An Introduction to LATEX F 8 f
Martins Bruveris http://www.brunel.ac.uk/~mastmmb
February 13, 2017
Illustration by Duane Bibby Contents
1 What are TEX, LATEX and Friends?
2 Document Types
3 Mathematics and Other Material
4 Typography Contents
1 What are TEX, LATEX and Friends?
2 Document Types
3 Mathematics and Other Material
4 Typography The Final Year Project
Is 50–70 pages long and contains Z ∞ x2 Mathematical equations e− dx = √π −∞ Graphs x 0 1 2 Tables y 0.5 0.5 7.5
if x > 0 Source code y = sqrt(x); See [1, Theorem 1.2.6] for a proof. end [1] S. Abbott. Understanding Analysis. References and a bibliography Undergraduate Texts in Mathematics. Springer, New York, 2015. What are TEX and LATEX, and Friends?
TEX From Greek τχ. Abbreviation of τχνη, meaning art or cra . ASCII TeX, /tEx/, /tEk/. A computer typesetting system created by Donald Knuth for ‘the creation of beautiful books’. First release 1978. (39 years ago!) LATEX A shortening of ‘Lamport-TEX’. ASCII LaTeX, /"leItEx/, /"leItEk/, /"lA:tEx/, /"lA:tEk/. A document preparation system by Leslie Lamport. First release 1985. Friends BibTEX, Biber, MakeIndex,... h p://www.ctan.org/what_is_tex.html Donald Knuth (1938–) American computer scientist, mathematician, and professor emeritus at Stanford University Author of the multi-volume work The Art of Computer Programming “Father of the analysis of algorithms”
“Science is what we understand well enough to explain to a computer. Art is everything else we do.” “If you optimize everything, you will always be unhappy.” Leslie Lamport (1941–) American computer scientist Laid the foundations of the theory of distributed systems
“A distributed system is one in which the failure of a computer you didn’t even know existed can render your own computer unusable.” Typesetting and Word Processing Apples and Oranges
Word Processors Typesetting Software Word, Google Docs, LibreOice LATEX, InDesign, Scribus What you see is what you get. Separation of content and Content and layout are presentation. generated at the same time. Layout can be globally Local style adjustments are optimised. easier to make. Uniform style easier to realise.
typese ing n. The activity of arranging printed text and images on the page when preparing a book, newspaper, etc. for printing. (Cambridge English Dictionary) Scalability
Impossible to do
MS Word
LATEX Eort and time consumption
Document complexity and size
Scalability of LATEX and Microso Word as a function of document size and complexity.
Redrawn from Marko Pinteric’s original (link). Example .tex File
\documentclass[a4paper,11pt]{article} An Introductory Paper \author{Martins Bruveris} Martins Bruveris \title{An Introductory Paper} \date{\today} February 5, 2017 \usepackage[english]{babel} Contents
\begin{document} 1 Introduction 1
\maketitle 2 State of the Art 1 \tableofcontents 2.1 Document Formats ...... 1
Abstract \begin{abstract} This paper introduces. . . This paper introduces\ldots \end{abstract} 1 Introduction We consider. . . \section{Introduction} 2 State of the Art We consider\ldots We look at. . .
\section{State of the Art} 2.1 Document Formats We look at\ldots There are many. . .
\subsection{Document Formats} There are many\ldots \end{document} 1
pdflatex Module Structure
Lecture Introduction to LATEX (happening right now) Labs Three computer labs for each group (W21–23) Mon, Tue or Thu 17–19 in HALB 213
Assignment Preparing a document, about two pages long Thematically connected to MA2895 assignment Due 3 April 2017 (TBC)
Assessment Contributes 20% towards MA2812 Where Do I Get It?
Online ShareLaTeX (www.sharelatex.com) Overleaf (www.overleaf.com)
Windows MikTEX, TEXLive Linux TEXLive Mac OS X MacTEX (based on TEXLive) Editors TeXmaker, TeXworks, TeXstudio, emacs (Mac OS X) TeXShop
LATEX Packages Use MikTEX or TEXLive’s package manager Documentation (Online) h p://texdoc.net/pkg/
Online Search the internet E.g. use ‘latex add table of contents’ in your favorite search engine. TEX Stack Exchange (h p://tex.stackexchange.com) The LATEX Wikibook (h p://en.wikibooks.org/wiki/latex)
Books George Graetzer, Practical LATEX. Springer, 2014. Electronic version available through the library. (Link) Helmut Kopka, Patric W. Daley, Guide to LATEX. Fourth Edition. Addison-Wesley, 2004. Electronic version available through the library. (Link)
Other LATEX Cheat Sheet (Link) The Not So Short Introduction to LATEX 2ε(Link) The ShareLaTeX Documentation (Link) Overleaf LATEXTutorial (Link) Why? From http://www.ctan.org/what_is_tex.html
Output Quality Freedom Professional quality output. It’s free. It knows typese ing. It runs anywhere.
Superior Engineering Popularity It’s fast. It’s standard in academia It’s stable. and science. It’s extensible. Plain text input. Many output types. Contents
1 What are TEX, LATEX and Friends?
2 Document Types
3 Mathematics and Other Material
4 Typography Article – The Basic Document
A blind text like this gives you information about the selected font, how the letters are written and the impression of the look. This text should contain all letters of the alphabet and it should be written in of the original language. A Wonderful Read There is no need for a special contents, but the length of words should match to the language.
A. Dummy Heading on level 4 (paragraph) Hello, here is some text without a meaning. This text should show, how a printed text will look like at this 3rd June 2011 place. If you read this text, you will get no information. Really? Is there no information? Is there a difference between this text and some nonsense like »Huardest gefburn«. Kjift – Never mind! A blind text like this gives 1 Heading on level 1 (section) you information about the selected font, how the letters are written and the impression of the look. This text should contain all letters of the alphabet Hello, here is some text without a meaning. This text should show, how a and it should be written in of the original language. There is no need for a printed text will look like at this place. If you read this text, you will get no special contents, but the length of words should match to the language. information. Really? Is there no information? Is there a difference between this text and some nonsense like »Huardest gefburn«. Kjift – Never mind! A blind text like this gives you information about the selected font, how the 2 Lists \documentclass{article} letters are written and the impression of the look. This text should contain all letters of the alphabet and it should be written in of the original language. 2.1 Example for list (itemize) There is no need for a special contents, but the length of words should match First item in a list to the language. • Second item in a list • 1.1 Heading on level 2 (subsection) Third item in a list • \author{...} Hello, here is some text without a meaning. This text should show, how a Fourth item in a list printed text will look like at this place. If you read this text, you will get no • information. Really? Is there no information? Is there a difference between Fifth item in a list • this text and some nonsense like »Huardest gefburn«. Kjift – Never mind! A blind text like this gives you information about the selected font, how the 2.1.1 Example for list (4*itemize) letters are written and the impression of the look. This text should contain First item in a list all letters of the alphabet and it should be written in of the original language. • \title{...} There is no need for a special contents, but the length of words should match – First item in a list to the language. First item in a list ∗ First item in a list 1.1.1 Heading on level 3 (subsubsection) · Second item in a list · Hello, here is some text without a meaning. This text should show, how a Second item in a list printed text will look like at this place. If you read this text, you will get no ∗ – Second item in a list information. Really? Is there no information? Is there a difference between this text and some nonsense like »Huardest gefburn«. Kjift – Never mind! Second item in a list • 1 2 \begin{document} \maketitle
2.2 Example for list (enumerate) Second item in a list \section 1. First item in a list Second item in a list {...} Second item in a list 2. Second item in a list Second item in a list 3. Third item in a list
4. Fourth item in a list ... 5. Fifth item in a list 2.2.1 Example for list (4*enumerate) 1. First item in a list
(a) First item in a list i. First item in a list \subsection{...} A. First item in a list B. Second item in a list ii. Second item in a list (b) Second item in a list
2. Second item in a list
\end{document} 2.3 Example for list (description) First item in a list
Second item in a list
Third item in a list
Fourth item in a list
Fifth item in a list
2.3.1 Example for list (4*description) First item in a list
First item in a list First item in a list First item in a list
3 4 Some Features of LATEX
Automatic generation of cross-referencing labels: \section{Introduction}\label{sec:intro} ... We saw in section \ref{sec:intro}... Automatic generation of lists: \tableofcontents, \listoffigures, \listoftables Automatic generation of bibliographies and indices: \cite{Knuth:1976}...\bibliography{references.bib} ...the Linux kernel\index{Linux!kernel}... \printindex Fully hyperlinked PDF with bookmarks: \usepackage{hyperref} Inclusion of selected pages from other PDFs (while inserting new page headers/footers!) \usepackage{pdfpages} \includepdf[pages={1,3-5,8},pagecommand=\thispagestyle{plain}]{file.pdf} ick language-switching with babel Your Final Year Project
A template for a university thesis.
My University Name
My College Name My Department Name Contents Chapter 1 Bibliography
My Course Name Sequences [1] S. Abbott. Understanding analysis. Second. Undergraduate Texts in Math- Abstract i ematics. Springer, New York, 2015, pp. xii+312. Acknowledgments ii [2] R. E. Bradley and C. E. Sandifer. Cauchy’s Cours d’analyse. Sources and 1.1 Sequences and convergence Studies in the History of Mathematics and Physical Sciences. An annotated 1 Sequences 1 translation. Springer, New York, 2009, pp. xx+411. 1.1 Sequences and convergence ...... 1 A sequence is an infinite list of numbers. Examples of sequences are [3] D. M. Burton. The History of Mathematics. Second. An introduction. W. 1.2 Bounded and unbounded sequences ...... 4 C. Brown Publishers, Dubuque, IA, 1991, pp. xii+678. 1.3 Properties of convergent sequences ...... 7 1, 2, 3, 4, 5, 6,... 1, 1, 1, 1, 1, 1,... Thesis Title − − − 1.4 Sequences and functions ...... 11 1 1 1 [4] C. H. Edwards Jr. The Historical Development of the Calculus. Springer- 4, 2, 1, , , ,... 2, 3, 5, 7, 11, 13,... 1.5 Some important limits ...... 11 2 4 8 Verlag, New York-Heidelberg, 1979, pp. xii+351. 1.6 Bounded sets ...... 13 3, 10, 5, 16, 8, 4, 2,... 3, 3.1, 3.14, 3.141, 3.1415, 3.14159,... [5] N. Huggett. Zeno’s paradoxes — The Stanford Encyclopedia of Philosophy. 1.7 Monotone sequences ...... 15 Ed. by E. N. Zalta. Winter 2010 Edition. url: http://plato.stanford. 1.8 Tail of a sequence ...... 17 The dots indicate that the sequence does not stop after 6 elements, but continues edu/archives/win2010/entries/paradox-zeno/. 1.9 Subsequences ...... 18 indefinitely. It is the finiteness of paper that forces us to stop at some point. [6] S. Kifowit. More proofs of divergence of the harmonic series. Online adden- 1.10 Theroem of Bolzano–Weierstrass ...... 20 In this regard the mathematical usage of the term ‘sequence’ differs from the dum to the article ”The harmonic series diverges again and again”. 2006. 1.11 Cauchy sequences ...... 21 colloqial one: in mathematics a finite, ordered list of numbers is a tuple. We can url: http://stevekifowit.com/pubs/harm2.pdf. speak of a 3-tuple (7, 2, 5) or an n-tuple (1, 2, . . . , n). A sequence however is an 2 Series 25 infinite list of numbers. Formally we have the following definition. [7] S. Kifowit and T. A. Stamps. Serious about the harmonic series II. Hand- 2.1 Definition ...... 25 out to presentation at 31st Annual Conference of the Illinois Mathematics 1 Definition 1.1. A sequence is a map x : N R. We will write xn := x(n) for John Doe Supervisor: 2.2 Necessary condition for convergence ...... 31 → Association of Community Colleges. 2006. url: http://stevekifowit. the nth element of the sequence and denote the whole sequence by x ∞ or Student Number: 1234567 Dr. Richard Smith 2.3 Comparison test ...... 33 { n}n=1 com/pubs/al1.pdf. xn . 2.4 D’Alembert test ...... 35 { } [8] S. Kifowit and T. A. Stamps. “The harmonic series diverges again and 2.5 Integral test ...... 37 How do we capture infinitely many elements on a finite sheet of paper? We again”. In: The AMATYC Review 27 (2006), pp. 31–43. 2.6 Alternating series test ...... 40 do this by providing the general rule that allows us to calculate any element of [9] J. J. O’Connor and E. F. Robertson. Augustin-Louis Cauchy — MacTutor 2.7 Absolute convergence ...... 42 the sequence. For example, the first four sequences shown above are defined by History of Mathematics archive. Accessed 11/11/2016. url: http://www- the following rules: 3 Power Series 47 history.mcs.st-andrews.ac.uk/Biographies/Cauchy.html.
3.1 Definition and convergence ...... 47 n [10] A. Stubhaug. Niels Henrik Abel and his times. Called too soon by flames Year of Submission: 2016 xn = n xn = ( 1) 3.2 Continuity and differentiability ...... 50 − 2 n afar, Translated from the second Norwegian (1996) edition by Richard H. xn = 2 − xn is the n-th prime number . 3.3 Taylor series ...... 54 Daly. Springer-Verlag, Berlin, 2000, pp. x+580. 3.4 Exponential and trigonometric functions ...... 58 1For the purpose of these notes, N = 1, 2, 3, 4,... . { } 3.5 Abel’s theorem ...... 60
iii 1 67
LATEXsource available at h ps://github.com/martinsbruveris/thesis-template. See also h ps://www.brunel.ac.uk/~mastmmb/mathwriting.html. Highly Congurable Documents memoir and KOMA-Script Classes
Sectional headings Running headers and footers Good font, colour and illustration choices
Image: A simple network. Illustration by ©Svilen Mushkatov (http://www.sxc.hu/profile/svilen001). Grid@USM
PWN Analyser
PWN PWN Analyser Analyser PWN Grid Computing Cluster Analyser Remote Host Remote Host Lexicon Lexicon Lexicon The Development and Integration of Dispenser Dispenser Dispenser Grid Services and Applications CONTENTS Remote Host Lexicon Dispenser Project Overview Sense-Tagger Introduction 2 PWN Remote Host Grid@USM: Developing & Integrating Grid Applications & Services 4 Syntactic Lexicon Analyser Project Milestones 7 Parser Dispenser SLB on utmkblex Project Expenditures 8 Grid@USM Figure 3: Blexisma2 agents are deployed on USM Campus Grid nodes using the Globus job submission toolkit. Sub-Projects 2008/09 Report Setting up USM Campus Grid 10 AP Chan Huah Yong, Ang Sin Keat, Tan Chin Min, Kheoh Hooi Leng, Cheng Wai Khuen, M. Muzzammil bin Mohd Salahudin Dynamic Replica Management in Data Grid Environment 14 AP Chan Huah Yong, Aloysius Indrayanto and Muhammad Muzzammil bin Mohd Salahudin Using Grid Technology to Create a Render-Farm for Blender 3D Animation 18 AP Phua Kia Ken and Zafri Muhammad Grid-enabled Blexisma2 23 AP Tang Enya Kong, Lim Lian Tze, Ye Hong Hoe and Dr Didier Schwab B2B Standards Component Modeling 27 Dr Vincent Khoo Kay Teong, Ting Tin Tin, Rinki Yadav, Johnson Foong and Kor Chan Hock An Automated Java Testing Tool on the Grid 31 Grid@USM: (a) Diferent meanings of star in context (b) Different meanings of school in context Dr Kamal Zuhairi Zamli, Dr Nor Ashidi Mat Isa, Mohammed Issam Younis and Saidatul Khatimah binti Said iNet-Grid 35 DEVELOPING & INTEGRATING Figure 4: SLB data generated by Blexisma2 agents used to determine most probable meanings of ambiguous lexical Prof. Sureswaran Ramadass, AP Rahmat Budiarto, AP Chan Huah Yong and Dr Ahmed M. Manasrah item. A Web interface to the Sense-Tagger is available at http://utmkblex.usmgrid.myren.net.my:8080/Blexisma2Servlets/ Grid Application to Wave Front Propagation and Containment of Vector Borne Diseases 40 CVSenseTagger. Prof. Koh Hock Lye, Dr Teh Su Yean and Tan Kah Bee GRID APPLICATIONS & SERVICES interested to improve its design to On the performance issues, we with Ontology-based Conceptual Project Activities a multilingual setting, where more may attempt several solutions for the Vectors. In Proceedings of the 5th In- Organised Events 46 complicated cross-lingual phenomena SLB bottleneck problem mentioned ternational Workshop on Natural Lan- will have to be considered. We also earlier: guage Processing and Cognitive Sci- Other Events 48 hope to improve the agent commu- ence (NLPCS’08). Barcelona, Spain; Publications 50 USM’S R&D SUSTAINABILITY for attaining and subsequently sus- Grid computing is by its na- nication mechanisms to reduce la- hardware (RAM) upgrades, pp. 153–158. taining RU status is the creation ture highly distributed geographically, further optimisation of PostgreSQL To attain the level of excellence as a tency. Apart from creating more of highly conducive research envi- consists of highly specialised equip- agents that implement different learn- server settings, Schwab, D. & Lim, L. T. (2008). Blex- research university (RU), USM in re- Edited by Bahari Belaton and Lim Lian Tze ronment and infrastructure. Grid ment (storage, grid engines and man- database connection pooling, isma2: a Distributed Agent Frame- cent years has seriously engaged her- ing algorithms and heuristics, we are computing is an example of such agement tools), as well as expensive. load balancing, work for Constructing a Semantic self in various efforts to formulate also planning agents responsible for Platform for Information & Communication Technology Research infrastructure, aiming at providing It is as such an ideal example of com- parallelising queries. Lexical Database based on Con- and chart her future research and other NLP tasks such as deep parsing, excellent research facilities by en- mon, core computational resources detecting named entities, etc. In other ceptual Vectors. In Proceedings development (R&D) directions. The Universiti Sains Malaysia suring good computational horse- to be created and pooled among as- of the International Conference on pinnacle of these efforts was trans- words, we hope to have agents of var- power to support high impact do- piring researchers who require high ious responsibilities so that they can Distributed Frameworks & Applica- lated into a 2 year strategic plan “USM mains in the bio-sciences, physical performance resources. PROJECT PUBLICATIONS tions 2008 (DFmA 2008). Penang, Research-Intensive University 2007– be ‘mixed-and-matched’ to construct sciences, information and communi- Malaysia; pp. 102–110. 2009”. new NLP applications, such as those Lim, L. T. & Schwab, D. (2008). Lim- cation technology (ICT), Environment Equally important, USM needs a fo- ri d mentioned in the introduction. G its of Lexical Semantic Relatedness U @ Note: The abbreviations Prof. and AP are used for Professor and Associate Professor respectively throughout this book. One of the crucial input elements sciences, Education, Arts and others. cused, holistic and dedicated effort S M
4 26 GRID-ENABLED BLEXISMA2 Intro Intro
Szeged}Bergen}oxygen}Gelugor} A First Presentation A First Presentation A First Presentation A First Presentation Lim Lian Tze Lim Lian Tze Who? Lim Lian Tze Lim Lian Tze
When? June 3, 2011June 3, 2011 June 3, 2011 December 28, 2011
www.usm.my
ALim First Lian Presentation Tze — A First Presentation 1/2
Intro Intro SomeSome BackgroundSome Background Background Some Background
Intro
Once uponOnce a time upon a time ◮ OnceOnce upon upona time a time There wereThere programmers were programmers ◮ ThereThere were programmerswere programmers
A First Presentation Lim Lian Tze — A FirstLim Presentation Lian Tze A First Presentation December 28, 2011 2/2 2/2
Presentation Slides
This presentation was made with LATEX. Many possible classes: powerdot, beamer
Intro
\documentclass{beamer} \usetheme{Warsaw} A First Presentation
\author ... Lim Lian Tze
June 3, 2011 \begin{document} \titleframe
Lim Lian Tze A First Presentation
Intro \section{Intro} Some Background
\begin{frame} \frametitle{Some Background} Once upon a time There were programmers ... \end{frame} \end{document}
Lim Lian Tze A First Presentation Oversized Posters
Many possible solutions: sciposter, flowfram, beamerposter, tikzposter
Low Cost Construction of a Multilingual Lexicon from Bilingual Lists
Introduction Adding a New Language ◮ Bilingual MRDs are good resources for building ◮ (Example: Malay–English–Chinese + French) multilingual lexicons, but heterogeneous structures ◮ Construct also French–English–Malay triples ◮ Lowest common denominator: list of ◮ Add French members to existing M E C clusters with source language item target language item(s) → common English & Malay members ◮ Proposal: Multilingual lexicon construction using only simple bilingual lists bengkeng erce ferocious garang garang + (cruel, , ) \documentclass{beamer} (féroce, erce, garang) One-time Inverse Consultation [1]
ferocious ö → ◮ Generates a bilingual lexicon for new language pair \usepackage[orientation=portrait, from existing bilingual lists ◮ JP–EN, EN–MS, MS–EN lexicons JP–MS féroce ⇒ bengkeng cruel Japanese English Malay , size=a0]{beamerposter} mark tanda erce garang p seal anjing laut ö → stamp tera ferocious imprint \usetheme{...} gauge Precision of 100 Random Translation Sets
E1 E2 2 α . score(‘tera’) = 2 | ∩ | = 2 = 0 57 . α . \author ... % Meta-information × E1 + E2 × 3 + 4 | | | | α = . ∴p ‘tera’ is most likely valid . = ↔ = .
Merging Translation Triples into Sets Precision . ◮ (Example: Malay–English–Chinese) β . . . . . . . . ◮ Retain OTIC ‘middle’ language links Precision generally around 0.70–0.82; max 0.86 \begin{document} ◮ For each ‘head’ language LI, discard triples with score ◮ < αX or score2 < βX, where X = max score of all F and Rand Index of Selected Translation Sets triples containing that LI 1 \begin{frame} (garang, ö) . ◮ Evaluating accuracy of sets with polysemous ‘middle’ (garang, ÑS) . (garang, ferocious, ö) language members, e.g. ‘plant’, ‘target’ (garang, bold, ÑS) (garang, erce, ö) Test Rand Index F1 Best accuracy when (garang, S) . word min max min max α β ... % Poster contents goes here (garang, ÀÈ) . (garang, bold, S) (garang, jazzy, ÀÈ) ‘bank’ 0.417 0.611 0.588 0.632 0.6 0.4 ‘plant’ 0.818 0.927 0.809 0.913 0.6 0.2 (garang, 'Æ) . ‘target’ 0.821 1.000 0.902 1.000 0.4 0.2 \end{frame} (garang, bold, 'Æ) ‘letter’ 0.709 0.818 0.724 0.792 0.8 0.2 \end ◮ Merge all triples with common bilingual pairs Discussion and Conclusion {document} bengkeng ◮ Low thresholds (α, β): more coverage; low precision (garang, ferocious, ö ) erce (garang, erce, ö) garang ◮ High thresholds: good precision; low coverage (bengkeng, erce, ö) α = 0 6, β = 0 2 gives good trade o between ferocious ö ◮ → coverage, precision and recall ◮ Results are encouraging for such simple input data! References ◮ Future plan: Integrate lexicon [1] F. Bond and K. Ogura. “Combining linguistic resources to create a into an MT system machine tractable Japanese–Malay dictionary”. In: Language with WSD Resources and Evaluation 42 (2008), pp. 127–136.
Lian Tze L Bali R M Enya Kong T [email protected] {ranaivo,enyakong}@mmu.edu.my NLP-SIG, Faculty of Information Technology, Multimedia University, Malaysia Lea ets
leaflet arranges contents into 6 pages on a foldable double-sided sheet.
Discussion References Low-Cost Construction of a Low thresholds (α, β): more coverage; low precision [ ] F. Bond and K. Ogura. “Combining linguistic resources to Multilingual Lexicon from High thresholds: good precision; low coverage create a machine tractable Japanese–Malay dictionary”. In: ▸ α . , β . gives good trade o between coverage, Language Resources and Evaluation ( ), pp. – . Bilingual Lists ▸ precision and recall [ ] P. Vossen. “EuroWordNet: A Multilingual Database of ▸ Results≈ are≈ encouraging for such simple input data! Autonomous and Language speci c Wordnets Connected via Especially suitable for under resourced language pairs an Inter Lingual Index”. In: Special Issue on Multilingual Lian Tze L ▸ Future plan: Integrate multilingual lexicon into an MT Databases, International Journal of Linguistics . ( ). Bali R M system with WSD and user interaction features [ ] D. Tu ş, D. Cristeau, and S. Stamou. “BalkaNet: Aims, Enya Kong T ▸ Methods, Results and Perspectives – A General Overview”. Related Work In: Romanian Journal of Information Science and Technology Special Issue . ( ), pp. – . NLP-SIG, Faculty of Information Technology Many multilingual lexicon projects [ , ]) aligned with [ ] C. Fellbaum, ed. WordNet: An Electronic Lexical Database. Multimedia University, Malaysia Princeton WordNet [ ] Language, Speech, and Communication. Cambridge, ▸ Overly ne sense distinctions in Princeton WordNet Massachusetts: MIT Press, . Pan Lexicon [ ]: compute context vectors of words from monolingual⊳ corpora of di erent languages, then [ ] M. Sammer and S. Soderland. “Building a Introduction sense distinguished multilingual lexicon from monolingual ▸ grouping into translation sets by matching context corpora and bilingual lexicons”. In: Proceedings of Machine Bilingual MRDs are good resources for building vectors via bilingual lexicons Translation Summit XI. Copenhagen, Denmark, , multilingual lexicons Sense distinctions derived from corpus evidence pp. – . ▸ But MRDs have heterogeneous contents and structures Produces many translation sets that contain [ ] K. Markó, S. Schulz, and U. Hahn. “Multilingual Lexical Not all contain rich information (gloss, domain) ⊳ semantically related but not synonymous words, Acquisition by Bootstrapping Cognate Seed Lexicons”. In: ▸ (Especially so for under resourced languages) ⊳ e.g. ‘shoot’ and ‘bullet’ (lower precision) Proceedings of the International Conference on Recent ⊳ Di erent structures (sense granularity, distinctions) precision based on evaluators’ opinions ( if Advances in Natural Language Processing (RANLP) . Lowest common denominator: list of source language inter evaluator agreement is not required) Borovets, Bulgaria, . item⊳ target language item(s) ⊳ Does not handle multi word expressions [ ] M. Lafourcade. “Automatically Populating Acception Lexical ▸ Construct multilingual lexicon using only bilingual lists Markó, Schulz and Hahn [ ] use cognate mappings to Database through Bilingual Dictionaries and Conceptual → ⊳ \documentclass[foldmark,a4paper] derive new translation pairs, validate by processing Vectors”. In: Proceedings of PAPILLON . Tokyo, Japan, One-time▸ Inverse Consultation [1] ▸ parallel corpora (medical domain) Aug. . Complex terms indexed on the level of sub words Generates a bilingual lexicon for a new language pair [ ] C. Boitet, M. Mangeot, and G. Sérasset. “ e PAPILLON e.g. ‘pseudo hypo para thyroid ism’ project: Cooperatively Building a Multilingual Lexical from existing bilingual lists ▸ ⊳ accuracy for each language pair Database to Derive Open Source Dictionaries & Lexicons”. Given bilingual lexicons L –L , L –L , L –L , generate ⊕ ⊕ ⊕ ⊕ {leaflet} Requires large aligned thesaurus corpora (easier to In: Proceedings of the nd Workshop on NLP and XML bilingual lexicon L –L ⊳ acquire for specialised domains?) (NLPXML’ ). Taipei, Taiwan, , pp. – . ▸ Example: JP–EN, EN–MS, MS–EN lexicons JP–MS ⊳ Cognate based approach not applicable for language Japanese English Malay ▸ ⇒ pairs that are not closely related mark tanda Lafourcade⊳ [ ]: compute contextual vectors for Contact p seal anjing laut translation pairs based on gloss text and associated class stamp tera \author Lian Tze L [email protected] ... ▸ % Meta-information labels from semantic hierarchy; compare vectors from imprint Bali R M [email protected] di erent bilingual lexicons to detect synonymy gauge Resource requirements not available for all language Enya Kong T [email protected] pairs, costly task of assigning class labels NLP-SIG E E ⊳ , Faculty of Information Technology score ‘tera’ . E E Multimedia University, Cyberjaya, Malaysia. ∩ http://fit.mmu.edu.my/sig/nlp/ p ‘tera’ is= more× likely to be= valid× = + + \begin{document} ∴ ↔
Merging Translation Triples into Sets Precision of 100 Random Translation Sets Algorithm : Generating trilingual translation chains Retain OTIC ‘middle’ language links α . forall the lexical items w L do . \maketitle For each ‘head’ language LI, lter only triples whose h α . translations of w in L ▸ score exceed thresholds (See Algorithm ) Wm h α = . forall the w do∈ . = ▸ Merge all triples with common bilingual pairs m Wm ← translations of w in L = Malay–English–Chinese example: Wt m .
forall the w∈ do Precision ▸ –u Kamus Inggeris–Melayu untuk Penterjemah t Wt Output← a translation triple w , w , w \section ... ▸ u–ñ XDict ñ–u CC CEDICT h m t . translations∈ of w in L Wmr t β . . (garang, ööö) . score wh , wm , wt . . (garang, ÑÑÑSSS) . ←common words in wmr Wmr and w| (garang, ferocious, ö) (garang, bold, ÑS) words ← in w Precision increases with threshold parameters α and β ö w m mr Wmr (garang, erce, ) W ∈ Precision generally around . – . ; max . end ... (garang, SSS) . ∈ ▸ Most false positives are not ranked at top of the list % Leaflet contents ∈ (garang, ÀÀÀÈÈÈ) . score w , w, w (garang, bold, S) w Wm h t ▸ Many errors caused by incorrect POS assignments (garang, jazzy, ÀÈ) score wh , wt ∈ Wm Wmr ▸ end ∑ (garang, '''ÆÆÆ) . ← × F▸ and Rand Index of Selected Translation Sets X maxw score wh , wt + (garang, bold, 'Æ) t Wt forall the distinct translation pairs w , w do False positives will frequently arise when ‘middle’ \end{document} ∈ h t ←if score wh , wt αX or score wh , wt βX language members are polysemous, e.g. ‘plant’, ‘target’ bengkeng then ▸ Evaluate accuracy of selected sets with polysemous (garang, ferocious, ö) erce Place wh L ≥, wm L , wt L from all≥ triples ‘middle’ language members (garang, erce, ö) garang w , w , w into same translation set ▸ h ... t TP (bengkeng, erce, ö) Record score∈ w , w∈ and score∈ w , w , w ferocious ö h t h m t Precision → else TP FP Discard all triples w , w , w = TP h ... t Recall + Adding More Languages // The sets are now grouped by TP FN wh , wt = Precision Recall Construct L –L –L triples F + Add L members to existing L –L –L clusters with end Precision Recall × × ▸ common L & L members end = TP TN RI + ▸ Example: Malay–English–Chinese + French, using end TP FP FN TN + ‘ready made’ triples from FeM Merge all sets containing triples with same wh , wm = ▸ Merge all sets containing triples with same wm , wt + + + bengkeng Test Rand Index F Best accuracy when erce cruel ferocious garang garang + ( , , ) word min max min max α β (féroce, erce, garang) Algorithm : Adding Lk to multilingual lexicon L of ‘bank’ . . . . . . ferocious ö → ‘plant’ . . . . . . L , L ,..., Lk + ‘target’ . . . . . . T translation triples of Lk , Lm , Ln generated by ‘letter’ . . . . . . Algorithm where Lm , Ln L , L ,..., Lk féroce ← + forall the wLm , wLn , wL T do bengkeng cruel k F and RI increases with α and β Add wLk to all entries∈ in L that contains both wLm and + But may decrease when they are too high and reject garang wLn + ∈ erce ▸ valid members (false negatives) end ▸ ferocious ö Flash Cards
\documentclass[avery5388,frame] {flashcards} \cardfrontstyle{headings} \cardfrontfoot{Linux} S
\begin{document} A digital representation of information that Certi cate identi es you and is issued by Cas, which are \begin{flashcard}[Security] often a trusted third party (TTP).
{Certificate} L
... S
\end{flashcard} Access to an object is restricted based on the MAC (Mandatory Access sensitivity of the object (de ned by the label that is assigned), and granted through Control) authorization (Clearance) to access that level of \begin{flashcard}[Security] data. {MAC ...} L ... \end{flashcard} \end{document} Contents
1 What are TEX, LATEX and Friends?
2 Document Types
3 Mathematics and Other Material
4 Typography Mathematics
Equation (1) relates the golden ratio and the Fibonacci 1 √ series. Recall that the golden ratio is ϕ = 2 (1 + 5).
X∞ ( 1)n+1 ϕ = 1 + − (1) F F n=1 n n+1
Equation \eqref{eq:gratio} relates the golden ratio and the Fibonacci series. Recall that the golden ratio is $\varphi = \frac{1}{2} (1 + \sqrt{5})$.
\begin{equation}\label{eq:gratio} \varphi = 1 + \sum_{n=1}^{\infty} \frac{ (-1)^{n+1} }{ F_n F_{n+1} } \end{equation} Program Listings
\usepackage{listings,xcolor} ... \begin{lstlisting}[language=matlab, basicstyle=\ttfamily, keywordstyle=\bfseries\color{red}, disp('Hello␣World'); commentstyle=\sffamily\color{green}, stringstyle=\rmfamily\color{orange}] % Calculate golden ratio disp('Hello World'); F = zeros(10, 1); F(1:2) = [1, 1]; % Calculate golden ratio phi = 1; % Initial value F = zeros(10, 1); F(1:2) = [1, 1]; for j=1:8 phi = 1; % Initial value F(j+2) = F(j+1) + F(j); phi = phi + (-1)^(j+1) ... for j=1:8 / (F(j+1) * F(j)); F(j+2) = F(j+1) + F(j); end phi = phi + (-1)^(j+1) ... / (F(j+1) * F(j)); end \end{lstlisting} Graphs and Diagrams
\usepackage[all]{xy}
\[ f \xymatrix{ A / B g h A \ar[r]^f \ar[dr]_{f \circ g} & g ◦ f g B \ar[d]^g \ar[dr]^{g \circ h} \\ ◦ C / D & C \ar[r]_h & D h } \] Tables
Year ending Mar 31 2016 2015 2014 Revenue 14580.20 11900.40 8290.30 Cost of sales 6740.20 5650.10 4524.20 Gross prot 7840.00 6250.30 3766.10
\usepackage{booktabs} ... \begin{tabular}{lrrr} \toprule Year ending Mar 31 & 2016 & 2015 & 2014 \\ \midrule Revenue & 14580.20 & 11900.40 & 8290.30 \\ Cost of sales & 6740.20 & 5650.10 & 4524.20 \\ \cmidrule(r){2-4} \emph{Gross profit} & 7840.00 & 6250.30 & 3766.10 \\ \bottomrule \end{tabular} Graph Plots
Contents of datafile.dat 1 10 Lα − dof La Lb Lβ 5 8.31e-02 1.80e-01 3 17 2.546e-02 3.75e-02 10− 49 7.407e-03 1.49e-02 129 2.10e-03 4.23e-03 5 10− 321 5.87e-04 1.30e-03 769 1.62e-04 3.88e-04 101 102 103 104 1793 4.44e-05 1.12e-04 4097 1.20e-05 3.20e-05 DoF 9217 3.26e-06 8.97e-06
\usepackage{pgfplots} ... \begin{tikzpicture} \begin{loglogaxis}[xlabel=DoF] \addplot table[x=dof,y=La]{datafile.dat}; \addlegendentry{$L_\alpha$}; \addplot table[x=dof,y=Lb]{datafile.dat}; \addlegendentry{$L_\beta$}; \end{loglogaxis} \end{tikzpicture} Gantt Charts
2016 2017 Preliminary Project 100% complete Objective 1 Task A Task B Objective 2 Task A Task B
\usepackage{pgfgantt} ... \begin{ganttchart}[...settings...]{1}{16} \gantttitle{2016}{4} \gantttitle{2017}{12} \\ \ganttbar[progress=100]{Preliminary Project}{1}{4} \\ \ganttgroup{Objective 1}{5}{16} \\ \ganttbar[progress=50, name=T1A]{Task A}{5}{10} \\ \ganttlinkedbar[progress=0]{Task B}{11}{16} \\ ... \end{ganttchart} Chemical Equations and Molecules
H O +2 OH– +2 OH– Zn2+ * Zn(OH) *[Zn(OH) ]2– H C C ) + 2 ) 4 −−−−−+−−−−2 H amphoteres Hydroxid↓ −−−−−+−−−−2H+ Hydroxozikat H H
\usepackage[version=3]{mhchem} % suicient for chemical equations \usepackage{chemfig} % for 2-D molecule drawings ... \ce{Zn^2+ <=>[\ce{+ 2OH-}][\ce{+ 2H+}] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$ <=> C[+2OH-][{+ 2H+}] $\underset{\text{Hydroxozikat}}{\cf{[Zn(OH)4]^2-}}$ }
\chemfig{H-C(-[2]H)(-[6]H)-C(-[7]H)=[1]O} Circuits and SI Units
10 Ω A v x 3.45 104 V2 lm3 F−1 S 20 Ω 5 Ω vx × 5 40 km/h, 85 km/h and 103 km/h B
\usepackage{siunitx} \usepackage[siunitx]{circuitikz} ... \begin{circuitikz} \draw (0,0) node[anchor=east] {B} to[short, o-*] (1,0) to[R=20<\ohm>, *-*] (1,2) to[R=10<\ohm>, v=$v_x$] (3,2) -- (4,2) to[ cI=$\frac{\si{\siemens}}{5} v_x$, *-*] (4,0) -- (3,0) to[R=5<\ohm>, *-*] (3,2) (3,0) -- (1,0) (1,2) to[short, -o] (0,2) node[anchor=east]{A} ;\end{circuitikz}
\SI{3.45d4}{\square\volt\cubic\lumen\per\farad} \SIlist[per-mode=symbol]{40;85;103}{\kilo\metre\per\hour} Bar Codes
ISBN 978-3-86541-114-3
L E 2 8 H S 9 Z
9 781860 742712 9 783865 411143
\usepackage{auto-pst-pdf} % Needed if running pdflatex; must use option -shell-escape \usepackage{pstricks,pst-barcode} ... \begin{pspicture} \psbarcode{MECARD:N:Malaysia Open Source Conference...}{eclevel=L}{qrcode} \psbarcode{9781860742712}{includetext guardwhitespace}{ean13} \psbarcode{978-3-86541-114}{includetext guardwhitespace}{isbn} \psbarcode{LE28HS9Z}{includetext}{royalmail} \psbarcode{^453^178^121^239}{columns=2 rows=10}{pdf417} \end{pspicture} ‘Smart Diagrams’
Assess Renew
Implement Plan Planning Cycle Renew
Plan
Implement Assess
\usepackage{smartdiagram} \usepackage{smartdiagram} \smartdiagram[bubble diagram]{ \smartdiagram Planning Cycle,Assess,Plan, [priority descriptive diagram]{ Implement,Renew} Assess,Plan,Implement,Renew} Crossword Puzzles
1 Across: 1 unit of measure Down: 1 η 3 unit of 2 3 4 2 ∗ 5 sectioning unit measure 4 nonproportional 5 font
\usepackage{cwpuzzle} \Clue{2}{AST}{\(\ast\)} ... \Clue{5}{PART}{sectioning unit} \begin{Puzzle}{5}{3} \end{PuzzleClues} |* |* |[1]E|X |* |. \begin{PuzzleClues}{ |[2]A|[3]S|T |* |[4]T|. \textbf{Down:} } |* |[5]P|A |R |T |. \Clue{1}{ETA}{\(\eta\)} \end{Puzzle} \Clue{3}{SP}{unit of measure} \begin{PuzzleClues}{ \Clue{4}{TT}{nonproportional font} \textbf{Across:} } \end{PuzzleClues} \Clue{1}{EX}{unit of measure} Song Books with Guitar Tabs
C G Am F Country road, take me home, to the place I belong.
C G F C West Virginia, mountain momma, take me home, country road.
\usepackage{gchords,guitar} ... \begin{guitar} \newcommand{\CMaj}{\chord{t}{n,p3,p2,n,p1,n}{C}} \newcommand{\Amin}... Country [\CMaj]road, take me [\GMaj]home, ... \end{guitar} Meh, What Good is That? Can’t Use it Anywhere Else.
Actually, you can.
\usepackage[active,tightpage]{preview} \PreviewEnvironment{texshade} ... \begin{texshade} ... \end{texshade}
Run pdflatex cropped PDF containing only contents of texshade → ImageMagick: convert -depth 150 texshade.pdf texshade.png Multiple environments multi-page PDF and multiple PNGs → Contents
1 What are TEX, LATEX and Friends?
2 Document Types
3 Mathematics and Other Material
4 Typography What Is Typography About?
Your final year project will consist of several elements: The mathematical content and the work you have done. The words and sentences you use to describe the work. The way words and graphs are presented on the page.
typography n. The art and technique of arranging type to make wri en language legible, readable, and appealing when displayed. (Wikipedia) Why Does Typography Matter?
Typography ma ers because it helps conserve the most valuable resource you have as a writer—reader a ention. A ention is the reader’s gi to you. That gi is precious. It is finite. And if you fail to be a respectful steward of that gi , it will be revoked. (Ma hew Bu erick, Typography for Lawyers) Bold and Italic Text
Within a larger body of Within a larger body of text, a piece in italics does text, a piece in italics does not stand out much; not stand out much; instead it signies a instead it signies a context di erence only context di erence only while the text is being read. while the text is being By contrast, a single word read. By contrast, a single in boldface attracts the word in boldface attracts human eyeball and is the human eyeball and is therefore recommended therefore recommended for keywords the reader for keywords the reader might be looking for. might be looking for. Bold and Italic in Use
Alfred Frölicher, Andreas Kriegl. Linear Spaces and Dierentiation Theory. John Wiley & Sons. 1988. Multiple Columns Page Margins
LibreOice LATEX article class
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nulla eget sagittis tortor, semper malesuada dui. Phasellus interdum, odio non interdum pellentesque, nulla arcu blandit massa, ac tempor mauris arcu et enim. Vestibulum sagittis tempor convallis. Aenean iaculis varius consequat. Sed volutpat ut neque ut mollis. Ut molestie mattis arcu a vestibulum. In nec tempor sem. Sed erat libero, auctor hendrerit risus at, tempus porta felis. Ut ultrices, neque vel imperdiet dignissim, diam ligula laoreet nisl, nec interdum justo Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nulla eget sagittis tortor, magna ut metus. Vestibulum eget felis eu dui aliquam ultricies at vel lorem. semper malesuada dui. Phasellus interdum, odio non interdum pellentesque, nulla arcu blandit massa, ac tempor mauris arcu et enim. Vestibulum sagittis tempor convallis. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos himenaeos. Vestibulum at Aenean iaculis varius consequat. Sed volutpat ut neque ut mollis. Ut molestie mattis erat et eros condimentum lacinia quis a lectus. Pellentesque habitant morbi tristique senectus et netus et arcu a vestibulum. In nec tempor sem. Sed erat libero, auctor hendrerit risus at, tempus malesuada fames ac turpis egestas. Quisque sed viverra nisi. Ut vulputate nunc sit amet lacus luctus porta felis. Ut ultrices, neque vel imperdiet dignissim, diam ligula laoreet nisl, nec tempus. Proin nec odio et mi pulvinar dictum. Pellentesque facilisis iaculis dictum. Duis et neque interdum justo magna ut metus. Vestibulum eget felis eu dui aliquam ultricies at vel tristique, posuere sapien vel, eleifend nibh. Nunc quis tortor placerat, cursus libero et, sodales augue. lorem. Nulla sed leo pulvinar, interdum leo ut, laoreet mi. Class aptent taciti sociosqu ad litora torquent per conubia nostra, per inceptos Morbi sem turpis, laoreet sed volutpat eget, auctor ut purus. Fusce pulvinar viverra magna, vel dapibus himenaeos. Vestibulum at erat et eros condimentum lacinia quis a lectus. Pellen- augue eleifend sit amet. Duis euismod magna sed tellus bibendum, sed sodales dolor malesuada. Ut vitae tesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. purus risus. Praesent vitae erat orci. Aenean nibh risus, consectetur a ante a, luctus maximus arcu. Quisque sed viverra nisi. Ut vulputate nunc sit amet lacus luctus tempus. Proin nec Curabitur sagittis mi eros, non volutpat nulla sodales at. Suspendisse in lorem purus. Suspendisse potenti. odio et mi pulvinar dictum. Pellentesque facilisis iaculis dictum. Duis et neque tris- tique, posuere sapien vel, eleifend nibh. Nunc quis tortor placerat, cursus libero et, Aenean scelerisque est quis molestie pulvinar. Praesent et tempus urna. Suspendisse quis turpis est. sodales augue. Nulla sed leo pulvinar, interdum leo ut, laoreet mi. Phasellus est urna, pellentesque non augue in, pulvinar posuere metus. Suspendisse cursus sagittis Morbi sem turpis, laoreet sed volutpat eget, auctor ut purus. Fusce pulvinar viverra condimentum. Nam non ornare est, cursus varius purus. Morbi ut turpis viverra lectus blandit gravida. magna, vel dapibus augue eleifend sit amet. Duis euismod magna sed tellus bibendum, Sed pulvinar cursus ligula vel rhoncus. Proin molestie imperdiet felis in commodo. Donec nec tellus sed sodales dolor malesuada. Ut vitae purus risus. Praesent vitae erat orci. Aenean pulvinar, fringilla massa et, vestibulum lectus. nibh risus, consectetur a ante a, luctus maximus arcu. Curabitur sagittis mi eros, non Ut vitae iaculis urna. Nulla id odio metus. Fusce suscipit felis a lectus ornare dapibus. Sed laoreet lectus volutpat nulla sodales at. Suspendisse in lorem purus. Suspendisse potenti. eget velit porttitor rutrum. Vivamus sollicitudin mi at eros tincidunt euismod nec vel leo. Praesent porta Aenean scelerisque est quis molestie pulvinar. Praesent et tempus urna. Suspendisse tempus semper. Suspendisse quis pharetra leo. Nunc interdum lorem ut ex tempor, ut accumsan risus quis turpis est. Phasellus est urna, pellentesque non augue in, pulvinar posuere metus. tincidunt. Suspendisse mattis faucibus lectus quis consectetur. Aliquam convallis volutpat justo. Sed Suspendisse cursus sagittis condimentum. Nam non ornare est, cursus varius purus. dignissim metus in vulputate tempor. Praesent auctor nisl et sapien gravida placerat. Duis sed ultrices sem. Morbi ut turpis viverra lectus blandit gravida. Sed pulvinar cursus ligula vel rhoncus. Duis rhoncus posuere purus consectetur ornare. Proin molestie imperdiet felis in commodo. Donec nec tellus pulvinar, fringilla massa et, vestibulum lectus. Cras congue eget dui eget mattis. Cras vestibulum sem eget convallis elementum. Mauris risus libero, Ut vitae iaculis urna. Nulla id odio metus. Fusce suscipit felis a lectus ornare viverra non felis non, consectetur dignissim tortor. Maecenas vestibulum, velit ut convallis cursus, odio dapibus. Sed laoreet lectus eget velit porttitor rutrum. Vivamus sollicitudin mi at urna consequat ex, eget congue justo ipsum in nunc. Phasellus condimentum, sem efficitur mattis finibus, eros tincidunt euismod nec vel leo. Praesent porta tempus semper. Suspendisse quis eros nisl rutrum magna, ut suscipit ex urna ac nunc. Nam ut commodo justo. Phasellus vehicula faucibus pharetra leo. Nunc interdum lorem ut ex tempor, ut accumsan risus tincidunt. Sus- augue sit amet aliquet. Aliquam aliquet suscipit justo, a dignissim augue finibus ac. Nulla euismod dui id pendisse mattis faucibus lectus quis consectetur. Aliquam convallis volutpat justo. Sed ullamcorper ultricies. Nam mollis felis eu turpis fringilla finibus. Etiam ac eleifend quam. In quis vehicula dignissim metus in vulputate tempor. Praesent auctor nisl et sapien gravida placerat. ligula. Maecenas in tellus elit. In pretium purus et blandit rhoncus. Mauris sagittis, odio id eleifend Duis sed ultrices sem. Duis rhoncus posuere purus consectetur ornare. aliquet, ipsum erat porttitor diam, in volutpat enim lectus ac sapien. Cras congue eget dui eget mattis. Cras vestibulum sem eget convallis elementum. Nullam ut ornare nibh. Sed scelerisque libero consequat justo blandit mattis. Sed iaculis egestas hendrerit. Mauris risus libero, viverra non felis non, consectetur dignissim tortor. Maecenas Donec faucibus dui sit amet rutrum volutpat. Vivamus commodo porta facilisis. Integer ultrices vulputate vestibulum, velit ut convallis cursus, odio urna consequat ex, eget congue justo ip- enim, quis finibus quam mollis scelerisque. Nam nec malesuada justo, et molestie magna. Ut diam ex, sum in nunc. Phasellus condimentum, sem efficitur mattis finibus, eros nisl rutrum fermentum a nisl a, molestie tempus risus. Nullam augue augue, mollis eget augue id, placerat tincidunt magna, ut suscipit ex urna ac nunc. Nam ut commodo justo. 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Margins: L 2cm, R 2cm, T 2cm, B 2cm Margins: L 3cm, R 3cm, T 3.5cm, B 5.5cm Characters/line: 103 Characters/line: 85 The Book of Kells
Source: Wikimedia Commons (link). The Gutenberg Bible
Source: Bayerische Staatsbibliothek (link). Manual Typesetting
69. Aufgaben zum II. Kapitel. 107 20. Man setze, ähnlich wie in der vorigen Aufgabe,
v~ +vä;+ .. ·+Yap p - sn ' und (s,/)" = x,.'
und zeige, da:fi x~' monoton fallend-+ ya1 a~ ••• aP strebt. 21. Das Intervall a .•. b (0 < a < b) werde in n gleiche Teile geteilt; x0 = a, x1 , x,11 ••• , x,. = b seien die Teilpunkte. Man zeige, da:6 deren geo- metrisches Mittel 1 1 n+1VXo·X1•X2 • • • Xn -+- (bb)b-a- e a"
und ihr harmonisches Mittel -+ bb-a strebt. 1og - 1oga 22. Man zeige, dafi im Falle der allgemeinen Folge in Aufgabe 5
x,. x1 - {J x0 strebt. a"-+ a(a= PI 23. Es sei x > 0 und die Folge (x,.) durch die Festsetzungen
x1 = x, x2 = i"' , Xa = 'lf"s' . • . ' x,. = i"" -1' • .. definiert. Für welche x fällt diese Folge konvergent aus? (Antwort: Dann und nur dann, wenn (+Y~x~3- ist.) Konrad Knopp. Theorie und 24. Es sei limx,.="• limx,.=,u, li~x,.'="' und fimx,.'=tt'. Was lll:6t sich über die Lage der Häutungsgrenzen der Folgen Anwendung der Unendlichen (- x,.) , (:,.) , (x,. + x,.') , (x,.- x,.') , (x,. · x,.') , (;;) Reihen. Zweite Auflage. aussagen? Man diskutiere alle möglichen Fälle I Springer. 1924. 21S. Es sei (a,.) beschränkt und (nach etwaiger Überspringung einiger Anfangsglieder) ( a,.) p,. log 1+- =- n n
g~esetzt. Dann haben (a,.) und (ß,.) dieselben Häufungsgrenzen. Dasselbe gilt, wenn 1 (1 1 IXn ) 1 ß,. og +-+--log =-+-•log gesetzt wird. n n n n n n 26. Gilt Satz 43, 3 noch, falls fJ = 0 oder = + oo ist? 27. Wenn die in 43,2 und 3 gegebenen Folgen x,. und y,. monoton sind, so sind es auch die dortigen Folgen x,.' und y,.'. 28. Ist die Folge (::) monoton und b,. > 0, so ist es auch die Folge
der Quotienten a 1 + a2 + ... + a,. 29. Es ist b1 + b2 + ... + b,. . lim ~". = lim a,.- a,. +1 b,. b,.- bn+1 ' falls der rechtsstehende Grenzwert existiert und falls (a,.) und (b,.) Nullfolgen sind, deren zweite monoton ist. 30. Bei positiven, monotonen c,. kann aus
x0 +x1+·· .+x,...... ; auf c0 x0 +c1 x1 + ... +c,.x,.-+s n + 1 · c0 + c1 + ... + c11 2 Manifolds with corners
Written with a Typewriter
2.1 Definition: A 9 uadrant Q ~ Rn is a subset of the form Q=!xERn : l1(x)~o, •.• ,lk(x)~01 where {11, •.. ,~1 is a linearly independent subset of (Rn )*,. Here 0 -:5k sn and k
is called the ~ of Q. If x E Q and exactly j of the li' s satisfy li (x) == 0, then x is called a corner of index j. The index of a corner depends only on x and Q and not on the special system 111, ••• ,~1 describing Q.
2.2 Let U ~ Q be an open subset of a quadrant Q. A function f: U -+ RP is called Cr (0 S r :s 00 ) if all partial derivatives of f of order sr exist and are continuous on U. By the Whitney extension theorem (cf. H. WHITNEY (1936), J.C. TOUGERON (1972» this is the case iff f can be extended to a Cr function f: U-+ RP, where U~ Rn is N open and u=Qn u.
2.3 The border ~Q of a quadrant, Q is {x ERn: 11 (x) = 0 or 12(x)::::0 or ••• or ~(x) =0\; it is the disjoint union of finitely many (plane) submanifolds of Rn , the faces, edges, corners etc. of Q. bQ is "stratified" by this set of submanifolds. Let U!;:; Q, U' ~ Q' be open subsets of quadrants in Rn. A mapping f: U-7 U' is a diffeomorphism iff f is bijective Peter Michor. Manifolds of and locally of maximal rank. It follows that f maps corners of index j in U to corners of index j in U'. So: Dierentiable Mappings. Shiva x E U £;; Q is of index j iff f(x) E U' ~ Q' is of index j. Publishing Limited, Orpington. 1980.
18 Written by Hand
Joe Roberts. Elementary Number Theory. A Problem Oriented Approach. The MIT Press, Cambridge. 1977. The End
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