Butler matrices
............Linear antenna arrays
............Log periodic antennas
............Microstrip antenna arrays
............Microwave antenna arrays
............Phased arrays
............Planar arrays
........Antenna radiation patterns
............Near-field radiation pattern
........Antenna theory
............Frequency selective surfaces
........Apertures
............Aperture antennas
............Aperture coupled antennas
........Broadband antennas
............Ultra wideband antennas
............Vivaldi antennas
........Dielectric resonator antennas
........Dipole antennas
........Directional antennas
........Directive antennas
........Feeds
............Antenna feeds
........Fractal antennas
........Helical antennas
........Horn antennas
........Leaky wave antennas
........Loaded antennas
........Log-periodic dipole antennas
........Microstrip antennas
........Microwave antennas
........Mobile antennas
........Multifrequency antennas
........Omnidirectional antennas
........Patch antennas
........Radar antennas
........Receiving antennas
........Rectennas
........Reflector antennas
........Satellite antennas
........Slot antennas
........Transmission line antennas
........Transmitting antennas
........UHF antennas
........Yagi-Uda antennas
....Electromagnetic propagation
........Electromagnetic diffraction
............Optical diffraction
............Physical theory of diffraction
............X-ray diffraction
........Electromagnetic propagation in
absorbing media
........Electromagnetic reflection
............Optical reflection
........Microwave propagation
........Millimeter wave propagation
........Optical propagation
............Optical surface waves
............Optical waveguides
........Propagation constant
........Propagation losses
........Radio propagation
........Radiowave propagation
........Submillimeter wave propagation
........UHF propagation
....Radio astronomy
Broadcast technology
....Broadcasting
........Digital audio broadcasting
............Digital audio players
............Digital Radio Mondiale
........Digital multimedia broadcasting
........Digital video broadcasting
........Radio broadcasting
............Frequency modulation
............Radio networks
........Satellite broadcasting
........TV broadcasting
Circuits and systems
....Circuits
........Active circuits
............Active inductors
............Gyrators
............Operational amplifiers
........Adders
........Analog circuits
............Analog integrated circuits
............Analog processing circuits
........Application specific integrated circuits
............System-on-chip
........Asynchronous circuits
........Bipolar integrated circuits
............BiCMOS integrated circuits
H. IEEE Index Terms
195
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 4
........Bipolar transistor circuits
............Bipolar integrated circuits
........Bistable circuits
............Latches
........Bridge circuits
........Charge pumps
........Circuit analysis
............Circuit analysis computing
............Coupled mode analysis
............Nonlinear network analysis
........Circuit faults
............Electrical fault detection
........Circuit noise
............Thermal noise
........Circuit simulation
........Circuit synthesis
............High level synthesis
............Integrated circuit synthesis
........Coprocessors
........Counting circuits
........Coupling circuits
........Digital circuits
............Circuit topology
............Digital integrated circuits
........Digital signal processors
........Distributed parameter circuits
........Driver circuits
........Electronic circuits
............Breadboard circuit
............Central Processing Unit
............Stripboard circuit
........Equivalent circuits
........Feedback
............Feedback circuits
............Negative feedback
............Neurofeedback
........Hybrid integrated circuits
........Integrated circuits
............Analog-digital integrated circuits
............Analog integrated circuits
............Application specific integrated
circuits
............Bipolar integrated circuits
............CMOS integrated circuits
............Coprocessors
............Current-mode circuits
............Digital integrated circuits
............FET integrated circuits
............Field programmable gate arrays
............Hybrid integrated circuits
............Integrated circuit interconnections
............Integrated circuit modeling
............Integrated circuit noise
............Integrated circuit synthesis
............Large scale integration
............MESFET integrated circuits
............Microprocessors
............Microwave integrated circuits
............Millimeter wave integrated circuits
............Mixed analog digital integrated
circuits
............Monolithic integrated circuits
............Photonic integrated circuits
............Power integrated circuits
............Radiofrequency integrated circuits
............Submillimeter wave integrated
circuits
............Superconducting integrated circuits
............Thick film circuits
............Thin film circuits
............Three-dimensional integrated
circuits
............Through-silicon vias
............UHF integrated circuits
............Ultra large scale integration
............Very high speed integrated circuits
............Very large scale integration
............Wafer scale integration
........Isolators
........Large scale integration
............Ultra large scale integration
............Very large scale integration
............Wafer scale integration
........Linear circuits
........Logic arrays
............Programmable logic arrays
........Logic circuits
............Combinational circuits
............Logic arrays
............Programmable logic arrays
............Superconducting logic circuits
........Magnetic circuits
........Microprocessors
............Automatic logic units
............Biomimetics
............Coprocessors
............Microcontrollers
............Microprocessor chips
............Vector processors
........Microwave circuits
........Millimeter wave circuits
............Millimeter wave integrated circuits
H. IEEE Index Terms
196
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 5
........Millimeter wave integrated circuits
............MIMICs
........Monolithic integrated circuits
............MIMICs
............MMICs
........MOSFET circuits
............CMOSFET circuits
............MOS integrated circuits
............Power MOSFET
........Multiplying circuits
........Nonlinear circuits
............Nonlinear network analysis
........Passive circuits
........Phase shifters
............Phase transformers
........Power dissipation
........Power integrated circuits
........Printed circuits
............Flexible printed circuits
........Programmable circuits
............Field programmable analog arrays
............Programmable logic arrays
............Programmable logic devices
........Programmable logic arrays
........Programmable logic devices
........Pulse circuits
............Flip-flops
........Radiation detector circuits
........Rail to rail operation
............Rail to rail amplifiers
............Rail to rail inputs
............Rail to rail outputs
........Rectifiers
........RLC circuits
........Sampled data circuits
........Sequential circuits
........Silicon-on-insulator
............Silicon on sapphire
........Submillimeter wave circuits
............Submillimeter wave integrated
circuits
........Summing circuits
........Switched circuits
............Switched capacitor circuits
........Switching circuits
............Choppers (circuits)
............Logic circuits
............Switching converters
............Zero current switching
............Zero voltage switching
........Thick film circuits
........Thin film circuits
........Thyristor circuits
........Time varying circuits
........Trigger circuits
........UHF circuits
............UHF integrated circuits
........UHF integrated circuits
........Ultra large scale integration
........Very large scale integration
............Neuromorphics
............Wafer scale integration
........VHF circuits
........Wafer scale integration
....Contacts
........Brushes
........Contact resistance
........Ohmic contacts
....Filtering
........Filters
............Active filters
............Anisotropic
............Bragg gratings
............Channel bank filters
............Digital filters
............Equalizers
............Filtering theory
............Gabor filters
............Harmonic filters
............IIR filters
............Kalman filters
............Low-pass filters
............Matched filters
............Microstrip filters
............Nonlinear filters
............Particle filters
............Power filters
............Resonator filters
............Spatial filters
............Superconducting filters
............Transversal filters
........Information filtering
............Information filters
............Recommender systems
....Integrated circuit technology
........CMOS technology
............CMOS process
............Silicon on sapphire
........Moore's Law
....Logic devices
........Logic gates
........Programmable logic devices
H. IEEE Index Terms
197
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 6
....Oscillators
........Digital-controlled oscillators
........Injection-locked oscillators
........Local oscillators
........Microwave oscillators
........Phase noise
........Ring oscillators
........Voltage-controlled oscillators
....Single electron devices
........Single electron memory
............Hetero-nanocrystal memory
........Single electron transistors
....Tunable circuits and devices
........RLC circuits
........Tuned circuits
Communications technology
....Communication equipment
........Auditory displays
........Codecs
............Speech codecs
............Video codecs
........Modems
........Optical communication equipment
............Optical transmitters
........Radio communication equipment
............Base stations
............Ham radios
............Land mobile radio equipment
............Radio transceivers
............Transponders
........Receivers
............Optical receivers
............RAKE receivers
............Receiving antennas
........Repeaters
........Speech codecs
........Telephone equipment
............Cellular phones
............Telephone sets
............Vocoders
........Transceivers
............Radio transceivers
........Transmitters
............Auxiliary transmitters
............Diversity methods
............Neurotransmitters
............Optical transmitters
............Radio transmitters
............Transmitting antennas
........Transponders
........TV equipment
............Large screen displays
............TV receivers
........Video codecs
........Video equipment
............Video codecs
........Vocoders
....Communication switching
........Code division multiplexing
........Electronic switching systems
........Frame relay
........Handover
........Multiprotocol label switching
........Packet switching
............Burst switching
............Frame relay
............Multiprotocol label switching
............Packet loss
....Communication systems
........ARPANET
........Biomedical communication
............Biomedical telemetry
............Telemedicine
........Broadband communication
............B-ISDN
............Broadband amplifiers
........Communication networks
............Central office
............Cyberspace
............Industrial communication
............Relay networks
(telecommunications)
............Software defined networking
........Communication system control
............Telecommunication control
........Communication system security
............Radio communication
countermeasures
........Communication system signaling
........Communication system software
............Streaming media
........Communication system traffic
........Communication system traffic control
........Computer networks
............Ad hoc networks
............Computer network management
............Content distribution networks
............Cyberspace
............Diffserv networks
............Domain Name System
H. IEEE Index Terms
198
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 7
............Ethernet networks
............Google
............Internet
............Intserv networks
............IP networks
............Metropolitan area networks
............Multiprocessor interconnection
networks
............Network servers
............Next generation networking
............Overlay networks
............Peer-to-peer computing
............Software defined networking
............Storage area networks
............Token networks
............Unicast
............Virtual private networks
............Wide area networks
........Cross layer design
........Data buses
............Backplanes
........Data communication
............Asynchronous communication
............Asynchronous transfer mode
............Data buses
............Data transfer
............Telecommunication buffers
............Telemetry
............Teleprinting
........Digital communication
............Baseband
............DICOM
............Digital audio broadcasting
............Digital images
............Digital multimedia broadcasting
............Digital video broadcasting
............DSL
............ISDN
............Passband
............Portable media players
............SONET
............Spread spectrum communication
........Facsimile
........FDDI
........Indoor communication
............Indoor environments
........Internet
............Crowdsourcing
............Instant messaging
............Internet of Things
............Internet telephony
............Internet topology
............Middleboxes
............Semantic Web
............Social computing
............Web 2.0
............Web services
........IP networks
............TCPIP
........ISDN
............B-ISDN
........Land mobile radio cellular systems
............Cellular networks
............Paging strategies
........Local area networks
............Wireless LAN
........Machine-to-machine communications
........Metropolitan area networks
........Microwave communication
............Rectennas
........Military communication
............Reconnaissance
........Millimeter wave communication
........MIMO
............Rician channels
........Mobile communication
............3G mobile communication
............4G mobile communication
............Ambient networks
............Dual band
............Land mobile radio
............Land mobile radio cellular systems
............Mobile nodes
............Mobile radio mobility management
............Software radio
........Molecular communication
........Multiaccess communication
............Direct-sequence code-division
multiple access
............Frequency division multiaccess
............Multicarrier code division multiple
access
............Subscriber loops
............Time division multiple access
............Time division synchronous code
division multiple access
........Multicast communication
............Multicast VPN
........Multimedia communication
........Narrowband
........Optical fiber communication
............FDDI
H. IEEE Index Terms
199
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 8
............Optical buffering
............Optical fiber networks
............Optical fiber subscriber loops
............Optical interconnections
............Optical packet switching
............Optical wavelength conversion
............Scheduling algorithms
............SONET
........Personal communication networks
........Protocols
............Access protocols
............Asynchronous transfer mode
............Cryptographic protocols
............Master-slave
............Multicast protocols
............Multiprotocol label switching
............Routing protocols
............Transport protocols
............Wireless application protocol
........Quality of service
............Admission control
........Radio communication
............Baseband
............Bluetooth
............Indoor radio communication
............Land mobile radio
............Land mobile radio cellular systems
............Packet radio networks
............Passband
............Personal area networks
............Radio broadcasting
............Radio communication
countermeasures
............Radio frequency
............Radio link
............Radio spectrum management
............Satellite communication
............Satellite ground stations
............Software radio
............Zigbee
........Routing
............Wavelength routing
........Satellite communication
............Downlink
............Satellite broadcasting
............Satellite ground stations
............Uplink
........Satellite ground stations
........SIMO
........SISO
........Spatial diversity
........Submillimeter wave communication
........Subscriber loops
........Switching systems
............Electronic switching systems
............Switching frequency
............Switching loss
............Telecommunication switching
........Synchronous digital hierarchy
........Telecommunications
............Ambient intelligence
............Feedback communications
............IP networks
............Radio access networks
............Railway communication
............Telecommunication computing
............Telecommunication network
topology
............Telecommunication services
............Telematics
........Teleconferencing
........Telegraphy
........Telephony
........Teleprinting
........Teletext
........Token networks
........UHF communication
........Underwater communication
........Videophone systems
........Videotex
........Visual communication
........Wide area networks
........Wideband
........Wireless communication
............Cognitive radio
............Cooperative communication
............GSM
............Open wireless architecture
............Roaming
............Spatial diversity
............WiMAX
............Wireless application protocol
............Wireless networks
........Wireless mesh networks
........Wireless sensor networks
............Body sensor networks
............Event detection
....Couplers
........Directional couplers
....High-speed electronics
........High-speed integrated circuits
........High-speed networks
H. IEEE Index Terms
200
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 9
........Ultrafast electronics
....Image communication
........Facsimile
........Picture archiving and communication
systems
....Message systems
........Electronic mail
............Unified messaging
............Unsolicited electronic mail
........Electronic messaging
............Instant messaging
............Unified messaging
........Postal services
........Publish subscribe systems
........Voice mail
....Modulation
........Amplitude modulation
............Amplitude shift keying
............Quadrature amplitude modulation
........Chirp modulation
........Demodulation
........Digital modulation
............Constellation diagram
............Partial response signaling
........Frequency modulation
............Frequency shift keying
........Magnetic modulators
........Modulation coding
............Interleaved codes
........Optical modulation
............Electrooptic modulators
............Intensity modulation
........Phase modulation
............Continuous phase modulation
............Differential phase shift keying
............Phase shift keying
........Pulse modulation
........Pulse width modulation
............Pulse width modulation inverters
............Space vector pulse width
modulation
....Multiplexing
........Code division multiplexing
........Demultiplexing
........Frequency division multiplexing
........Multiplexing equipment
............Add-drop multiplexers
........OFDM
............Multiple access interference
............OFDM modulation
............Partial transmit sequences
............Peak to average power ratio
........Time division multiplexing
........Wavelength division multiplexing
............WDM networks
....Network topology
........Complex networks
........Computer network reliability
....Presence network agents
....TV
........Cable TV
........Digital TV
............Analog TV
............HDTV
............IPTV
........Mobile TV
........Three-dimensional television
....UHF technology
........UHF antennas
........UHF circuits
............UHF integrated circuits
........UHF communication
........UHF devices
........UHF integrated circuits
....Ultra wideband technology
........Ultra wideband antennas
........Ultra wideband communication
........Ultra wideband radar
....VHF devices
Components, packaging, and
manufacturing technology
....Component architectures
....Electronic components
........Capacitors
............Power capacitors
............Varactors
........Coils
............Superconducting coils
........Connectors
............Plugs
............Sockets
........Diodes
............Diode lasers
........Electrodes
............Anodes
............Cathodes
............Microelectrodes
........Fuses
........Inductors
............Active inductors
H. IEEE Index Terms
201
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 10
............Thick film inductors
............Thin film inductors
........Resistors
............Memristors
............Switched capacitor networks
............Varistors
........Structural plates
........Switches
............Contactors
............Microswitches
............Optical switches
........Transducers
............Acoustic transducers
............Biomedical transducers
............Chemical transducers
............Piezoelectric transducers
............Ultrasonic transducer arrays
....Electronic equipment manufacture
........Damascene integration
........Micromachining
........Radiation hardening (electronics)
........Semiconductor device manufacture
............Diffusion processes
............Flip-chip devices
............High-K gate dielectrics
............Quasi-doping
............Semiconductor device doping
............Semiconductor epitaxial layers
............Semiconductor growth
............Silicidation
............Wafer bonding
....Electronics packaging
........Chip scale packaging
....Environmentally friendly manufacturing
techniques
....Integrated circuit manufacture
........Surface-mount technology
....Integrated circuit packaging
........Multichip modules
........Plastic integrated circuit packaging
....Semiconductor device packaging
....Thermal management of electronics
........Electronic packaging thermal
management
........Electronics cooling
Computational and artificial intelligence
....Artificial intelligence
........Context awareness
........Cooperative systems
........Decision support systems
........Intelligent systems
............Intelligent robots
........Knowledge based systems
............Expert systems
............Mobile agents
........Knowledge engineering
............Inference mechanisms
............Knowledge acquisition
............Knowledge discovery
............Knowledge representation
........Learning (artificial intelligence)
............Distance learning
............Electronic learning
........Learning systems
............Backpropagation
............Learning automata
............Semisupervised learning
............Supervised learning
............Unsupervised learning
........Machine learning
............Boosting
............Statistical learning
........Prediction methods
............Linear predictive coding
............Predictive coding
............Predictive encoding
............Predictive models
....Autonomous mental development
....Computational intelligence
........Computation theory
............Computational complexity
............Concurrent computing
............Greedy algorithms
............Support vector machines
........Evolutionary computation
............Particle swarm optimization
........Fuzzy systems
............Fuzzy control
............Fuzzy neural networks
............Hybrid intelligent systems
........Genetic algorithms
....Logic
........Fuzzy logic
............Fuzzy cognitive maps
............Takagi-Sugeno model
........Multivalued logic
........Probabilistic logic
........Sufficient conditions
....Machine intelligence
........Pattern analysis
H. IEEE Index Terms
202
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 11
....Neural networks
........Artificial neural networks
............Hebbian theory
............Self-organizing feature maps
........Biological neural networks
........Cellular neural networks
........Feedforward neural networks
............Multilayer perceptrons
........Multi-layer neural network
........Neural network hardware
........Radial basis function networks
........Recurrent neural networks
............Hopfield neural networks
Computers and information processing
....Computer applications
........Affective computing
........Application virtualization
........Computer aided analysis
........Computer aided engineering
........Computer aided instruction
........Computer generated music
........Computer integrated manufacturing
........Control engineering computing
........Green computing
........High energy physics instrumentation
computing
............Linear particle accelerator
........Knowledge management
............Knowledge transfer
........Medical information systems
............Electronic medical records
........Military computing
........Physics computing
........Power engineering computing
........Power system analysis computing
........Publishing
............Bibliometrics
............Company reports
............Desktop publishing
............Electronic publishing
............Open Access
............Scientific publishing
........Scientific computing
........Telecommunication computing
............Internetworking
............Soft switching
........Virtual enterprises
........Virtual manufacturing
............Virtual machining
........Web sites
............Facebook
............MySpace
............Uniform resource locators
............Web design
............YouTube
........World Wide Web
............Mashups
....Computer architecture
........Accelerator architectures
........Data structures
............Arrays
............Binary decision diagrams
............Null value
............Octrees
............Table lookup
............Tree data structures
........Dynamic voltage scaling
........Memory architecture
........Memory management
........Multiprocessor interconnection
............Hypercubes
........Parallel architectures
............Multicore processing
........Reconfigurable architectures
....Computer interfaces
........Application programming interfaces
............WebRTC
........Browsers
........Field buses
........Firewire
........Haptic interfaces
............Data gloves
............Force feedback
............Grasping
........Hypertext systems
........Interface phenomena
............Network interfaces
........Interface states
........Musical instrument digital interfaces
........Ports (Computers)
........System buses
....Computer networks
........Ad hoc networks
............AODV
............Mesh networks
............Mobile ad hoc networks
............Vehicular ad hoc networks
........Computer network management
............Computer network reliability
............Disruption tolerant networking
H. IEEE Index Terms
203
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 12
............Management information base
............Middleboxes
............Network address translation
............Network synthesis
........Content distribution networks
........Cyberspace
........Diffserv networks
........Domain Name System
........Ethernet networks
............EPON
........Google
........Internet
............Crowdsourcing
............Instant messaging
............Internet of Things
............Internet telephony
............Internet topology
............Middleboxes
............Semantic Web
............Social computing
............Web 2.0
............Web services
........Intserv networks
........IP networks
............TCPIP
........Metropolitan area networks
........Multiprocessor interconnection
networks
........Network servers
........Next generation networking
........Overlay networks
........Peer-to-peer computing
........Software defined networking
........Storage area networks
........Token networks
........Unicast
........Virtual private networks
............Extranets
........Wide area networks
....Computer performance
........Computer errors
............Computer crashes
........Performance loss
....Computer peripherals
........Disk drives
........Keyboards
........Modems
........Printers
....Computers
........Analog computers
........Calculators
............Difference engines
........Microcomputers
............Portable computers
............Workstations
........Parallel machines
........Supercomputers
........Tablet computers
........Wearable computers
....Computer science
........Formal languages
............Computer languages
............Runtime library
........Network theory (graphs)
........Programming
............Augmented reality
............Automatic programming
............Concatenated codes
............Functional programming
............Granular computing
............Integer linear programming
............Logic programming
............Microprogramming
............Object oriented methods
............Object oriented programming
............Opportunistic software systems
development
............Parallel programming
............Performance analysis
............Programming profession
............Robot programming
....Concurrency control
........Processor scheduling
............Scheduling algorithms
....Database machines
....Data systems
........Data acquisition
............Fastbus
............User-generated content
........Data compression
............Adaptive coding
............Audio compression
............Huffman coding
............Source coding
............Test data compression
............Transform coding
........Data conversion
............Analog-digital conversion
............Digital-analog conversion
........Data engineering
........Data handling
............Data assimilation
H. IEEE Index Terms
204
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 13
............Data encapsulation
............Document handling
............Merging
............Sorting
........Data processing
............Associative processing
............Business data processing
............Data analysis
............Data collection
............Data integration
............Data preprocessing
............Data transfer
............Information exchange
............Spreadsheet programs
............Text processing
............Virtual enterprises
........Data storage systems
........Data warehouses
....Digital systems
........Internet
............Crowdsourcing
............Instant messaging
............Internet of Things
............Internet telephony
............Internet topology
............Middleboxes
............Semantic Web
............Social computing
............Web 2.0
............Web services
........ISDN
............B-ISDN
........Local area networks
............Wireless LAN
........Metropolitan area networks
........Token networks
....Distributed computing
........Client-server systems
............Middleware
............Servers
........Collaborative work
............Cooperative communication
............Crowdsourcing
............Social computing
........Diffserv networks
........Distributed databases
........Distributed information systems
............Publish-subscribe
........Internet
............Crowdsourcing
............Instant messaging
............Internet of Things
............Internet telephony
............Internet topology
............Middleboxes
............Semantic Web
............Social computing
............Web 2.0
............Web services
........Metacomputing
............Grid computing
........Peer-to-peer computing
....DNA computing
....File servers
....Hardware
........Open source hardware
....High performance computing
....Image processing
........Active shape model
........Feature extraction
........Geophysical image processing
........Gray-scale
........Image analysis
............Image classification
............Image motion analysis
............Image quality
............Image sequence analysis
............Image texture analysis
............Object detection
............Subtraction techniques
........Image coding
........Image color analysis
........Image decomposition
........Image denoising
........Image enhancement
........Image fusion
........Image generation
............Plasma displays
............Visual effects
........Image recognition
............Image edge detection
........Image reconstruction
........Image registration
........Image representation
........Image resolution
............High-resolution imaging
............Spatial resolution
........Image restoration
........Image sampling
........Image segmentation
........Image sequences
........Image texture
H. IEEE Index Terms
205
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 14
........Machine vision
............Object recognition
............Object segmentation
........Morphological operations
........Optical feedback
........Smart pixels
........Spatial coherence
........Table lookup
....Memory
........Analog memory
........Associative memory
........Buffer storage
............Computer buffers
........Cache memory
............Cache storage
........Content addressable storage
........Flash memories
............Flash memory cells
........Magnetic memory
............Floppy disks
............Hard disks
........Memory management
........Nonvolatile memory
............Nonvolatile single electron memory
........Phase change memory
............Phase change random access
memory
........Random access memory
............DRAM chips
............Phase change random access
memory
............SDRAM
............SRAM cells
............SRAM chips
........Read only memory
............PROM
........Read-write memory
........Registers
............Shift registers
........Scanning probe data storage
........Semiconductor memory
....Mobile computing
....Molecular computing
....Multitasking
........Parametric study
....Open systems
........Open Access
............Public domain software
........Physical layer
....Optical computing
....Parallel processing
........Multiprocessing systems
............Data flow computing
............Processor scheduling
............Systolic arrays
........Multithreading
........Parallel algorithms
........Pipeline processing
....Pattern recognition
........Active shape model
........Character recognition
........Clustering methods
............Pattern clustering
........Data mining
............Association rules
............Data privacy
............Text analysis
............Text mining
............Web mining
........Face recognition
........Fingerprint recognition
........Gesture recognition
............Sign language
........Handwriting recognition
............Forgery
........Pattern matching
............Image matching
........Speech recognition
............Automatic speech recognition
............Speech analysis
........Text recognition
....Pervasive computing
........Ubiquitous computing
............Context-aware services
........Wearable computers
....Petascale computing
....Platform virtualization
....Quantum computing
........Quantum cellular automata
....Real-time systems
........WebRTC
....Software
........Application software
........Embedded software
........Middleware
............Mediation
............Message-oriented middleware
............Web services
........Open source software
........Optical character recognition software
........Public domain software
........Software agents
H. IEEE Index Terms
206
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 15
............Autonomous agents
............Intelligent agents
........Software as a service
........Software debugging
............Software design
........Software maintenance
........Software packages
............EMTDC
............MATLAB
............PSCAD
............SPICE
........Software performance
........Software quality
........Software reusability
........Software safety
........Software systems
........Software tools
............Authoring systems
........System software
............File systems
............Operating systems
............Program processors
............Utility programs
....Software engineering
........Capability maturity model
........Computer aided software engineering
........Formal verification
........Programming environments
........Reasoning about programs
........Runtime
............Dynamic compiler
............Runtime environment
........Software architecture
............Client-server systems
............Microarchitecture
............Representational state transfer
........Software libraries
....System recovery
........Checkpointing
........Core dumps
........Debugging
....Time sharing computer systems
....Virtual machine monitors
Consumer electronics
....Ambient intelligence
....Audio systems
........Audio-visual systems
........Auditory displays
........Headphones
........Loudspeakers
........Microphones
............Microphone arrays
........Portable media players
........Sonification
....Home automation
........Portable media players
........Refrigerators
........Smart homes
........Washing machines
....Home computing
....Low-power electronics
....Microwave ovens
....Multimedia systems
........Multimedia communication
........Multimedia computing
........Multimedia databases
Control systems
....Automatic control
........Power generation control
....Automatic generation control
....Bidirectional control
....CAMAC
....Centralized control
....Closed loop systems
....Control design
....Control engineering
....Control equipment
........Actuators
............Electrostatic actuators
............Hydraulic actuators
............Intelligent actuators
............Microactuators
............Piezoelectric actuators
............Pneumatic actuators
........Fasteners
........Microcontrollers
........Regulators
........Servosystems
............Servomotors
........Switches
............Contactors
............Microswitches
............Optical switches
........Switchgear
............Circuit breakers
............Interrupters
............Relays
........Telecontrol equipment
H. IEEE Index Terms
207
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 16
........Thermostats
....Controllability
....Control system synthesis
....Decentralized control
........Distributed parameter systems
....Delay systems
........Added delay
........Delay lines
....Digital control
........Programmable control
............Flow graphs
....Feedback
........Feedback circuits
............Output feedback
........Negative feedback
........Neurofeedback
....Fluid flow control
....Fluidics
........Microfluidics
........Nanofluidics
....Linear feedback control systems
........Frequency locked loops
........Phase locked loops
........State feedback
........Tracking loops
....Magnetic variables control
....Mechanical variables control
........Displacement control
........Force control
........Level control
............Gyroscopes
........Motion control
............Collision avoidance
............Collision mitigation
............Kinetic theory
............Motion planning
............Path planning
............Visual servoing
........Position control
............Nanopositioning
........Shape control
........Size control
........Strain control
........Stress control
........Thickness control
........Torque control
........Velocity control
............Angular velocity control
........Vibration control
........Weight control
....Medical control systems
....Moisture control
........Humidity control
....Motion compensation
....Networked control systems
....Nonlinear control systems
....Open loop systems
....Optical control
........Lighting control
........Optical variables control
....Optimal control
........Bang-bang control
........Infinite horizon
....PD control
....Pi control
....Pneumatic systems
....Pressure control
....Proportional control
....Radio control
....Robot control
........Robot motion
....SCADA systems
....Sensorless control
....Sliding mode control
....Supervisory control
........SCADA systems
....Thermal variables control
........Temperature control
............Cooling
............Heating
........Thermal analysis
............Thermomechanical processes
....Traffic control
........Queueing analysis
........Vehicle routing
Dielectrics and electrical insulation
....Dielectrics
........Dielectric constant
............High-K gate dielectrics
........Dielectric devices
............Capacitors
............Ferroelectric devices
............Piezoelectric devices
............Pyroelectric devices
........Dielectric losses
........Dielectric substrates
........Dielectrophoresis
........Electrohydrodynamics
........Electrokinetics
........Electrostriction
H. IEEE Index Terms
208
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 17
....Electric breakdown
........Avalanche breakdown
........Corona
........Dielectric breakdown
............Arc discharges
............Discharges (electric)
............Electrostatic discharges
............Flashover
............Glow discharges
............Partial discharges
............Surface discharges
............Vacuum breakdown
........Sparks
....Insulation
........Cable insulation
............Power cable insulation
........Ceramics
............Porcelain
........Gas insulation
............Sulfur hexafluoride
........Insulators
............Metal-insulator structures
............Plastic insulators
............Rubber
............Topological insulators
............Trees - insulation
........Isolation technology
........Oil insulation
............Oil filled cables
........Plastic insulation
Education
....Computer science education
....Continuing education
........Education courses
....Educational institutions
....Educational technology
........Computer aided instruction
........Courseware
........Electronic learning
....Engineering education
........Biomedical engineering education
........Communication engineering education
........Control engineering education
........Electrical engineering education
............Electronics engineering education
........Engineering students
........Power engineering education
........Student experiments
........Systems engineering education
....Physics education
....Power engineering education
....Qualifications
....Training
........Industrial training
........Management training
........On the job training
........Vocational training
Electromagnetic compatibility and
interference
....Electromagnetic compatibility
........Immunity testing
........Reverberation chambers
....Electromagnetics
........Electromagnetic analysis
............Air gaps
............Computational electromagnetics
............Delay effects
............Electromagnetic fields
............Electromagnetic forces
............Electromagnetic refraction
............Permeability
............Spark gaps
............Time-domain analysis
........Electromagnetic coupling
............Mutual coupling
............Optical coupling
........Electromagnetic devices
........Electromagnetic induction
............Eddy currents
............Inductive power transmission
........Electromagnetic metamaterials
........Electromagnetic radiation
............Correlators
............Electromagnetic wave absorption
............Frequency
............Gamma-rays
............Line-of-sight propagation
........Electromagnetic shielding
............Cable shielding
............Magnetic shielding
........Electromagnetic transients
............EMP radiation effects
............EMTDC
............EMTP
............Power system transients
............Surges
........Proximity effects
....Interference
H. IEEE Index Terms
209
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 18
........Clutter
........Crosstalk
........Diffraction
........Echo interference
........Electromagnetic interference
............Radiofrequency interference
............Specific absorption rate
........Electromagnetic radiative interference
........Electrostatic interference
............Immunity testing
........Interchannel interference
........Interference cancellation
........Interference channels
........Interference constraints
........Interference elimination
........Interference suppression
........Intersymbol interference
........Rain fading
........Terrain factors
........TV interference
Electron devices
....Cathode ray tubes
....Electron guns
....Electron multipliers
....Electron tubes
........Field emitter arrays
........Klystrons
........Magnetrons
........Thyratrons
....Mechatronics
........Biomechatronics
....Microelectromechanical systems
........Microelectromechanical devices
............Microactuators
............Micromotors
............Micropumps
............Microvalves
........Radiofrequency
microelectromechanical systems
....Microfluidics
....Micromechanical devices
........Biomedical microelectromechanical
systems
........Fluidic microsystems
........Microfabrication
....Photoelectricity
........Photovoltaic effects
............Shunts (electrical)
....Photovoltaic cells
........Light trapping
....Quantum computing
........Quantum cellular automata
....Quantum well devices
........Quantum well lasers
............Quantum cascade lasers
........Quantum wells
........Two dimensional hole gas
....Semiconductivity
....Semiconductor devices
........Flip-chip devices
........Gunn devices
........Hall effect devices
........Junctions
............Heterojunctions
............Hybrid junctions
............P-n junctions
............Waveguide junctions
........MIS devices
............Charge coupled devices
............MOS devices
........MONOS devices
........Piezoresistive devices
........P-i-n diodes
........Power semiconductor devices
............Power transistors
........Power semiconductor switches
............Bipolar transistors
............Thyristors
........Quantum dots
........Quantum well lasers
............Quantum cascade lasers
........Schottky diodes
........Semiconductor counters
........Semiconductor detectors
........Semiconductor device modeling
........Semiconductor device noise
........Semiconductor diodes
............P-i-n diodes
............Schottky diodes
............Semiconductor-metal interfaces
............Superluminescent diodes
............Varactors
........Semiconductor-insulator interfaces
........Semiconductor lasers
............Laser tuning
............Quantum dot lasers
............Quantum well lasers
............Semiconductor laser arrays
............Semiconductor optical amplifiers
............Surface emitting lasers
H. IEEE Index Terms
210
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 19
........Semiconductor waveguides
........Silicon devices
........SONOS devices
........Superluminescent diodes
........Surface emitting lasers
............Vertical cavity surface emitting
lasers
........Thermistors
........Transistors
............Field effect transistors
............Heterojunction bipolar transistors
............Millimeter wave transistors
............Phototransistors
....Single electron devices
........Single electron memory
............Hetero-nanocrystal memory
........Single electron transistors
....Thick film devices
........Thick film inductors
....Thin film devices
........Film bulk acoustic resonators
........Thin film inductors
........Thin film transistors
............Organic thin film transistors
....Tunneling
........Gate leakage
........Josephson effect
........Magnetic tunneling
........Resonant tunneling devices
........Tunneling magnetoresistance
....Vacuum technology
........Photomultipliers
........Vacuum systems
............Gettering
Electronic design automation and
methodology
....Design automation
........CADCAM
........Logic design
............Reconfigurable logic
........PSCAD
....Design methodology
........Design for disassembly
........Design for experiments
........Design for manufacture
........Design for quality
........Design for testability
........Graphics
............Animation
............Art
............Character generation
............Computer graphics
............Engineering drawings
............Layout
............Shape
............Symbols
............Virtual reality
............Visualization
........Green design
............Ecodesign
............Green computing
........Process design
............Pattern formation
........Product design
........Prototypes
........Technical drawing
........Time to market
........User centered design
........Virtual prototyping
Engineering - general
....Acoustical engineering
....Agricultural engineering
....Chemical engineering
....Civil engineering
........Railway engineering
............Railway safety
........Structural engineering
............Offshore installations
....Concurrent engineering
....Design engineering
....Electrical engineering
........Electrical engineering computing
....Engineering profession
....Maintenance engineering
........Predictive maintenance
........Preventive maintenance
............Condition monitoring
....Mechanical engineering
........Mechanical power transmission
............Torque converters
........Mechanical systems
............Mechanical energy
............Micromechanical devices
....Precision engineering
....Production engineering
........Production planning
............Capacity planning
............Materials requirements planning
H. IEEE Index Terms
211
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 20
............Process planning
....Research and development
....Reverse engineering
....Sanitary engineering
....Standardization
........Formal specifications
........Guidelines
........Standards
............ANSI standards
............Code standards
............Communication standards
............IEC standards
............IEEE standards
............ISO standards
............Measurement standards
............Military standards
............Software standards
............Standards activities board
............Standards organizations
............Telecommunication standards
............Universal Serial Bus
....Thermal engineering
Engineering in medicine and biology
....Bioinformatics
....Biology
........Biochemistry
............Amino acids
............Biochemical analysis
............Peptides
............Proteins
........Biodiversity
............Biogeography
........Bioelectric phenomena
............Electric shock
........Biological cells
............Cells (biology)
............Chromosome mapping
............Fibroblasts
............RNA
............Stem cells
........Biological information theory
........Biological processes
............Biological interactions
............Chronobiology
............Circadian rhythm
............Coagulation
............Symbiosis
........Biological system modeling
........Biological systems
............Anatomy
............Molecular communication
............Organisms
........Biology computing
........Biophotonics
........Biophysics
............Aerospace biophysics
............Biomagnetics
............Cellular biophysics
............Molecular biophysics
........Evolution (biology)
............Memetics
............Phylogeny
........Genetics
............DNA
............Gene therapy
............Genetic communication
............Genetic expression
............Genetic programming
............Genomics
........Microinjection
........Nanobioscience
............DNA computing
............Nanobiotechnology
........Physiology
........Predator prey systems
........Synthetic biology
........Systematics
........Systems biology
........Vegetation
............Crops
............Marine vegetation
........Zoology
............Animals
....Biomedical communication
........Biomedical telemetry
........Telemedicine
....Biomedical computing
........Biomedical informatics
........Medical expert systems
........Medical information systems
............Electronic medical records
....Biomedical engineering
........Bioimpedance
........Biological techniques
........Biomedical applications of radiation
........Biomedical electronics
........Biomedical signal processing
............Biomedical image processing
........Biotechnology
........Cloning
H. IEEE Index Terms
212
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 21
........Drug delivery
............Targeted drug delivery
........Neural engineering
............Neural microtechnology
............Neural nanotechnology
............Neural prosthesis
........Protein engineering
........Tissue engineering
............Regeneration engineering
....Biomedical equipment
........Assistive technology
............Assistive devices
............Wheelchairs
........Biomedical electrodes
........Biomedical telemetry
........Biomedical transducers
........Catheters
........Cybercare
........Endoscopes
........Gerontechnology
........Hypodermic needles
........Implantable biomedical devices
........Implants
............Auditory implants
............Brainstem implants
............Cochlear implants
............Microelectronic implants
........Intracranial pressure sensors
........Lithotriptors
........Pacemakers
........Stethoscope
........Surgical instruments
............Laparoscopes
....Biomedical imaging
........Angiocardiography
........Angiography
........Biomedical optical imaging
........Cardiography
............Echocardiography
............Electrocardiography
............Phonocardiography
........DICOM
........Encephalography
........Mammography
........Medical diagnostic imaging
............Anatomical structure
........Molecular imaging
........Phantoms
....Bionanotechnology
....Bioterrorism
....Computational biology
........Computational biochemistry
........Computational biophysics
........Computational systems biology
....Genetic engineering
....Medical services
........Assisted living
........Catheterization
........Clinical diagnosis
........Cybercare
........Health information management
........Hospitals
........In vitro
............In vitro fertilization
........In vivo
........Medical conditions
............Aneurysm
............Arteriosclerosis
............Arthritis
............Atrophy
............Blindness
............Cancer
............Deafness
............Diabetes
............Diseases
............Epilepsy
............Hemorrhaging
............Hypertension
............Hyperthermia
............Influenza
............Injuries
............Pregnancy
............Retinopathy
............Sleep apnea
............Thrombosis
............Tumors
........Medical diagnosis
............Autopsy
............Bronchoscopy
............Colonography
............Computer aided diagnosis
............Medical signal detection
............Nanomedicine
............Plethysmography
............Sensitivity and specificity
........Medical tests
............Amniocentesis
............Biopsy
............Cancer detection
............Colonoscopy
............Pregnancy test
........Medical treatment
H. IEEE Index Terms
213
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 22
............Anesthesia
............Angioplasty
............Brachytherapy
............Brain stimulation
............Cardiology
............Chemotherapy
............Clinical trials
............Defibrillation
............Dentistry
............Electrical stimulation
............Electronic medical prescriptions
............Embolization
............Fibrillation
............Gastroenterology
............Gerontology
............Gynecology
............Hepatectomy
............Hospitals
............Hyperthermia
............Lithotripsy
............Magnetic stimulation
............Neonatology
............Neuromuscular stimulation
............Neutron capture therapy
............Noninvasive treatment
............Oncology
............Orthopedic procedures
............Orthotics
............Pathology
............Patient rehabilitation
............Pediatrics
............Pharmaceuticals
............Surgery
........Occupational medicine
........Prosthetics
............Artificial biological organs
............Artificial limbs
............Prosthetic hand
............Prosthetic limbs
............Visual prosthesis
........Public healthcare
........Sensory aids
............Hearing aids
........Vaccines
........X-rays
............X-ray applications
............X-ray detection
............X-ray scattering
............X-ray tomography
....Nuclear medicine
....Synthetic biology
Engineering management
....Business
........Business data processing
........Industrial relations
........Management
............Asset management
............Best practices
............Business continuity
............Business process re-engineering
............Communication system operations
and management
............Content management
............Contingency management
............Contracts
............Customer relationship management
............Decision making
............Enterprise resource planning
............Facilities management
............Financial management
............Governmental factors
............Human resource management
............Information management
............International collaboration
............Knowledge management
............Marketing management
............Organizational aspects
............Outsourcing
............Process planning
............Production management
............Project management
............Public relations
............Quality management
............Research and development
management
............Resource management
............Risk analysis
............Storage management
............Supply chain management
........Operations research
............Inventory control
............Virtual enterprises
........Organizations
............BNSC
............Companies
............Government
............Sociotechnical systems
....Commercialization
....Economics
........Costs
............Cost benefit analysis
........Econometrics
H. IEEE Index Terms
214
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 23
............Economic forecasting
........Economic indicators
............Share prices
........Electronic commerce
........Environmental economics
............Carbon tax
........Exchange rates
........Fuel economy
........International trade
........Macroeconomics
............Privatization
........Microeconomics
............Economies of scale
............Industrial economics
........Monopoly
........Oligopoly
........Power generation economics
............Electricity supply industry
deregulation
........Profitability
........Stock markets
........Supply and demand
........Trade agreements
........Venture capital
........Virtual enterprises
....Innovation management
....Legal factors
........Copyright protection
............Software protection
........Law
............Censorship
............Commercial law
............Consumer protection
............Contract law
............Criminal law
............Employment law
............Forensics
............Law enforcement
............Patent law
............Trademarks
........Law enforcement
........Patents
........Product liability
............Warranties
........Software protection
........Trademarks
....Market research
....Product development
........Graphical user interfaces
............Avatars
........Product customization
........Product life cycle management
............Prognostics and health
management
........Time to market
....Project engineering
........Scheduling
............Adaptive scheduling
............Dynamic scheduling
............Job shop scheduling
............Single machine scheduling
....Research and development
management
........Innovation management
....Research initiatives
....Software development management
........Agile software development
............Scrum (Software development)
....Technology management
Geoscience and remote sensing
....Environmental factors
........Biosphere
........Ecosystems
........Environmental economics
............Carbon tax
........Environmental monitoring
........Global warming
........Green products
............Green buildings
............Green cleaning
........Pollution
............Air pollution
............Industrial pollution
............Land pollution
............Oil pollution
............Radioactive pollution
............Thermal pollution
............Urban pollution
............Water pollution
....Geographic information systems
........Geospatial analysis
........Gunshot detection systems
....Geophysical measurements
........Geodesy
............Level measurement
........Sea measurements
............Geoacoustic inversion
........Seismic measurements
....Geophysical measurement techniques
....Geophysical signal processing
H. IEEE Index Terms
215
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 24
....Geoscience
........Antarctica
............South Pole
........Arctic
............North Pole
........Atmosphere
............Atmospheric modeling
............Atmospheric waves
........Biosphere
........Continents
............Africa
............Asia
............Australia
............Europe
............North America
............South America
........Cyclones
............Hurricanes
............Tropical cyclones
........Earth
........Earthquakes
............Earthquake engineering
........Forestry
........Geoengineering
........Geography
............Cities and towns
............Rural areas
............Urban areas
........Geology
............Minerals
............Rocks
........Geophysics
............EMTDC
............Extraterrestrial phenomena
............Geodynamics
............Geophysics computing
............Meteorology
............Moisture
............Seismology
............Surface waves
............Well logging
........Ice
............Ice shelf
............Ice surface
............Ice thickness
............Sea ice
........Lakes
........Land surface
........Levee
........Meteorological factors
........Oceans
............Ocean salinity
............Ocean temperature
............Sea coast
............Sea floor
............Sea level
............Sea surface
............Tides
........Rivers
........Sediments
........Soil
............Soil moisture
............Soil properties
............Soil texture
........Tornadoes
........Tsunami
........Volcanoes
............Planetary volcanoes
............Volcanic activity
............Volcanic ash
....Land surface temperature
....Photometry
....Radar
........Airborne radar
........Bistatic radar
........Doppler radar
........Ground penetrating radar
........Laser radar
........Meteorological radar
........Millimeter wave radar
........Multistatic radar
............MIMO radar
........Passive radar
........Radar applications
............Radar countermeasures
............Radar detection
............Radar imaging
............Radar measurements
............Radar polarimetry
............Radar remote sensing
............Radar tracking
........Radar clutter
........Radar cross-sections
........Radar equipment
........Radar theory
........Spaceborne radar
........Spread spectrum radar
........Synthetic aperture radar
............Inverse synthetic aperture radar
............Polarimetric synthetic aperture
radar
........Ultra wideband radar
H. IEEE Index Terms
216
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 25
....Radiometry
........Microwave radiometry
........Radiometers
............Spectroradiometers
....Remote sensing
........Hyperspectral sensors
............Hyperspectral imaging
........Passive microwave remote sensing
........Remote monitoring
....Terrain mapping
........Digital elevation models
....Terrestrial atmosphere
........Clouds
........Global warming
........Ionosphere
........Magnetosphere
....Vegetation mapping
IEEE organizational topics
....IEEE activities
........Awards activities
............Corporate recognition awards
............External awards
............Honorary membership
............Medals
............Prize paper awards
............Scholarships
............Service awards
............Student awards
............Technical field awards
........Conferences
........Corporate activities
............Calendars
............Ethics
............Finance
............Legislation
............Meetings
............Member relations
............Membership development
............Motion-planning
............Planning
............Public relations
............Strategic planning
............Technology planning
........Educational activities
............Accreditation
............Career development
............Continuing education
............Curriculum development
............Educational programs
............Scholarships
........Intersociety activities
........Local activities
........Member and Geographic Activities
............Conferences
............Meetings
........Nominations and elections
........Organizing
........Professional activities
............Career development
............Certification
............Consortia
............Continuing education
............Employment
............Ethics
............Intellectual property
............Legislation
............Meetings
............Professional aspects
............Public policy
........Publishing activities
............Books
............CD-ROMs
............Conference proceedings
............Indexes
............Standards publication
........Standards activities
............Standards development
............Standards publication
........Student activities
........Technical activities
............Conferences
............Meetings
............Technical Activities Guide - TAG
........United States activities
............Career development
............Continuing education
............Employment
............Ethics
............Intellectual property
............Legislation
............PACE network
............Public policy
........Volunteer activities
............Audit Committee
............Board of Directors Awards Board
Committee
............Credentials Committee
............Ethics Committee
............Executive Committee
............Fellow Committee
H. IEEE Index Terms
217
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 26
............Life Members Committee
............Member Conduct Committee
............Nominations and elections
............Strategic Planning Committee
............Tellers Committee
............Women in Engineering Committee
....IEEE entities
........Boards
............Board of Directors
............Educational Activities Board
............IEEE Press Editorial Board
............IEEE Spectrum Editorial Board
............Member and Geographic Activities
Board
............Proceedings Editorial Board
............Publications Board
............Standards Board
............Technical Activities Board
............The Institute Editorial Board
............United States Activities Board
........Center for the History of Electrical
Engineering
............History
........Chapters
............Student Chapters
........Committees
............Awards committees
............Board committees
........Communities
............New Technology Connections
Portal
............Online Communities/Technical
Collaboration
............Standards Working Groups
........Councils
............Accreditation Policy Council
............Career Policy Council
............Geographic Councils
............IEEE Biometrics Council
............IEEE Council on Electronic Design
Automation
............IEEE Council on Superconductivity
............IEEE Nanotechnology Council
............IEEE Sensors Council
............IEEE Systems Council
............IEEE Technology Management
Council
............Lifelong Learning Council
............Member Activities Council
............Metropolitan Councils
............Nanotechnology Council
............Operations Council
............Outreach Council
............Professional Activities Council
............Systems Council
............Technical Councils
............Technical Field Awards Council
............Technology Policy Council
........IEEE Computer Society Press
........IEEE Foundation
........IEEE Press
........Regions
............Chapters
............Region 1
............Region 10
............Region 2
............Region 3
............Region 4
............Region 5
............Region 6
............Region 7
............Region 8
............Region 9
............Sections
............Student Chapters
........Sections
............Chapters
............Student Chapters
........Societies
............IEEE Aerospace and Electronic
Systems Society
............IEEE Antennas and Propagation
Society
............IEEE Broadcast Technology
Society
............IEEE Circuits and Systems Society
............IEEE Communications Society
............IEEE Components, Packaging, and
Manufacturing Technology Society
............IEEE Computational Intelligence
Society
............IEEE Computer Society
............IEEE Consumer Electronics Society
............IEEE Control Systems Society
............IEEE Dielectrics and Electrical
Insulation Society
............IEEE Education Society
............IEEE Electromagnetic Compatibility
Society
............IEEE Electron Devices Society
............IEEE Engineering in Medicine and
Biology Society
H. IEEE Index Terms
218
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 27
............IEEE Engineering Management
Society
............IEEE Geoscience and Remote
Sensing Society
............IEEE Industrial Electronics Society
............IEEE Industry Applications Society
............IEEE Information Theory Society
............IEEE Instrumentation and
Measurement Society
............IEEE Intelligent Transportation
Systems Society
............IEEE Lasers and Electro-Optics
Society
............IEEE Magnetics Society
............IEEE Microwave Theory and
Techniques Society
............IEEE Nuclear and Plasma Sciences
Society
............IEEE Oceanic Engineering Society
............IEEE Photonics Society
............IEEE Power Electronics Society
............IEEE Power & Energy Society
............IEEE Reliability Society
............IEEE Robotics and Automation
Society
............IEEE Signal Processing Society
............IEEE Society on Social Implications
of Technology
............IEEE Solid-State Circuits Society
............IEEE Systems, Man, and
Cybernetics Society
............IEEE Technology Management
Council
............IEEE Ultrasonics, Ferroelectrics,
and Frequency Control Society
............IEEE Vehicular Technology Society
........Student Chapters
....IEEE governance
........Bylaws
........Constitution
........IEEE Policy and Procedures
........IEEE Staff
........Mission and Vision
........Organization Charts
....IEEE members
........Associate members
........Fellows
........Joining IEEE
............Signup web site
........Life members
........Senior members
........Student members
....IEEE news
........Chapter news
........Region news
........Section news
........Society news
....IEEE products
........Audio tapes
........Catalogs
............Educational Activities Product
Catalog
............IEEE catalog
............IEEE Electronic catalog
............IEEE standards catalog
............New products catalog
........Conference proceedings
........Educational products
............Reading series
............Self-study courses
............Videos
........IEEE standards
............IEEE 1394 Standard
............IEEE 802.11 Standards
............IEEE 802.15 Standards
............IEEE 802.16 Standards
............IEEE 802.3 Standards
........IEEE Xplore
............IEL
........Merchandise
........Reading series
........Self-study courses
........Videos
....IEEE publications
........IEEE conference proceedings
........IEEE directories
............IEEE Membership Directory
............IEEE Staff Directory
........IEEE indexing
............Awards
............Book reviews
............CD-ROM reviews
............Editorials
............Interviews
............Obituaries
............Software reviews
............Special issues and sections
............Tutorials
............Video reviews
........IEEE journals
............IEEE Canadian Journal of Electrical
and Computer Engineering
H. IEEE Index Terms
219
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 28
............IEEE Communications Letters
............IEEE Communications Surveys &
Tutorials
............IEEE Computer Architecture Letters
............IEEE Electrochemical and Solid-
State Letters
............IEEE Electron Device Letters
............IEEE Embedded Systems Letters
............IEEE Journal of
Microelectromechanical Systems
............IEEE Journal of Oceanic
Engineering
............IEEE Journal of Quantum
Electronics
............IEEE Journal of Robotics and
Automation
............IEEE Journal of Selected Topics in
Applied Earth Observation and Remote
Sensing
............IEEE Journal of Selected Topics in
Quantum Electronics
............IEEE Journal of Selected Topics in
Signal Processing
............IEEE Journal of Solid-State Circuits
............IEEE Journal of Technology
Computer Aided Design
............IEEE Journal on Selected Areas in
Communications
............IEEE Latin America Learning
Technologies Journal [IEEE-RITA]
............IEEE Learning Technology
............IEEE Magnetics Letters
............IEEE Microwave and Guided Wave
Letters
............IEEE/OSA Journal of Display
Technology
............IEEE/OSA Journal of Lightwave
Technology
............IEEE/OSA Journal of Optical
Communications and Networking
............IEEE Photonics Journal
............IEEE Photonics Technology Letters
............IEEE Reviews in Biomedical
Engineering
............IEEE Signal Processing Letters
............IEEE Systems Journal
............Proceedings of the IEEE
........IEEE magazines
............IEEE Aerospace and Electronics
Society Magazine
............IEEE Annals of the History of
Computing
............IEEE Antennas and Propagation
Magazine
............IEEE Circuits and Devices
............IEEE Communications Magazine
............IEEE Computational Intelligence
............IEEE Computational Science and
Engineering
............IEEE Computer Applications in
Power
............IEEE Computer Graphics and
Applications
............IEEE Computer Magazine
............IEEE Concurrency
............IEEE Control Systems
............IEEE Design and Test of
Computers
............IEEE Electrical Insulation Magazine
............IEEE Engineering in Medicine and
Biology Magazine
............IEEE Engineering Management
Review
............IEEE Industrial Electronics
Magazine
............IEEE Industry Applications
Magazine
............IEEE Instrumentation and
Measurement Magazine
............IEEE Intelligent Systems and their
Applications
............IEEE Intelligent Transportation
Systems Magazine
............IEEE Internet Computing
............IEEE Micro
............IEEE Multidisciplinary Engineering
Education Magazine
............IEEE Multimedia
............IEEE Nanotechnology Magazine
............IEEE Network
............IEEE Personal Communications
............IEEE Potentials
............IEEE Power Engineering Review
............IEEE Robotics and Automation
Magazine
............IEEE Signal Processing Magazine
............IEEE Software
............IEEE Solid-State Circuits Magazine
............IEEE Spectrum
............IEEE Technology and Society
Magazine
H. IEEE Index Terms
220
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 29
............IEEE-USA Today's Engineer
........IEEE newsletters
............Broadcast Technology Society
Newsletter
............Center for the History of Electrical
Engineering Newsletter
............Circuits and Systems Society
Newsletter
............Components, Packaging, and
Manufacturing Technology Society
Newsletter
............Consumer Electronics Society
Newsletter
............Education Society Newsletter
............Electromagnetic Compatibility
Society Newsletter
............Electron Devices Society
Newsletter
............Electronics and the Environment
Newsletter
............Engineering Management Society
Newsletter
............Geoscience and Remote Sensing
Society Newsletter
............IEEE Circuitboard
............IEEE Looking Forward
............IEEE Publications Bulletin
............Industrial Electronics Society
Newsletter
............Information Theory Society
Newsletter
............Instrumentation and Measurement
Society Newsletter
............Lasers and Electro-Optics Society
Newsletter
............Magnetics Society Newsletter
............Microwave Theory and Techniques
Society Newsletter
............Nuclear and Plasma Sciences
Society Newsletter
............Oceanic Engineering Society
Newsletter
............Power Electronics Society
Newsletter
............Professional Communication
Society Newsletter
............Reliability Society Newsletter
............Systems, Man and Cybernetics
Society Newsletter
............The Institute
............The Staff Circuit
............Ultrasonics, Ferroelectrics, and
Frequency Control Society Newsletter
............Vehicular Technology Society
Newsletter
........IEEE online publications
............IEEE Bibliographies On-line
............IEEE Circuitboard
............IEEE Communications Interactive
............IEEE Communications Surveys &
Tutorials
............IEEE Distributed Systems Online
............IEEE Electrochemical and Solid-
State Letters
............IEEE Electronic catalog
............IEEE Journal of Technology
Computer Aided Design
............IEEE Journals and Transactions
On-LINE - OpeRA
............IEEE Latin America Learning
Technologies Journal [IEEE-RITA]
............IEEE Latin America Transactions
[Revista IEEE America Latina]
............IEEE Learning Technology
............IEEE Looking Forward
............IEEE Multidisciplinary Engineering
Education Magazine
............IEEE Network Interactive
............IEEE Personal Communications
Interactive
............IEEE Photonics Journal
............IEEE Transactions on
Computational Intelligence and AI in
Games
............IEEE Transactions on Learning
Technologies
............IEEE Transactions on Network and
Service Management
............IEEE Transactions on Services
Computing
........IEEE standard glossaries
........IEEE transactions
............IEEE/ACM Transactions on
Networking
............IEEE Biometrics Compendium
............IEEE Latin America Transactions
[Revista IEEE America Latina]
............IEEE Transactions on Aerospace
and Electronic Systems
............IEEE Transactions on Affective
Computing
H. IEEE Index Terms
221
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 30
............IEEE Transactions on Antennas
and Propagation
............IEEE Transactions on Applied
Superconductivity
............IEEE Transactions on Audio,
Speech, and Language Processing
............IEEE Transactions on Automatic
Control
............IEEE Transactions on Automation
Science and Engineering
............IEEE Transactions on Autonomous
Mental Development
............IEEE Transactions on Biomedical
Circuits and Systems
............IEEE Transactions on Biomedical
Engineering
............IEEE Transactions on Broadcasting
............IEEE Transactions on Circuits and
Systems for Video Technology
............IEEE Transactions on Circuits and
Systems I: Fundamental Theory and
Applications
............IEEE Transactions on Circuits and
Systems II: Analog and Digital Signal
Processing
............IEEE Transactions on
Communications
............IEEE Transactions on Components,
Packaging, and Manufacturing Technology
Part A
............IEEE Transactions on Components,
Packaging, and Manufacturing Technology
Part B
............IEEE Transactions on Components,
Packaging, and Manufacturing Technology
Part C
............IEEE Transactions on
Computational Intelligence and AI in
Games
............IEEE Transactions on Computer-
Aided Design of Integrated Circuits and
Systems
............IEEE Transactions on Computers
............IEEE Transactions on Consumer
Electronics
............IEEE Transactions on Control
Systems Technology
............IEEE Transactions on Dielectrics
and Electrical Insulation
............IEEE Transactions on Education
............IEEE Transactions on
Electromagnetic Compatibility
............IEEE Transactions on Electron
Devices
............IEEE Transactions on Energy
Conversion
............IEEE Transactions on Engineering
Management
............IEEE Transactions on Evolutionary
Computation
............IEEE Transactions on Fuzzy
Systems
............IEEE Transactions on Geoscience
and Remote Sensing
............IEEE Transactions on Haptics
............IEEE Transactions on Image
Processing
............IEEE Transactions on Industrial
Electronics
............IEEE Transactions on Industry
Applications
............IEEE Transactions on Information
Forensics and Security
............IEEE Transactions on Information
Technology in Biomedicine
............IEEE Transactions on Information
Theory
............IEEE Transactions on
Instrumentation and Measurement
............IEEE Transactions on Knowledge
and Data Engineering
............IEEE Transactions on Learning
Technologies
............IEEE Transactions on Magnetics
............IEEE Transactions on Mechatronics
............IEEE Transactions on Medical
Imaging
............IEEE Transactions on Microwave
Theory and Techniques
............IEEE Transactions on
Nanotechnology
............IEEE Transactions on Network and
Service Management
............IEEE Transactions on Neural
Networks
............IEEE Transactions on Nuclear
Science
............IEEE Transactions on Pattern
Analysis and Machine Intelligence
............IEEE Transactions on Plasma
Science
H. IEEE Index Terms
222
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 31
............IEEE Transactions on Power
Delivery
............IEEE Transactions on Power
Electronics
............IEEE Transactions on Power
Systems
............IEEE Transactions on Professional
Communication
............IEEE Transactions on Rehabilitation
Engineering
............IEEE Transactions on Reliability
............IEEE Transactions on Robotics
............IEEE Transactions on Robotics and
Automation
............IEEE Transactions on
Semiconductor Manufacturing
............IEEE Transactions on Services
Computing
............IEEE Transactions on Signal
Processing
............IEEE Transactions on Smart Grid
............IEEE Transactions on Software
Engineering
............IEEE Transactions on Speech and
Audio Processing
............IEEE Transactions on Sustainable
Energy
............IEEE Transactions on Systems,
Man, and Cybernetics Part A: Systems and
Humans
............IEEE Transactions on Systems,
Man, and Cybernetics Part B: Cybernetics
............IEEE Transactions on Systems,
Man, and Cybernetics Part C: Applications
and Reviews
............IEEE Transactions on Ultrasonics,
Ferroelectrics and Frequency Control
............IEEE Transactions on Vehicular
Technology
............IEEE Transactions on Very Large
Scale Integration - VLSI
............IEEE Transactions on Visualization
and Computer Graphics
............IEEE Women in Engineering
........Notice of Violation
....IEEE services
........Ask IEEE
........Conference management
........Meeting services
........Member services
............Career development
............Electronic mail
............Financial advantage program
............IEEE Bibliographies On-line
............IEEE Electronic catalog
............Job listing service
............Membership renewal
............Travel services
............Web and internet services
........Subscriptions
........Web and internet services
............Electronic mail
............IEEE Electronic catalog
............IEEE Journals and Transactions
On-LINE - OpeRA
............Online banking
....IEEE web sites
........Society home pages
........Web page design
Imaging
....Biomedical imaging
........Angiocardiography
........Angiography
........Biomedical optical imaging
........Cardiography
............Echocardiography
............Electrocardiography
............Phonocardiography
........DICOM
........Encephalography
........Mammography
........Medical diagnostic imaging
............Anatomical structure
........Molecular imaging
........Phantoms
....Cameras
........Digital cameras
........Webcams
....Focusing
....Ground penetrating radar
....Holography
....Image converters
........Image intensifiers
....Image sensors
........Active pixel sensors
........CCD image sensors
........Charge-coupled image sensors
........CMOS image sensors
........Infrared image sensors
....Image storage
H. IEEE Index Terms
223
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 32
....Infrared imaging
........Night vision
....Magnetic resonance imaging
........Diffusion tensor imaging
....Magneto electrical resistivity imaging
technique
....Microscopy
........Atomic force microscopy
........Electron microscopy
............Photoelectron microscopy
............Scanning electron microscopy
............Transmission electron microscopy
........Scanning probe microscopy
....Microwave imaging
....Motion pictures
....Multispectral imaging
....Nuclear imaging
........Energy resolution
....Optical imaging
........Talbot effect
........Thermoreflectance imaging
....Photography
........Cinematography
........Digital photography
........Image forensics
........Photomicrography
....Radiation imaging
....Radiography
........Diagnostic radiography
....Stereo vision
........Stereo image processing
....Tomography
........Computed tomography
........Electrical capacitance tomography
........Positron emission tomography
............Whole-body PET
........Reconstruction algorithms
........Single photon emission computed
tomography
Industrial electronics
....Assembly systems
........Flexible electronics
........Robotic assembly
....Computer aided manufacturing
........CADCAM
........Silicon compiler
....Cryogenic electronics
....Industrial control
........Process control
............Predictive control
............Three-term control
............Two-term control
........Production control
............Continuous production
............Lot sizing
............Optimized production technology
............Scheduling
....Integrated manufacturing systems
....Machine control
........Machine vector control
....Manufacturing automation
........Computer aided manufacturing
............CADCAM
............Silicon compiler
........Computer integrated manufacturing
........Computer numerical control
........Flexible manufacturing systems
....Testing
........Aerospace testing
........Automatic testing
............Automatic test pattern generation
............Ring generators
........Benchmark testing
........Built-in self-test
........Circuit testing
............Integrated circuit measurements
........Electronic equipment testing
............Immunity testing
........Error analysis
............Bit error rate
............Finite wordlength effects
........Error-free operations
........Failure analysis
............Equipment failure
............Semiconductor device breakdown
........Frequency response
........Impulse testing
........Insulator testing
............Insulation testing
........Integrated circuit testing
............Integrated circuit yield
............Logic testing
........Life testing
........Materials testing
............Accelerated aging
............Acoustic testing
............Adhesive strength
............Bonding forces
............Delamination
............Elastic recovery
H. IEEE Index Terms
224
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 33
............Nondestructive testing
........Optical fiber testing
........Remaining life assessment
........Ring generators
........Semiconductor device testing
........Software testing
........System testing
............Model checking
........Test equipment
............Automatic test equipment
........Test facilities
............Anechoic chambers
............Laboratories
............Large Hadron Collider
............Open area test sites
............TEM cells
Industry applications
....Accident prevention
........Accidents
............Aerospace accidents
............Electrical accidents
............Industrial accidents
............Marine accidents
............Railway accidents
............Road accidents
....Chemical technology
........Chemical reactors
............Bioreactors
............Continuous-stirred tank reactor
............Ignition
........Chemical sensors
........Crystallizers
........Distillation equipment
........Fluidization
........Pharmaceutical technology
........Vitrification
....Cryogenics
....Electrochemical devices
........Amperometric sensors
........Batteries
............Lithium batteries
........Battery management systems
........Fuel cells
........Supercapacitors
....Electrochemical processes
....Electromechanical systems
........Electromechanical devices
............Armature
............SAW filters
....Electrostatic devices
....Electrostatic precipitators
....Electrostatic processes
........Aerosols
........Electrophotography
........Electrostatic analysis
........Electrostatic induction
........Electrostatics
............Electrostatic levitation
........Particle charging
........Particle production
........Space charge
........Surface charging
............Triboelectricity
........Triboelectricity
....Engines
........Heat engines
............Steam engines
............Stirling engines
........Internal combustion engines
............Diesel engines
............Ignition
........Jet engines
....Environmental management
........Biodegradation
............Biodegradable materials
........Land use planning
........Pest control
........Pollution control
........Recycling
........Renewable energy sources
............Biomass
........Sustainable development
........Waste management
............Waste disposal
............Waste handling
............Waste recovery
............Waste reduction
........Water conservation
............Desalination
........Water resources
............Desalination
............Reservoirs
....Food technology
........Food preservation
....High-temperature techniques
........Rapid thermal processing
....Industrial engineering
........Industrial communication
....Industries
........Agriculture
H. IEEE Index Terms
225
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 34
............Agricultural products
............Aquaculture
............Fertilizers
............Greenhouses
............Irrigation
........Architecture
........Banking
........Beverage industry
........Chemical industry
........Coal industry
........Communication industry
........Computer industry
........Construction
............Buildings
............Green buildings
............Modular construction
............Prefabricated construction
........Construction industry
............Prefabricated construction
........Defense industry
........Entertainment industry
........Gas industry
........Manufacturing industries
............Aerospace industry
............Cement industry
............Ceramics industry
............Clothing industry
............Electrical products industry
............Electronics industry
............Food industry
............Footwear industry
............Fuel processing industries
............Glass industry
............Machinery production industries
............Metal product industries
............Plastics industry
............Pulp and paper industry
............Rubber industry
............Shipbuilding industry
............Textile industry
............Toy manufacturing industry
........Metals industry
........Mining industry
............Coal mining
........Natural gas industry
........Petroleum industry
............Oil drilling
............Oil refineries
............Well logging
........Power industry
............Electrical equipment industry
............Electricity supply industry
............Nuclear facility regulation
............Power system interconnection
........Sugar industry
............Sugar refining
........Textile technology
............Spinning
............Weaving
........Toy industry
........Wood industry
....Inspection
........Automatic optical inspection
....Machinery
........Agricultural machinery
........Ball bearings
........Belts
........Drives
............Hydraulic drives
............Motor drives
............Variable speed drives
........Electric machines
............AC machines
............Alternators
............Brushless machines
............Compressors
............Conductors
............DC machines
............Electric fences
............Generators
............Permanent magnet machines
............Rotating machines
............Rotors
............Stators
............Washing machines
........Fans
........Furnaces
............Blast furnaces
............Kilns
........Gears
........Hydraulic systems
............Electrohydraulics
............Hydraulic equipment
............Hydraulic fluids
........Machine components
............Air cleaners
............Belts
............Cams
............Engine cylinders
............Exhaust systems
............Impellers
............Intake systems
H. IEEE Index Terms
226
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 35
............Manifolds
............Mechanical splines
............Pistons
............Rotors
............Shafts
............Valves
........Motors
............AC motors
............Brushless motors
............Commutation
............DC motors
............Electric motors
............Hysteresis motors
............Induction motors
............Micromotors
............Permanent magnet motors
............Servomotors
............Traction motors
............Universal motors
........Printing machinery
........Pumps
............Fuel pumps
............Heat pumps
............Micropumps
........Textile machinery
............Spinning machines
....Manufacturing
........Assembly
............Fitting
............Microassembly
............Preforms
............Soldering
........Assembly systems
............Flexible electronics
............Robotic assembly
........Embossing
........Fabrication
............Bonding processes
............Microfabrication
............Optical device fabrication
............Soldering
............Welding
........Lithography
............Colloidal lithography
............Interferometric lithography
............Nanolithography
............Soft lithography
............Stereolithography
............X-ray lithography
........Manufactured products
............Ceramic products
............Chemical products
............Consumer products
............Electrical products
............Food products
............Fuels
............Glass products
............Mechanical products
............Metal products
............Paper products
............Paper pulp
............Plastic products
............Rubber products
............Sports equipment
............Textile products
............Windows
........Manufacturing systems
............Agile manufacturing
............Automobile manufacture
............Batch production systems
............Blanking
............Cellular manufacturing
............Flow production systems
............Food manufacturing
............Forging
............Glass manufacturing
............Integrated manufacturing systems
............Intelligent manufacturing systems
............Job production systems
............Joining processes
............Layered manufacturing
............Lean production
............Manufacturing processes
............Mass production
............Melt processing
............Pulp manufacturing
............Sheet metal processing
............Thermoforming
........Mass customization
........Tolerance analysis
....Packaging
........Bagging
........Bottling
........Canning
........Encapsulation
........Labeling
........Multichip modules
........Plastic packaging
........Wrapping
....Paper technology
....Production
........Ball milling
H. IEEE Index Terms
227
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 36
........Compression molding
........Embossing
........Food products
............Dairy products
............Fats
............Sugar
........Group technology
........Injection molding
........Materials processing
............Annealing
............Bleaching
............Casting
............Coatings
............Curing
............Etching
............Heat treatment
............Joining processes
............Lamination
............Machining
............Melt processing
............Plasma materials processing
............Pressing
............Punching
............Refining
............Shearing
............Smelting
............Softening
............Swaging
........Mechanical products
............Automotive components
............Axles
............Bellows
............Blades
............Couplings
............Fasteners
............Flanges
............Gears
............Hoses
............Machine components
............Mechanical guides
............Needles
............Orifices
............Pistons
............Seals
............Springs
............Steering systems
............Structural shapes
............Suspensions
............Tires
............Vents
............Wheels
........Process planning
............Cause effect analysis
........Production control
............Continuous production
............Lot sizing
............Optimized production technology
............Scheduling
........Production engineering
............Production planning
........Production equipment
............Applicators
............Clamps
............Cutting tools
............Fixtures
............Machine tools
............Mining equipment
............Molding equipment
............Packaging machines
............Paper making machines
............Polishing machines
............Soldering equipment
........Production facilities
............Foundries
............Greenhouses
............Industrial plants
............Machine shops
............Paper mills
........Production management
............Control charts
............Inventory management
............Lead time reduction
............Logistics
............Process planning
............Production planning
........Production materials
............Abrasives
............Aerospace materials
............Automotive materials
............Inhibitors
............Ink
............Joining materials
............Lubricants
............Retardants
........Production systems
............Assembly systems
............Exhaust systems
............Intelligent manufacturing systems
............Lean production
............Manufacturing systems
............Steering systems
........Productivity
H. IEEE Index Terms
228
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 37
........Shafts
............Camshafts
........Springs
........Suspensions
............Shock absorbers
........Transfer molding
....Safety
........Aerospace safety
............Air safety
........Domestic safety
........Emergency services
........Explosion protection
........Hazards
............Biohazards
............Chemical hazards
............Explosions
............Fires
............Flammability
............Floods
............Hazardous areas
............Hazardous materials
............Toxicology
........Health and safety
............Occupational health
............Occupational safety
........Marine safety
........Product safety
........Protection
............Explosion protection
............Lightning protection
........Radiation safety
........Safety devices
............Eye protection
............Protective clothing
........Vehicle safety
....Security
........Access control
............Authorization
........Alarm systems
............Smoke detectors
........Computer security
............Authentication
............Computer crime
............Computer hacking
............Firewalls (computing)
............Identity management systems
............Invasive software
............Permission
........Cryptography
............Ciphers
............Encryption
............Public key
............Random number generation
........Data security
............Cryptography
............Message authentication
........Digital signatures
........Information security
............Intrusion detection
........Power system security
........Reconnaissance
........Terrorism
............Bioterrorism
............National security
........Watermarking
....Wine industry
........Wineries
Information theory
....Audio coding
....Biological information theory
....Channel coding
........Block codes
............Linear codes
........Combined source-channel coding
........Turbo codes
....Codes
........Binary codes
............Reflective binary codes
........Convolutional codes
........Cyclic redundancy check codes
........Error correction codes
............Reed-Solomon codes
........Parity check codes
............Iterative decoding
........Product codes
............Bar codes
........Space-time codes
....Communication channels
........Channel allocation
........Channel capacity
........Channel estimation
........Channel models
........Channel spacing
........Channel state information
........Gaussian channels
............AWGN channels
........Multipath channels
........Multiuser channels
........Partial response channels
........Throughput
H. IEEE Index Terms
229
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 38
........Time-varying channels
....Decoding
........Maximum likelihood decoding
....Encoding
........Audio coding
........Channel coding
............Block codes
............Combined source-channel coding
............Turbo codes
........Entropy coding
............Huffman coding
........Source coding
........Speech coding
........Transcoding
....Error compensation
....Genetic communication
....Hamming distance
....Hamming weight
....Information entropy
....Mutual information
....Network coding
....Rate-distortion
....Rate distortion theory
........Channel rate control
....Source coding
....Speech coding
Instrumentation and measurement
....Computerized instrumentation
....Electric variables
........Admittance
........Capacitance
............Parasitic capacitance
............Quantum capacitance
........Capacitance-voltage characteristics
........Conductivity
............Photoconductivity
............Semiconductivity
............Transconductance
........Current
............Bioimpedance
............Current slump
............Dark current
............Fault currents
............Leakage currents
............Persistent currents
............Short-circuit currents
............Threshold current
........Current-voltage characteristics
........Electric potential
........Gain
........Impedance
........Impedance matching
........Inductance
........Permittivity
........Piezoresistance
........Q-factor
........Resistance
............Electric resistance
............Piezoresistance
............Surface resistance
............Thermal resistance
............Viscosity
........Voltage
............Breakdown voltage
............Dynamic voltage scaling
............Threshold voltage
............Voltage fluctuations
........Wiring
....High energy physics instrumentation
computing
........Linear particle accelerator
....Instruments
........Compass
........Goniometers
........Microscopy
............Atomic force microscopy
............Electron microscopy
............Scanning probe microscopy
........Oscilloscopes
........Potentiometers
........Pressure gauges
........Probes
........Radiometers
............Spectroradiometers
........Telescopes
........Theodolites
........Tuners
........Vibrometers
........Voltmeters
........Watthour meters
........Wattmeters
....Measurement
........Accelerometers
........Acoustic measurements
........Antenna measurements
........Anthropometry
........Area measurement
........Atmospheric measurements
........Atomic measurements
........Biomedical measurement
H. IEEE Index Terms
230
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 39
............Biomarkers
............Biomedical monitoring
............Electroencephalography
............Electromyography
............Electrooculography
............Electrophysiology
............Photoplethysmography
............Reproducibility of results
............Sensitivity and specificity
........Calorimetry
........Coordinate measuring machines
........Density measurement
............Hydrometers
........Distance measurement
............Euclidean distance
........Distortion measurement
............Total harmonic distortion
........Doppler measurement
........Dosimetry
........Dynamic range
........Electric variables measurement
............Admittance measurement
............Ammeters
............Attenuation measurement
............Capacitance measurement
............Conductivity measurement
............Current measurement
............Dielectric measurement
............Electrical resistance measurement
............Electrostatic measurements
............Energy measurement
............Impedance measurement
............Inductance measurement
............Partial discharge measurement
............Phasor measurement units
............Power measurement
............Q measurement
............Transmission line measurements
............Voltage measurement
........Electromagnetic measurements
............Electromagnetic modeling
............Linearity
............Microwave measurement
............Millimeter wave measurements
............Parameter extraction
............Polarimetry
............Radiometry
............Submillimeter wave measurements
........Extraterrestrial measurements
........Fluid flow measurement
........Frequency measurement
............Frequency-domain analysis
............Frequency estimation
........Gain measurement
........Gas chromatography
........Geologic measurements
............Geophysical image processing
........Geophysical measurements
............Geodesy
............Sea measurements
............Seismic measurements
........Interferometry
............Fabry-Perot
............Interferometers
............Optical interferometry
............Phase shifting interferometry
............Radar interferometry
............Radio interferometry
............Sagnac interferometers
........Length measurement
........Lifetime estimation
........Loss measurement
............Packet loss
........Magnetic variables measurement
............Magnetic field measurement
............Magnetometers
............Permeability measurement
........Measurement by laser beam
............Laser velocimetry
........Measurement techniques
............Calibration
............Dynamic equilibrium
........Measurement uncertainty
........Measurement units
............Nanometers
........Mechanical variables measurement
............Angular velocity
............Displacement measurement
............Force measurement
............Motion measurement
............Position measurement
............Rotation measurement
............Strain measurement
............Stress measurement
............Thickness measurement
............Torque measurement
............Velocity measurement
............Vibration measurement
............Volume measurement
............Weight measurement
........Moisture measurement
............Humidity measurement
H. IEEE Index Terms
231
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 40
........Noise measurement
............Multiple signal classification
............Noise figure
............Noise shaping
........Nuclear measurements
............Particle tracking
........Optical variables measurement
............Ellipsometry
............Photometry
............Reflection coefficient
............Refractive index
........Particle beam measurements
........Particle measurements
........Performance evaluation
........Phase measurement
........pH measurement
........Plasma measurements
........Plethysmography
........Pollution measurement
........Pressure measurement
............Altimetry
............Tire pressure
........Pulse measurements
........Reflectometry
........Reproducibility of results
........Scintillation counters
............Solid scintillation detectors
........Sea state
........Semiconductor device measurement
........Sensitivity
............Sensitivity analysis
........Shape measurement
........Size measurement
........Software measurement
............Software metrics
........Soil measurements
........Spectroscopy
............Electrochemical impedance
spectroscopy
............Kirchhoff's Law
............Mass spectroscopy
............MERIS
............Neutron spin echo
............Photoacoustic effects
............Resonance light scattering
........Thermal variables measurement
............Temperature measurement
........Time measurement
............Clocks
............Time dissemination
............Timing
........UHF measurements
........Ultrasonic variables measurement
........Viscosity
........Wavelength measurement
........Wide area measurements
....Monitoring
........Computerized monitoring
........Environmental monitoring
........Patient monitoring
........Radiation monitoring
............Radiation dosage
........Remote monitoring
........Surveillance
............Infrared surveillance
............Video surveillance
....Testing
........Aerospace testing
........Automatic testing
............Automatic test pattern generation
............Ring generators
........Benchmark testing
........Built-in self-test
........Circuit testing
............Integrated circuit measurements
........Electronic equipment testing
............Immunity testing
........Error analysis
............Bit error rate
............Finite wordlength effects
........Error-free operations
........Failure analysis
............Equipment failure
............Semiconductor device breakdown
........Frequency response
........Impulse testing
........Insulator testing
............Insulation testing
........Integrated circuit testing
............Integrated circuit yield
............Logic testing
........Life testing
........Materials testing
............Accelerated aging
............Acoustic testing
............Adhesive strength
............Bonding forces
............Delamination
............Elastic recovery
............Nondestructive testing
........Optical fiber testing
........Remaining life assessment
H. IEEE Index Terms
232
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 41
........Ring generators
........Semiconductor device testing
........Software testing
........System testing
............Model checking
........Test equipment
............Automatic test equipment
........Test facilities
............Anechoic chambers
............Laboratories
............Large Hadron Collider
............Open area test sites
............TEM cells
Intelligent transportation systems
....Automated highways
....Geographic information systems
........Geospatial analysis
........Gunshot detection systems
....Intelligent vehicles
........Vehicle routing
....Navigation
........Aircraft navigation
........Course correction
........Dead reckoning
........Inertial navigation
........Marine navigation
........Radio navigation
........Satellite navigation systems
............Global Positioning System
............Satellite constellations
........Sonar navigation
....Transportation
........Air transportation
............Aircraft
............Airports
........Land transportation
............Rail transportation
............Road transportation
........Vehicles
............Land vehicles
............Remotely operated vehicles
............Space vehicles
Lasers and electrooptics
....Electrooptic devices
........Electrochromic devices
........Electrooptic deflectors
........Electrooptic modulators
....Electrooptic effects
........Electrochromism
........Kerr effect
........Optical bistability
........Stark effect
....Lasers
........Atom lasers
........Chemical lasers
........Diode lasers
........Free electron lasers
........Gas lasers
........Laser applications
............Dark states
............Distributed feedback devices
............Laser ablation
............Laser beam cutting
............Laser fusion
............Laser theory
............Magnetooptic recording
........Laser excitation
............Optical pumping
........Laser modes
............Laser mode locking
........Laser stability
........Laser transitions
........Power lasers
........Pump lasers
........Quantum well lasers
............Quantum cascade lasers
........Ring lasers
............Fiber lasers
........Semiconductor lasers
............Laser tuning
............Quantum dot lasers
............Quantum well lasers
............Semiconductor laser arrays
............Semiconductor optical amplifiers
............Surface emitting lasers
........Solid lasers
............Microchip lasers
............Quantum well lasers
............Semiconductor lasers
............Surface emitting lasers
........Surface emitting lasers
............Vertical cavity surface emitting
lasers
........X-ray lasers
....Optics
........Adaptive optics
........Birefringence
........Brightness
H. IEEE Index Terms
233
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 42
............Brightness temperature
........Color
............Pigmentation
........Electron optics
........Extinction coefficients
............Extinction ratio
........Fiber optics
............Fiber nonlinear optics
............Optical fibers
........Fluorescence
........Four-wave mixing
........Geometrical optics
............Ray tracing
........Integrated optics
........Light sources
............Electroluminescent devices
............Fast light
............Luminescent devices
............Phosphors
............Slow light
............Stray light
............Superluminescent diodes
............Ultraviolet sources
........Luminescence
............Bioluminescence
............Electroluminescence
............Fluorescence
............Phosphorescence
............Photoluminescence
............Thermoluminescence
........Microoptics
............Micromirrors
........Nonlinear optics
............Fiber nonlinear optics
............Nonlinear optical devices
............Optical mixing
............Optical saturation
............Photorefractive effect
............Raman scattering
............Supercontinuum generation
........Optical amplifiers
............Doped fiber amplifiers
............Erbium-doped fiber amplifiers
............Semiconductor optical amplifiers
........Optical crosstalk
........Optical design
............Optical design techniques
........Optical devices
............Bragg gratings
............Collimators
............Displays
............Holographic optical components
............Lenses
............Light deflectors
............Lighting
............Luminescent devices
............Mirrors
............Optical arrays
............Optical attenuators
............Optical collimators
............Optical device fabrication
............Optical filters
............Optical resonators
............Optical sensors
............Thermooptical devices
........Optical distortion
........Optical fiber applications
............Optical fiber devices
........Optical harmonic generation
........Optical losses
........Optical microscopy
........Optical mixing
............Multiwave mixing
........Optical polarization
............Polarization shift keying
............Stokes parameters
........Optical pulses
........Optical retarders
........Optical saturation
........Optical solitons
........Optical tuning
........Particle beam optics
............Atom optics
............Electron optics
............Stimulated emission
........Photoluminescence
........Physical optics
............Optical refraction
............Optical vortices
........Ray tracing
........Stray light
........Ultrafast optics
........Whispering gallery modes
....Optoelectronic devices
........Charge-coupled image sensors
........Integrated optoelectronics
........Light emitting diodes
............Inorganic light emitting diodes
............LED lamps
............Organic light emitting diodes
............Superluminescent diodes
........Photoconducting devices
H. IEEE Index Terms
234
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 43
............Electrophotography
........Photodetectors
............Photodiodes
............Phototransistors
............Superconducting photodetectors
........Superluminescent diodes
....Photonics
........Biophotonics
........Microwave photonics
........Nanophotonics
........Photochromism
........Photothermal effects
........Silicon photonics
........Spontaneous emission
............Radiative recombination
Magnetics
....Biomagnetics
........Magnetoencephalography
....Demagnetization
....Gyromagnetism
....Magnetic analysis
........Magnetization
....Magnetic anisotropy
........Magnetic domains
........Magnetic domain walls
........Magnetic moments
........Perpendicular magnetic anisotropy
....Magnetic devices
........Accelerator magnets
........Ferrite devices
............Circulators
........Magnetic cores
............Transformer cores
........Magnetic heads
........Magnetic memory
............Floppy disks
............Hard disks
........Magnetic modulators
........Magnetooptic devices
........Magnetoresistive devices
........Magnetostrictive devices
........Solenoids
........Transformer cores
........Undulators
....Magnetic fields
........Geomagnetism
........Magnetic reconnection
........Magnetic separation
........Magnetostatics
........Toroidal magnetic fields
....Magnetic flux
........Flux pinning
........Magnetic flux density
........Magnetic flux leakage
....Magnetic force microscopy
....Magnetic forces
........Coercive force
....Magnetic hysteresis
....Magnetic levitation
....Magnetic losses
....Magnetic materials
........Amorphous magnetic materials
........Antiferromagnetic materials
........Diamagnetic materials
........Ferrimagnetic films
............Ferrite films
............Garnet films
........Ferrimagnetic materials
............Ferrimagnetic films
............Ferrite films
............Ferrites
............Garnet films
............Garnets
........Ferrite films
........Ferrites
............Ferrite films
........Garnet films
........Garnets
............Garnet films
........Magnetic films
............Ferrimagnetic films
............Ferrite films
............Garnet films
........Magnetic liquids
........Magnetic semiconductors
........Magnetic superlattices
........Paramagnetic materials
........Soft magnetic materials
....Magnetic multilayers
....Magnetic particles
....Magnetic properties
....Magnetic sensors
........Spin valves
....Magnetic susceptibility
....Magnetic switching
....Magnetization processes
........Magnetization reversal
........Saturation magnetization
....Magnetoacoustic effects
....Magnetoelectric effects
H. IEEE Index Terms
235
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 44
........Hall effect
........Magnetic tunneling
........Magnetoelectronics
............Spin polarized transport
........Magnetoresistance
............Anisotropic magnetoresistance
............Ballistic magnetoresistance
............Colossal magnetoresistance
............Enhanced magnetoresistance
............Extraordinary magnetoresistance
............Giant magnetoresistance
............Ordinary magnetoresistance
............Tunneling magnetoresistance
....Magnetomechanical effects
........Magnetic field induced strain
........Magnetoelasticity
............Magnetostriction
........Magnetostriction
....Magnetooptic effects
........Faraday effect
........Gyrotropism
....Magnets
........Electromagnets
............Superconducting magnets
........Micromagnetics
........Permanent magnets
....Microwave magnetics
....Nonlinear magnetics
....Remanence
Materials, elements, and compounds
....Chemical elements
........Boron
............Boron alloys
........Carbon
........Cerium
........Darmstadtium
........Helium
........Hydrogen
............Deuterium
........Isotopes
........Lutetium
........Nitrogen
............Silicon nitride
........Oxygen
........Roentgenium
........Tellurium
........Titanium
............Titanium alloys
............Titanium compounds
........Ytterbium
........Zirconium
....Compounds
........Bismuth compounds
........Gallium compounds
............Aluminum gallium nitride
............Gallium arsenide
............Gallium nitride
............Indium gallium arsenide
............Indium gallium nitride
........Indium compounds
............Indium gallium arsenide
............Indium tin oxide
........Inorganic compounds
........Lead compounds
........Organic compounds
............Carbon compounds
............Organic semiconductors
............Volatile organic compounds
........Silicon compounds
............Silicides
............Silicon carbide
............Silicon nitride
....Materials
........Acoustic materials
........Additives
........Aggregates
........Amorphous materials
............Diamond-like carbon
............Glass
........Auxetic materials
........Biological materials
........Biomedical materials
............Bioceramics
............Biomembranes
........Building materials
............Asphalt
............Concrete
............Floors
............Mortar
............Tiles
............Windows
........Ceramics
............Porcelain
........Composite materials
........Conducting materials
........Corrosion inhibitors
........Crystalline materials
............Nanocrystals
............Superlattices
........Crystals
H. IEEE Index Terms
236
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 45
............Colloidal crystals
............Crystallography
............Crystal microstructure
............Grain boundaries
............Grain size
............Liquid crystals
........Dielectric materials
............Dielectric films
............Dielectric liquids
............Electrets
............Epoxy resins
............High K dielectric materials
............Piezoelectric materials
........Films
............Conductive films
............Dielectric films
............Epitaxial layers
............Ferrimagnetic films
............Ferrite films
............Garnet films
............Magnetic films
............Optical films
............Piezoelectric films
............Plastic films
............Polymer films
............Semiconductor films
............Thick films
............Thin films
........Fluids
............Fluid dynamics
............Gases
............Hydraulic fluids
............Liquids
............Viscosity
........Hazardous materials
........Inorganic materials
........Lacquers
........Laminates
........Magnetic materials
............Amorphous magnetic materials
............Antiferromagnetic materials
............Diamagnetic materials
............Ferrimagnetic films
............Ferrimagnetic materials
............Ferrite films
............Ferrites
............Garnet films
............Garnets
............Magnetic films
............Magnetic liquids
............Magnetic semiconductors
............Magnetic superlattices
............Paramagnetic materials
............Soft magnetic materials
........Material properties
............Creep
............Elasticity
............Resilience
........Media
............Nonhomogeneous media
............Random media
........Mesoporous materials
........Metal foam
........Metamaterials
............Electromagnetic metamaterials
............Optical cloaking
............Optical metamaterials
........Nanostructured materials
............Nanocomposites
............Nanoporous materials
........Oils
............Lubricating oils
............Vegetable oils
........Optical materials
............Optical cloaking
............Optical polymers
............Optical retarders
............Optical superlattices
............Photorefractive materials
........Organic inorganic hybrid materials
........Organic materials
........Paints
........Paper pulp
........Petrochemicals
........Phase change materials
........Photoconducting materials
........Plastics
............Epoxy resins
............Fiber reinforced plastics
............Plastic films
............Plastic optical fiber
........Polymer foams
........Polymer gels
........Polymers
............Liquid crystal polymers
............Optical polymers
............Polyethylene
............Polyimides
........Production materials
............Abrasives
............Aerospace materials
............Automotive materials
H. IEEE Index Terms
237
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 46
............Inhibitors
............Ink
............Joining materials
............Lubricants
............Retardants
........Radioactive materials
............Nuclear fuels
............Radioactive decay
............Radioactive waste
........Raw materials
........Resins
............Epoxy resins
........Resists
........Semiconductor materials
............Amorphous semiconductors
............Elemental semiconductors
............Gallium
............Gallium arsenide
............Germanium
............III-V semiconductor materials
............II-VI semiconductor materials
............Indium gallium arsenide
............Indium phosphide
............Magnetic semiconductors
............Organic semiconductors
............Semiconductor superlattices
............Silicon
............Silicon germanium
............Substrates
............Wide band gap semiconductors
........Sheet materials
........Solids
............Young's modulus
........Superconducting materials
............Granular superconductors
............High-temperature superconductors
............Multifilamentary superconductors
............Niobium-tin
............Type II superconductors
........Textiles
............Cotton
............Fabrics
............Textile fibers
............Wool
........Waste materials
............Effluents
............Electronic waste
............Industrial waste
............Radioactive waste
............Slurries
............Wastewater
........Wire
....Materials science and technology
........Absorption
........Aging
............Accelerated aging
........Chemical analysis
............Activation analysis
............Chemical processes
............Chemicals
............Electronic noses
............pH measurement
........Contamination
............Surface contamination
........Degradation
........Filtration
............Microfiltration
........Hysteresis
........Impurities
............Semiconductor impurities
........Materials handling
............Cleaning
............Decontamination
............Freight handling
............Materials handling equipment
............Remote handling
........Materials preparation
............Doping
............Firing
............Ion implantation
............Laser sintering
............Sputtering
........Materials reliability
........Materials testing
............Accelerated aging
............Acoustic testing
............Adhesive strength
............Bonding forces
............Delamination
............Elastic recovery
............Nondestructive testing
........Microstructure
........Periodic structures
............Gratings
............Photonic crystals
........Pigmentation
............Pigments
........Separation processes
............Fractionation
............Particle separators
........Surface engineering
........Surfaces
H. IEEE Index Terms
238
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 47
............Corrosion
............Corrugated surfaces
............Rough surfaces
............Surface impedance
............Surface morphology
............Surface resistance
............Surface roughness
............Surface soil
............Surface structures
............Surface tension
............Surface texture
............Surface topography
............Surface treatment
....Material storage
........Bulk storage
........Containers
............Freight containers
........Fuel storage
........Secure storage
........Stacking
........Storage automation
........Warehousing
........Water storage
............Reservoirs
....Metals
........Alloying
............Intermetallic
............Shape memory alloys
........Aluminum
............Aluminum alloys
............Aluminum compounds
........Barium
............Barium compounds
........Bismuth
........Boron
............Boron alloys
........Cadmium
............Cadmium compounds
........Calcium
............Calcium compounds
........Chromium
............Chromium alloys
........Cobalt
............Cobalt alloys
........Copper
............Copper alloys
............Copper compounds
........Digital alloys
........Erbium
........Gallium
............Gallium alloys
........Germanium
............Germanium alloys
........Gold
............Gold alloys
........Hafnium
............Hafnium compounds
........Indium
........Iron
............Cast iron
............Iron alloys
........Lanthanum
............Lanthanum compounds
........Lead
............Lead isotopes
........Lithium
............Lithium compounds
........Magnesium
............Magnesium compounds
........Manganese
............Manganese alloys
........Mercury (metals)
........Metallization
............Integrated circuit metallization
........Neodymium
............Neodymium alloys
............Neodymium compounds
........Nickel
............Nickel alloys
........Niobium
............Niobium alloys
............Niobium compounds
........Palladium
........Platinum
............Platinum alloys
........Rare earth metals
........Samarium
............Samarium alloys
........Silver
........Steel
........Strontium
............Strontium compounds
........Tin
............Tin alloys
............Tin compounds
........Titanium
............Titanium alloys
............Titanium compounds
........Tungsten
........Yttrium
............Yttrium compounds
........Zinc
H. IEEE Index Terms
239
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 48
............Zinc compounds
Mathematics
....Accuracy
....Algebra
........Abstract algebra
............Galois fields
............Modules (abstract algebra)
........Boolean algebra
............Boolean functions
........Linear algebra
............Linear programming
............Matrices
............Vectors
........Set theory
............Fuzzy sets
............Fuzzy set theory
............Rough sets
....Algorithms
........Adaptive algorithms
............Adaptation models
........Algorithm design and analysis
........Approximation algorithms
........Backpropagation algorithms
........Basis algorithms
........Change detection algorithms
........Classification algorithms
........Clustering algorithms
........Compression algorithms
........Density estimation robust algorithm
........Detection algorithms
........Distributed algorithms
........Dynamic programming
........Filtering algorithms
........Genetic algorithms
........Heuristic algorithms
........Inference algorithms
........Least mean square algorithms
........Machine learning algorithms
........Matching pursuit algorithms
........Maximum likelihood detection
........MLFMA
........Multicast algorithms
........Parallel algorithms
........Partitioning algorithms
........Prediction algorithms
........Projection algorithms
........Pursuit algorithms
........Signal processing algorithms
........Software algorithms
........Viterbi algorithm
....Arithmetic
........Digital arithmetic
........Fixed-point arithmetic
........Floating-point arithmetic
....Azimuth
........Azimuthal angle
........Azimuthal component
........Azimuthal current
........Azimuthal harmonics
........Azimuthal plane
....Boundary value problems
........Boundary conditions
............Upper bound
....Calculus
........Differential equations
............Differential algebraic equations
............Navier-Stokes equations
............Partial differential equations
............Transfer functions
........Integral equations
............Probability density function
........Level set
....Closed-form solutions
....Combinatorial mathematics
........Graph theory
............Bipartite graph
............Optimal matching
............Reachability analysis
............Shortest path problem
............Tree graphs
........Steiner trees
....Computational efficiency
....Conformal mapping
....Convergence
....Convex functions
....Cyclic redundancy check
........Cyclic redundancy check codes
....Eigenvalues and eigenfunctions
....Equations
........Boltzmann equation
........Difference equations
........Integrodifferential equations
........Maxwell equations
........Nonlinear equations
............Bifurcation
........Polynomials
........Riccati equations
....Estimation
........Estimation error
........Estimation theory
H. IEEE Index Terms
240
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 49
............Cramer-Rao bounds
............Maximum a posteriori estimation
........Life estimation
........Maximum likelihood estimation
........State estimation
............Observers
........Yield estimation
....Euclidean distance
........Hilbert space
....Finite difference methods
....Finite element analysis
....Fourier series
....Functional analysis
....Geometry
........Computational geometry
............Fractals
........Elliptic curves
........Elliptic design
............Ellipsoids
........Information geometry
........Surface topography
............Nanotopography
....Gradient methods
....Graph theory
........Bipartite graph
........Optimal matching
........Reachability analysis
........Shortest path problem
........Tree graphs
....Harmonic analysis
....Iterative methods
........Expectation-maximization algorithms
........Iterative algorithms
............Belief propagation
............Iterative closest point algorithm
............Sum product algorithm
....Kernel
........Null space
....Laplace equations
....Lattices
........Lattice Boltzmann methods
....Limit-cycles
....Linearization techniques
....Linear matrix inequalities
....Linear systems
....Mathematical model
........Mathematical analysis
............Formal concept analysis
............Fractional calculus
............Modal analysis
....Mathematical programming
....Method of moments
....Minimization
........Minimization methods
....Mode matching methods
....Network theory (graphs)
....Nonlinear equations
........Bifurcation
....Nonlinear systems
........Chaos
............Chaotic communication
............Complexity theory
............Spatiotemporal phenomena
........Nonlinear dynamical systems
....Numerical analysis
........Adaptive mesh refinement
........Approximation methods
............Approximation error
............Chebyshev approximation
............Curve fitting
............Extrapolation
............Function approximation
............Interpolation
............Least squares approximations
............Linear approximation
............Perturbation methods
........Convergence of numerical methods
........Finite difference methods
........Finite element analysis
........Finite volume methods
........Gradient methods
........Independent component analysis
........Iterative methods
............Expectation-maximization
algorithms
............Iterative algorithms
........Method of moments
........Mode matching methods
........Multigrid methods
........Newton method
........Numerical simulation
........Numerical stability
........Relaxation methods
........Sparse matrices
........Splines (mathematics)
........Surface fitting
............Response surface methodology
........Symmetric matrices
........Transmission line matrix methods
....Optimization
........Cost function
........Optimal scheduling
H. IEEE Index Terms
241
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 50
........Optimization methods
............Circuit optimization
............Design optimization
............Gradient methods
............H infinity control
............Mathematical programming
............Optimized production technology
............Pareto optimization
............Quadratic programming
............Simulated annealing
....Piecewise linear techniques
........Piecewise linear approximation
....Predator prey systems
....Probability
........Ant colony optimization
........Bayes methods
............Recursive estimation
........Error probability
........Forecasting
............Demand forecasting
............Economic forecasting
............Forecast uncertainty
............Technology forecasting
........Memoryless systems
........Pairwise error probability
........Possibility theory
........Probability distribution
............Exponential distribution
............Log-normal distribution
............Maxwell-Boltzmann distribution
............Nakagami distribution
........Random variables
........Statistical distributions
............Distribution functions
............Gaussian distribution
............Weibull distribution
........Uncertainty
............Forecast uncertainty
....Quaternions
....Random processes
........Brownian motion
....Root mean square
....Sequences
........Binary sequences
........Random sequences
....Set theory
........Fuzzy sets
........Fuzzy set theory
........Rough sets
....Simulated annealing
....Smoothing methods
....Spirals
....Statistics
........Adaptive estimation
........Autoregressive processes
........Boltzmann distribution
............Lattice Boltzmann methods
........Correlation
............Autocorrelation
........Correlation coefficient
........Covariance matrices
........Gaussian mixture model
........Higher order statistics
........Histograms
........Least squares methods
............Least mean squares methods
............Least squares approximations
........Linear discriminant analysis
........Maximum likelihood estimation
........Mean square error methods
........Minimax techniques
........Parametric statistics
........Prediction theory
........Ranking (statistics)
........Root mean square
........Sampling methods
............Compressed sensing
............Nonuniform sampling
........Statistical analysis
............Analysis of variance
............Mode matching methods
............Monte Carlo methods
............Parameter estimation
............Pareto analysis
............Principal component analysis
............Regression analysis
........Time series analysis
....Stochastic processes
........Gaussian processes
............Gaussian mixture model
........Markov processes
............Markov random fields
....Taylor series
....Topology
....Transforms
........Discrete transforms
............Discrete cosine transforms
........Empirical mode decomposition
........Fourier transforms
............Discrete Fourier transforms
............Fast Fourier transforms
........Karhunen-Loeve transforms
H. IEEE Index Terms
242
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 51
........Poincare invariance
........Wavelet transforms
............Biorthogonal modulation
............Continuous wavelet transforms
............Discrete wavelet transforms
............Wavelet coefficients
............Wavelet packets
....Transmission line matrix methods
....Uncertain systems
....Utility theory
Microwave theory and techniques
....Microwave technology
........Beam steering
........Circulators
........Masers
............Gyrotrons
........Microwave bands
............C-band
............K-band
............L-band
........Microwave circuits
........Microwave communication
............Rectennas
........Microwave devices
............Masers
............Microwave amplifiers
............Microwave filters
............Microwave transistors
........Microwave generation
............High power microwave generation
........Microwave photonics
........Microwave sensors
....Millimeter wave technology
........Millimeter wave circuits
............Millimeter wave integrated circuits
........Millimeter wave communication
........Millimeter wave devices
............Millimeter wave transistors
........Millimeter wave integrated circuits
............MIMICs
........Millimeter wave radar
....Submillimeter wave technology
........Submillimeter wave circuits
............Submillimeter wave integrated
circuits
........Submillimeter wave communication
........Submillimeter wave devices
............Submillimeter wave filters
........Submillimeter wave integrated circuits
Nanotechnology
....Bionanotechnology
....Casimir effect
....Molecular computing
....Molecular electronics
....Nanobioscience
........DNA computing
........Nanobiotechnology
....Nanoelectromechanical systems
....Nanoelectronics
....Nanofabrication
....Nanofluidics
....Nanolithography
....Nanomaterials
....Nanopatterning
........Colloidal lithography
....Nanophotonics
....Nanopositioning
....Nanoscale devices
........Nanocontacts
........Nanotube devices
....Nanosensors
....Nanostructured materials
........Nanocomposites
........Nanoporous materials
....Nanostructures
........Nanoparticles
............Nanocrystals
........Nanotubes
............Carbon nanotubes
............Semiconductor nanotubes
........Nanowires
........Semiconductor nanostructures
....Self-assembly
........Electrostatic self-assembly
....Self-replicating machines
Nuclear and plasma sciences
....Biomedical applications of radiation
....Colliding beam devices
........Colliding beam accelerators
........Muon colliders
....Electron emission
........Ballistic transport
............Electronic ballasts
....Elementary particles
........Charge carriers
............Charge carrier density
............Charge carrier lifetime
............Charge carrier mobility
H. IEEE Index Terms
243
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 52
............Charge carrier processes
............Hot carriers
........Electrons
............Electron sources
............Quantum wells
............Trions
........Elementary particle exchange
interactions
........Elementary particle vacuum
........Ions
............Ionization
............Ion sources
........Mesons
........Neutrino sources
........Neutrons
........Particle beams
............Atomic beams
............Electron beams
............Ion beams
........Particle collisions
........Phonons
........Positrons
........Protons
....Fusion power generation
....Fusion reactors
........Fusion reactor design
........Tokamaks
............Tokamak devices
....Gamma-rays
........Gamma-ray bursts
........Gamma-ray detection
........Gamma-ray effects
....Gas discharge devices
........Glow discharge devices
....High energy physics instrumentation
computing
........Linear particle accelerator
....Ion beam applications
........Ion implantation
............Plasma immersion ion implantation
....Ion emission
....Nuclear electronics
....Nuclear imaging
........Energy resolution
....Nuclear medicine
....Nuclear physics
........Alpha particles
........Beta rays
........Ignition
........Ion sources
........Isotopes
........Nuclear phase transformations
........Nuclear thermodynamics
........Relativistic effects
....Particle accelerators
........Accelerator magnets
........Colliding beam accelerators
........Cyclotrons
........Electron accelerators
........Ion accelerators
........Linear accelerators
........Photon collider
........Plasma accelerators
........Proton accelerators
........Storage rings
........Synchrocyclotrons
........Synchrotrons
............Synchrotron radiation
............Undulators
....Particle beam handling
....Particle beam injection
....Plasmas
........Atmospheric-pressure plasmas
........Plasma applications
............Plasma devices
............Plasma immersion ion implantation
............Plasma welding
............Tokamaks
........Plasma confinement
............Inertial confinement
............Magnetic confinement
........Plasma diagnostics
........Plasma properties
............Dusty plasmas
............Plasma chemistry
............Plasma density
............Plasma sheaths
............Plasma stability
............Plasma temperature
............Plasmons
........Plasma simulation
........Plasma sources
........Plasma transport processes
....Radiation effects
........Biological effects of radiation
........Gamma-ray effects
........Ion radiation effects
........Neutron radiation effects
....Radiation hardening (electronics)
....Radiation monitoring
........Radiation dosage
....Radiation safety
H. IEEE Index Terms
244
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 53
....Reactor instrumentation
....Scintillation counters
........Solid scintillation detectors
....Thermionic emission
Oceanic engineering and marine
technology
....Marine navigation
....Marine technology
........Marine equipment
........Marine transportation
............Marine vehicles
........Underwater cables
........Underwater communication
........Underwater equipment
............Rebreathing equipment
........Underwater structures
........Underwater technology
............Underwater communication
............Underwater equipment
............Underwater structures
....Oceanographic techniques
....Ocean temperature
....Water pollution
........Marine pollution
Power electronics
....Converters
........AC-AC converters
........DC-AC power converters
........Digital-to-frequency converters
........Frequency conversion
............Mixers
............Optical frequency conversion
........Power conversion
............AC-AC converters
............AC-DC power converters
............DC-AC power converters
............DC-DC power converters
............Matrix converters
............Power conversion harmonics
........Pulse width modulation converters
........Static power converters
........Wavelength converters
....Current limiters
........Fault current limiters
....Inverters
........Pulse inverters
........Resonant inverters
....Phase control
....Power conditioning
........Power smoothing
....Power semiconductor devices
........Power transistors
....Power semiconductor switches
........Bipolar transistors
............Insulated gate bipolar transistors
............Kirk field collapse effect
........Thyristors
............Photothyristors
....Snubbers
....Three-phase electric power
Power engineering and energy
....Electric variables control
........Current control
............Electrical ballasts
............Electric current control
........Gain control
........Power control
........Power system control
............Bidirectional power flow
............Load flow control
............SCADA systems
........Reactive power control
........Voltage control
............Automatic voltage control
....Energy
........Energy barrier
........Energy capture
........Energy consumption
........Energy conversion
............Batteries
............Fuel cells
............Motors
............Photovoltaic cells
............Potential well
............Solar heating
............Thermoelectricity
............Waste heat
........Energy dissipation
........Energy exchange
............Inductive charging
........Energy harvesting
........Energy management
............Energy conservation
............Energy efficiency
............Load management
........Energy resources
H. IEEE Index Terms
245
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 54
............Fuels
............Geothermal energy
............Nuclear fuels
............Solar energy
............Wave power
............Wind energy
............Wind farms
........Energy states
............Effective mass
............Orbital calculations
........Energy storage
............Batteries
............Flywheels
............Fuel cells
............Hydrogen storage
............Supercapacitors
............Superconducting magnetic energy
storage
....Power engineering
........Ferroresonance
........High-voltage techniques
........Power engineering computing
........Power system simulation
....Power generation
........Automatic generation control
........Cogeneration
........Distributed power generation
........Geothermal power generation
........Hydroelectric power generation
............Hydroelectric-thermal power
generation
............Microhydro power
............Picohydro power
........Magnetohydrodynamic power
generation
........Nuclear power generation
............Fission reactors
............Fusion power generation
........Power generation control
........Power generation dispatch
........Power generation planning
........Solar power generation
............Maximum power point trackers
............Photovoltaic systems
........Trigeneration
........Turbomachinery
............Turbines
............Turbogenerators
........Wind energy generation
............Wind energy integration
........Wind power generation
....Power systems
........Hybrid power systems
........Industrial power systems
........Power distribution
............Power distribution faults
............Power distribution lines
........Power grids
............Microgrids
............Smart grids
........Power supplies
............Battery chargers
............Charging stations
............Current supplies
............Emergency power supplies
............Inductive charging
............Islanding
............Power demand
............Power quality
............Power system restoration
............Switched-mode power supply
............Traction power supplies
............Umbilical cable
........Power system analysis computing
........Power system dynamics
........Power system economics
........Power system faults
........Power system harmonics
............Power harmonic filters
........Power system management
............Load flow
........Power system measurements
............Meter reading
........Power system planning
............Power demand
........Power system protection
............Electrical safety
............Substation protection
............Surge protection
........Power system reliability
........Power system stability
........Power transmission
............Flexible AC transmission systems
............HVDC transmission
............Inductive power transmission
............Static VAr compensators
............Transmission lines
........PSCAD
........Pulse power systems
............Pulsed power supplies
........Reactive power
........Substations
H. IEEE Index Terms
246
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 55
............Substation automation
............Substation protection
........Transformers
............Current transformers
............Flyback transformers
............Instrument transformers
............Phase transformers
............Power transformers
............Pulse transformers
........Uninterruptible power systems
........Wind energy integration
Product safety engineering
....Consumer protection
....Power system protection
........Electrical safety
............Fault protection
............Grounding
........Substation protection
........Surge protection
............Arresters
....Safety
........Aerospace safety
............Air safety
........Domestic safety
........Emergency services
........Explosion protection
........Hazards
............Biohazards
............Chemical hazards
............Explosions
............Fires
............Flammability
............Floods
............Hazardous areas
............Hazardous materials
............Toxicology
........Health and safety
............Occupational health
............Occupational safety
........Marine safety
........Product safety
........Protection
............Explosion protection
............Lightning protection
........Radiation safety
........Safety devices
............Eye protection
............Protective clothing
........Vehicle safety
....Vehicle crash testing
Professional communication
....Collaboration
........Collaborative tools
............Call conference
............Collaborative software
............Videoconferences
........Discussion forums
........Teamwork
........Virtual groups
....Communication aids
....Communication effectiveness
....Communication symbols
........Semiotics
............Pragmatics
............Semantics
............Syntactics
....Context
....Databases
........Database systems
............Audio databases
............Deductive databases
............Image databases
............Indexes
............Multimedia databases
............Object oriented databases
............Query processing
........Deductive databases
........Distributed databases
........Image databases
............Image retrieval
........Multimedia databases
........Object oriented databases
........Relational databases
........Spatial databases
........Transaction databases
............Itemsets
........Visual databases
....Global communication
........Cross-cultural communication
........Geographic information systems
............Geospatial analysis
............Gunshot detection systems
....Grammar
....Information analysis
........Indexing
....Information resources
....Information retrieval
........Blogs
H. IEEE Index Terms
247
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 56
........Content-based retrieval
........Hypertext systems
........Information filtering
............Information filters
............Recommender systems
........Information rates
........Music information retrieval
........Online services
........Search engines
........Search methods
............Keyword search
............Metasearch
............Nearest neighbor searches
............Search problems
............Web search
........Social network services
............Computer mediated communication
............Facebook
............LinkedIn
............MySpace
............Second Life
............Twitter
............YouTube
........Tagging
............Tag clouds
........Taxonomy
........Terminology
............Dictionaries
........Video sharing
............Facebook
............MySpace
............YouTube
........Vocabulary
........Web sites
............Facebook
............MySpace
............Uniform resource locators
............Web design
............YouTube
....Information science
....Information services
........Ask IEEE
........Dictionaries
........Document delivery
............Ask IEEE
........Encyclopedias
........Libraries
............Software libraries
........Teletext
........Videotex
........Wikipedia
....Information systems
........Database systems
............Audio databases
............Deductive databases
............Image databases
............Indexes
............Multimedia databases
............Object oriented databases
............Query processing
........Data systems
............Data acquisition
............Data compression
............Data conversion
............Data engineering
............Data handling
............Data processing
............Data storage systems
............Data warehouses
........Distributed information systems
............Publish-subscribe
........Identity management systems
........Informatics
............Biomedical informatics
............Cognitive informatics
........Information architecture
........Information management
............Competitive intelligence
............Document handling
............Information security
............Information sharing
............Knowledge transfer
........Information processing
............Informatics
............Information exchange
............Sonification
........Management information systems
............Portals
........Medical information systems
............Electronic medical records
....Information technology
........Information representation
........Printing
............Digital printing
............Teleprinting
........Service computing
........Telematics
........Universal Serial Bus
....Manuals
....Oral communication
........Public speaking
........Speech
H. IEEE Index Terms
248
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 57
....Plagiarism
....Portfolios
....Professional societies
....Public speaking
....Rhetoric
....Writing
........Abstracts
........Bibliographies
........Biographies
............Autobiographies
........Dictionaries
........Documentation
........Grammar
........Readability metrics
........Resumes
........Reviews
........Thesauri
Reliability
....Availability
....Fault diagnosis
........Dissolved gas analysis
........Fault location
....Fault tolerance
........Redundancy
....Fluctuations
....Integrated circuit reliability
....Maintenance
....Maldistribution
....Materials reliability
....Reliability engineering
....Reliability theory
....Robustness
....Semiconductor device reliability
....Software reliability
....Stability
........Circuit stability
........Robust stability
........Stability analysis
............Stability criteria
........Thermal stability
....Telecommunication network reliability
Resonance
....Ferroresonance
....Magnetic resonance
........Nuclear magnetic resonance
........Paramagnetic resonance
....Resonance light scattering
....Stochastic resonance
Robotics and automation
....Animatronics
....Automation
........Automated highways
........Automatic generation control
........Automatic testing
............Automatic test pattern generation
............Ring generators
........Building automation
........Manufacturing automation
............Computer aided manufacturing
............Computer integrated manufacturing
............Computer numerical control
............Flexible manufacturing systems
........Office automation
............Workflow management software
........Storage automation
....Multi-robot systems
....Robots
........Androids
........Aquatic robots
........Automata
............Turing machines
........Cognitive robotics
........Computer vision
............Active appearance model
............Face detection
............Smart cameras
........Educational robots
........Humanoid robots
........Intelligent robots
........Manipulators
............End effectors
............Manipulator dynamics
............Micromanipulators
........Medical robotics
............Rehabilitation robotics
........Mobile robots
............Climbing robots
............Legged locomotion
........Orbital robotics
........Parallel robots
........Robot control
............Robot motion
........Robot kinematics
............Motion analysis
........Robot programming
........Robot sensing systems
............Robot vision systems
H. IEEE Index Terms
249
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 58
............Simultaneous localization and
mapping
............Tactile sensors
........Service robots
........Telerobotics
............Teleoperators
Science - general
....Astronomy
........Astrophysics
........Observatories
........Orbits (stellar)
........Planets
............Earth
............Extrasolar planets
............Jupiter
............Mars
............Mercury (planets)
............Pluto
............Saturn
............Sun
............Venus
........Radio astronomy
........Solar system
............Kuiper belt
........Stellar dynamics
............Stellar motion
....Biology
........Biochemistry
............Amino acids
............Biochemical analysis
............Peptides
............Proteins
........Biodiversity
............Biogeography
........Bioelectric phenomena
............Electric shock
........Biological cells
............Cells (biology)
............Chromosome mapping
............Fibroblasts
............RNA
............Stem cells
........Biological information theory
........Biological processes
............Biological interactions
............Chronobiology
............Circadian rhythm
............Coagulation
............Symbiosis
........Biological system modeling
........Biological systems
............Anatomy
............Molecular communication
............Organisms
........Biology computing
........Biophotonics
........Biophysics
............Aerospace biophysics
............Biomagnetics
............Cellular biophysics
............Molecular biophysics
........Evolution (biology)
............Memetics
............Phylogeny
........Genetics
............DNA
............Gene therapy
............Genetic communication
............Genetic expression
............Genetic programming
............Genomics
........Microinjection
........Nanobioscience
............DNA computing
............Nanobiotechnology
........Physiology
........Predator prey systems
........Synthetic biology
........Systematics
........Systems biology
........Vegetation
............Crops
............Marine vegetation
........Zoology
............Animals
....Chemistry
........Astrochemistry
........Biochemistry
............Amino acids
............Biochemical analysis
............Peptides
............Proteins
........Chemical analysis
............Activation analysis
............Chemical processes
............Chemicals
............Electronic noses
............pH measurement
........Chemical compounds
............Anti-freeze
H. IEEE Index Terms
250
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 59
............Ethanol
............Methanol
........Inorganic chemicals
........Interstellar chemistry
........Organic chemicals
............Hydrocarbons
........Photochemistry
............Photobleaching
....Electricity
........Photoelectricity
............Photovoltaic effects
........Piezoelectricity
............Piezoelectric effect
............Piezoelectric polarization
........Pyroelectricity
........Thermoelectricity
............Electrothermal effects
............Thermoelectric devices
........Triboelectricity
....Geoscience
........Antarctica
............South Pole
........Arctic
............North Pole
........Atmosphere
............Atmospheric modeling
............Atmospheric waves
........Biosphere
........Continents
............Africa
............Asia
............Australia
............Europe
............North America
............South America
........Cyclones
............Hurricanes
............Tropical cyclones
........Earth
........Earthquakes
............Earthquake engineering
........Forestry
........Geoengineering
........Geography
............Cities and towns
............Rural areas
............Urban areas
........Geology
............Minerals
............Rocks
........Geophysics
............EMTDC
............Extraterrestrial phenomena
............Geodynamics
............Geophysics computing
............Meteorology
............Moisture
............Seismology
............Surface waves
............Well logging
........Ice
............Ice shelf
............Ice surface
............Ice thickness
............Sea ice
........Lakes
........Land surface
........Levee
........Meteorological factors
........Oceans
............Ocean salinity
............Ocean temperature
............Sea coast
............Sea floor
............Sea level
............Sea surface
............Tides
........Rivers
........Sediments
........Soil
............Soil moisture
............Soil properties
............Soil texture
........Tornadoes
........Tsunami
........Volcanoes
............Planetary volcanoes
............Volcanic activity
............Volcanic ash
....Metrology
....Physics
........Acoustics
............Acoustic applications
............Acoustic devices
............Acoustic emission
............Acoustic noise
............Acoustic propagation
............Acoustic pulses
............Acoustic waves
............Acoustooptic effects
............Biomedical acoustics
............Cepstral analysis
H. IEEE Index Terms
251
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 60
............Music
............Nonlinear acoustics
............Psychoacoustics
............Reverberation
............Spectral shape
............Underwater acoustics
........Astrophysics
........Beams
............Acoustic beams
............Laser beams
............Molecular beams
............Optical beams
............Particle beams
........Biophysics
............Aerospace biophysics
............Biomagnetics
............Cellular biophysics
............Molecular biophysics
........Dark energy
........Entropy
........Fluid flow
............Fluid dynamics
............Hydraulic diameter
............Hydrology
............Pipelines
............Valves
........Geophysics
............EMTDC
............Extraterrestrial phenomena
............Geodynamics
............Geophysics computing
............Meteorology
............Moisture
............Seismology
............Surface waves
............Well logging
........Kinetic theory
............Kinetic energy
........Levitation
............Electrostatic levitation
............Magnetic levitation
........Lorentz covariance
........Mechanical factors
............Acceleration
............Aerodynamics
............Biomechanics
............Damping
............Dynamics
............Fatigue
............Force
............Friction
............Hydrodynamics
............Kinematics
............Lubrication
............Magnetohydrodynamics
............Photoelasticity
............Pressure effects
............Shock (mechanics)
............Strain
............Stress
............Surface cracks
............Torque
............Vibrations
............Volume relaxation
............Workability
........Network theory (graphs)
........Orbits
........Physics education
........Quantum mechanics
............Density functional theory
............Lagrangian functions
............Proton effects
............Quantum capacitance
............Quantum entanglement
............Relativistic quantum mechanics
............Schrodinger equation
............Stationary state
............Teleportation
............Tunneling
........String theory
........Thermal factors
............Temperature
............Temperature dependence
............Thermal conductivity
............Thermal expansion
............Thermal management
............Thermal stresses
............Thermoelasticity
............Thermoelectricity
............Thermolysis
............Thermooptic effects
............Thermoresistivity
........Waves
............Atmospheric waves
............Berry phase
............Doppler effect
............Electrodynamics
............Magnetostatic waves
............Matter waves
............Plasma waves
............Propagation
............Reflectivity
H. IEEE Index Terms
252
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 61
............Seismic waves
............Shock waves
............Solitons
............Surface acoustic waves
............Wave functions
....Sociology
........Digital divide
....Thermodynamics
........Isobaric
........Isothermal processes
Sensors
....Acoustic sensors
....Chemical and biological sensors
........Biosensors
........Gas detectors
............Amperometric sensors
....Electromechanical sensors
........Microsensors
....Force sensors
....Infrared sensors
....Intelligent sensors
....Intracranial pressure sensors
....Ionizing radiation sensors
........Position sensitive particle detectors
........Radiation detectors
............Bolometers
............Gamma-ray detectors
............Infrared detectors
............Photodetectors
............Semiconductor radiation detectors
............Silicon radiation detectors
........X-ray detectors
....Magnetic sensors
........Spin valves
....Mechanical sensors
........Capacitive sensors
....Multimodal sensors
....Nanosensors
....Optical sensors
........Optical detectors
............Bar codes
........Optical fiber sensors
....Optoelectronic and photonic sensors
....Sensor phenomena and characterization
....Sensor systems and applications
........Detectors
............Envelope detectors
............Semiconductor detectors
........Electric sensing devices
........Leak detection
........Radiofrequency identification
............RFID tags
........Robot sensing systems
............Robot vision systems
............Simultaneous localization and
mapping
............Tactile sensors
........Sensor arrays
............Sensor fusion
........Sensor systems
............Gunshot detection systems
....Thermal sensors
........Temperature sensors
....Thick film sensors
....Thin film sensors
....Wearable sensors
Signal processing
....Acoustic signal processing
........Active noise reduction
............Echo cancellers
........Speech processing
............Human voice
............Speech enhancement
............Speech synthesis
....Adaptive signal processing
........Adaptive filters
........Adaptive signal detection
....Amplifiers
........Broadband amplifiers
........Cavity resonators
............Laser cavity resonators
........Differential amplifiers
........Distributed amplifiers
........Low-noise amplifiers
........Operational amplifiers
............Feedback amplifier
........Power amplifiers
............High power amplifiers
............Predistortion
........Preamplifiers
........Pulse amplifiers
........Radiofrequency amplifiers
....Array signal processing
....Attenuators
........Optical attenuators
....Chirp
....Convolution
........Convolvers
H. IEEE Index Terms
253
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 62
....Decorrelation
....Digital signal processing
........Delta modulation
............Delta-sigma modulation
............Sigma-delta modulation
........Digital signal processing chips
....Dispersion
........Chromatic dispersion
........Optical fiber dispersion
....Distortion
........Acoustic distortion
........Four-wave mixing
........Jitter
............Timing jitter
........Nonlinear distortion
............Harmonic distortion
............Intermodulation distortion
........Phase distortion
....Error correction
........Forward error correction
....Fading
........Frequency-selective fading channels
........Rayleigh channels
........Weibull fading channels
....Filters
........Active filters
............Band-pass filters
........Anisotropic
........Bragg gratings
............Fiber gratings
........Channel bank filters
........Digital filters
............Finite impulse response filters
........Equalizers
............Adaptive equalizers
............Blind equalizers
............Decision feedback equalizers
........Filtering theory
........Gabor filters
........Harmonic filters
........IIR filters
........Kalman filters
........Low-pass filters
........Matched filters
........Microstrip filters
........Nonlinear filters
........Particle filters
........Power filters
............Spurline
........Resonator filters
........Spatial filters
........Superconducting filters
........Transversal filters
....Frequency locked loops
....Geophysical signal processing
....Limiting
....Modulation
........Amplitude modulation
............Amplitude shift keying
............Quadrature amplitude modulation
........Chirp modulation
........Demodulation
........Digital modulation
............Constellation diagram
............Partial response signaling
........Frequency modulation
............Frequency shift keying
........Magnetic modulators
........Modulation coding
............Interleaved codes
........Optical modulation
............Electrooptic modulators
............Intensity modulation
........Phase modulation
............Continuous phase modulation
............Differential phase shift keying
............Phase shift keying
........Pulse modulation
........Pulse width modulation
............Pulse width modulation inverters
............Space vector pulse width
modulation
....Multidimensional signal processing
........Video signal processing
............Video coding
............Video compression
....Noise
........1f noise
........Additive noise
............Additive white noise
............AWGN
........Colored noise
........Gaussian noise
............AWGN
........Laser noise
............Laser feedback
........Low-frequency noise
........Noise cancellation
........Phase noise
........Signal to noise ratio
............PSNR
........Superconducting device noise
H. IEEE Index Terms
254
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 63
........White noise
............AWGN
....Optical signal processing
........Laser noise
............Laser feedback
....Optical wavelength conversion
....Phase locked loops
....Pulse compression methods
........Optical pulse compression
....Pulse shaping methods
........Optical pulse shaping
....Quantization (signal)
........Vector quantization
....Radar signal processing
....Recording
........Audio recording
........Digital recording
........Disk recording
........Magnetic recording
............Digital magnetic recording
............Heat-assisted magnetic recording
............Magnetic noise
............Magnetooptic recording
............Microwave-assisted magnetic
recording
............Perpendicular magnetic recording
........Optical recording
............CD recording
........Video recording
............High definition video
............Webcams
....RF signals
....Signal analysis
........Discrete-event systems
........Harmonic analysis
........Parameter estimation
............Amplitude estimation
............Direction-of-arrival estimation
............Frequency estimation
............Motion estimation
............Phase estimation
............Time of arrival estimation
........Signal mapping
........Spectral analysis
............Infrared spectra
............Judd-Ofelt theory
............Spectroradiometers
....Signal design
....Signal detection
........Acoustic signal detection
............Sonar detection
........Motion detection
........Multiuser detection
........Optical signal detection
........Phase detection
............Phase frequency detector
........Radar detection
....Signal generators
........Noise generators
........Pulse generation
............Optical pulse generation
....Signal reconstruction
........Signal denoising
....Signal resolution
........Diversity reception
....Signal restoration
....Signal sampling
....Signal synthesis
....Source separation
........Blind source separation
....Spectrogram
....Tracking loops
Social implications of technology
....Cultural differences
....Environmental factors
........Biosphere
........Ecosystems
........Environmental economics
............Carbon tax
........Environmental monitoring
........Global warming
........Green products
............Green buildings
............Green cleaning
........Pollution
............Air pollution
............Industrial pollution
............Land pollution
............Oil pollution
............Radioactive pollution
............Thermal pollution
............Urban pollution
............Water pollution
....Ethical aspects
....Globalization
....International relations
....Peace technology
....Philosophical considerations
....Social factors
........Demography
H. IEEE Index Terms
255
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 64
........Technology social factors
............Privacy
....Sustainable development
....Technology
........Appropriate technology
........Technological innovation
........Technology social factors
............Privacy
........Technology transfer
............Small business technology transfer
Solid state circuits
....Circuit subsystems
....Circuit theory
....FET circuits
........FET integrated circuits
............Field effect MMIC
............MESFET integrated circuits
........JFET circuits
............JFET integrated circuits
........MESFET circuits
............MESFET integrated circuits
........MODFET circuits
............MODFET integrated circuits
........MOSFET circuits
............CMOSFET circuits
............MOS integrated circuits
............Power MOSFET
....Gate leakage
....Solid state circuit design
....Transistors
........Field effect transistors
............CNTFETs
............Double-gate FETs
............HEMTs
............JFETs
............MESFETs
............MISFETs
............MODFETs
............MOSFET
............MOSHFETs
............OFETs
............Schottky gate field effect transistors
............Thin film transistors
........Heterojunction bipolar transistors
............Double heterojunction bipolar
transistors
........Millimeter wave transistors
........Phototransistors
Superconductivity
....Bean model
....Critical current density
(superconductivity)
........Critical current density
....Flux pinning
....Superconducting devices
........Josephson junctions
........SQUIDs
........Superconducting coils
........Superconducting magnets
........Superconducting microwave devices
........Superconducting photodetectors
....Superconducting filaments and wires
....Superconducting films
........Superconducting thin films
....Superconducting integrated circuits
....Superconducting magnetic energy
storage
....Superconducting materials
........Granular superconductors
........High-temperature superconductors
............Yttrium barium copper oxide
........Multifilamentary superconductors
........Niobium-tin
........Type II superconductors
....Superconducting transition temperature
Systems engineering and theory
....Adaptive systems
........Adaptive control
........Line enhancers
........Multi-agent systems
........Variable structure systems
....Hierarchical systems
........Multilevel systems
....Modeling
........Analytical models
........Atmospheric modeling
........Brain modeling
........Computational modeling
............Computational cultural modeling
........Context modeling
........Data models
........Deformable models
........Digital elevation models
........Emulation
........Graphical models
........Green's function methods
........Hidden Markov models
........Input variables
........Integrated circuit modeling
H. IEEE Index Terms
256
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 65
............Cutoff frequency
........Inverse problems
............Deconvolution
........Load modeling
........Metamodeling
........Numerical models
........Object oriented modeling
........Power system modeling
............Load modeling
........Semiconductor device modeling
........Semiconductor process modeling
........Signal representation
........Simulation
............Computer simulation
............Digital simulation
............Medical simulation
........Solid modeling
........System identification
....Multidimensional systems
....Reduced order systems
....Stochastic systems
....System analysis and design
........Asymptotic stability
........Control system analysis
............State-space methods
........Diakoptics
........Distributed processing
............Message passing
........Distributed vision networks
........Fault detection
........Fault tolerant systems
........Interconnected systems
........Large-scale systems
........Lyapunov methods
........Open systems
............Open Access
............Physical layer
........Petri nets
........Robust control
........Scalability
........Scattering parameters
........Sequential analysis
........Sequential diagnosis
........Software prototyping
........System-level design
........System performance
............Cooperative caching
........Time factors
............Continuous time systems
............Discrete-time systems
............Time invariant systems
............Time-varying systems
....Systems engineering education
Systems, man, and cybernetics
....Behavioral science
........Animal behavior
........Cognition
........Consumer behavior
........Psychiatry
............Mental disorders
........Psychology
............Industrial psychology
............Mood
............Psychometric testing
....Biological control systems
........Biomarkers
............Molecular biomarkers
....Computational linguistics
........Sentiment analysis
....Cybernetics
........Adaptive systems
............Adaptive control
............Line enhancers
............Multi-agent systems
............Variable structure systems
........Cognitive informatics
........Cognitive science
............Problem-solving
........Control theory
............Control nonlinearities
............Observability
........Decision theory
............Decision trees
........Econophysics
........Emergent phenomena
........Intelligent control
............Feedforward systems
............Neurocontrollers
........Linear feedback control systems
............Frequency locked loops
............Phase locked loops
............State feedback
............Tracking loops
....Ergonomics
........Job design
....Human factors
........Affective computing
........Anthropomorphism
....Identification of persons
........Biometrics (access control)
H. IEEE Index Terms
257
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 66
............Gait recognition
............Iris recognition
........Face recognition
........Fingerprint recognition
........Handwriting recognition
............Forgery
........Speaker recognition
........Speech recognition
............Automatic speech recognition
............Speech analysis
....Man machine systems
........Interactive systems
....Natural languages
........Natural language processing
............Morphology
............Sentiment analysis
....Pervasive computing
........Ubiquitous computing
............Context-aware services
........Wearable computers
....Posthuman
....Teleworking
....Transhuman
....User interfaces
........Audio user interfaces
........Brain-computer interfaces
........Data visualization
............Isosurfaces
........Emotion recognition
........Exoskeletons
........Graphical user interfaces
............Avatars
........Human computer interaction
........Human-robot interaction
........Smart cards
Ultrasonics, ferroelectrics, and
frequency control
....Ferroelectric materials
........Ferroelectric films
........Relaxor ferroelectrics
....Frequency control
........Automatic frequency control
........Tunable circuits and devices
............RLC circuits
............Tuned circuits
........Tuning
............Laser tuning
............Optical tuning
............Tuners
....Piezoelectricity
........Piezoelectric effect
........Piezoelectric polarization
....Pyroelectricity
....Ultrasonic imaging
........Ultrasonography
............Sonogram
....Ultrasonic transducers
Vehicular and wireless technologies
....Automotive engineering
........Automotive applications
........Automotive electronics
........Power steering
........Vehicle crash testing
........Vehicle detection
........Vehicle driving
........Vehicle dynamics
........Vehicle safety
....Land mobile radio equipment
........Mobile antennas
....Navigation
........Aircraft navigation
........Course correction
........Dead reckoning
........Inertial navigation
........Marine navigation
........Radio navigation
........Satellite navigation systems
............Global Positioning System
............Satellite constellations
........Sonar navigation
....Propulsion
........Aircraft propulsion
............Propellers
........Electromagnetic launching
............Coilguns
............Railguns
........Electrothermal launching
........Rockets
....Vehicles
........Land vehicles
............Bicycles
............Electric vehicles
............Road vehicles
........Remotely operated vehicles
............Unmanned aerial vehicles
........Space vehicles
............Space shuttles
....Wireless sensor networks
H. IEEE Index Terms
258
2014 IEEE Taxonomy
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0
International License (CC BY-NC-ND 4.0). Created by The Institute of Electrical and Electronics
Engineers (IEEE) for the benefit of humanity. Page 67
........Body sensor networks
........Event detection
H. IEEE Index Terms
259
Appendix I
PUBLICATION LIST AND AWARD
Journal (example only)
1. ¨
O. Aksın, H. T¨
urkmen, L. Artok, B. C¸ etinkaya, C. Ni, O. B¨
uy¨
ukg¨
ung¨
or, and
E. ¨
Ozkal, “Effect of immobilization on catalytic characteristics of saturated
pd-n-heterocyclic carbenes in mizoroki-heck reactions,” Journal of Organometallic
Chemistry, vol. 691, no. 13, pp. 3027–3036, 2006.
2. . . .
Conference
1. . . .
2. . . .
Others
1. . . .
2. . . .
Award
1. . . .
2. . . .
260
Appendix J
VITA
Juan Z. dela Cruz received the B.Sc., M.Sc., and Ph.D. degrees in
chemistry all from the Pamantasan ng Pilipinas, San Juan, Metro Manila, Philippines, in
2011, 2013 and 2016 respectively. He is currently taking up his B.Sc. Electronics and
Communications Engineering studies. He has developed several high-speed
packet-switched network systems and node modules. His research interests include
high-speed packet-switched networks, high speed radio interface design, discrete
simulation and statistical models for packet switches.
Nat Y. Franco received the B.Sc., M.Sc., and Ph.D. degrees in
chemistry all from the Pamantasan ng Pilipinas, San Juan, Metro Manila, Philippines, in
2011, 2013 and 2016 respectively. He is currently taking up his B.Sc. Electronics and
Communications Engineering studies. He has developed several high-speed
packet-switched network systems and node modules. His research interests include
high-speed packet-switched networks, high speed radio interface design, discrete
simulation and statistical models for packet switches.
Sebastian X. Garcia received the B.Sc., M.Sc., and Ph.D. degrees in
chemistry all from the Pamantasan ng Pilipinas, San Juan, Metro Manila, Philippines, in
2011, 2013 and 2016 respectively. He is currently taking up his B.Sc. Electronics and
Communications Engineering studies. He has developed several high-speed
261
J. Vita
packet-switched network systems and node modules. His research interests include
high-speed packet-switched networks, high speed radio interface design, discrete
simulation and statistical models for packet switches.
Isabella W. Martinez received the B.Sc., M.Sc., and Ph.D. degrees in
chemistry all from the Pamantasan ng Pilipinas, San Juan, Metro Manila, Philippines, in
2011, 2013 and 2016 respectively. He is currently taking up his B.Sc. Electronics and
Communications Engineering studies. He has developed several high-speed
packet-switched network systems and node modules. His research interests include
high-speed packet-switched networks, high speed radio interface design, discrete
simulation and statistical models for packet switches.
Max V. Rianzares received the B.Sc., M.Sc., and Ph.D. degrees in
chemistry all from the Pamantasan ng Pilipinas, San Juan, Metro Manila, Philippines, in
2011, 2013 and 2016 respectively. He is currently taking up his B.Sc. Electronics and
Communications Engineering studies. He has developed several high-speed
packet-switched network systems and node modules. His research interests include
high-speed packet-switched networks, high speed radio interface design, discrete
simulation and statistical models for packet switches.
262
INDEX
contributions, 34
Fourier operator, 89
Fredholm integral, 89
summary, 4
263

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