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A Short List of the Symbols Available in TX Fonts

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Introduction IAbout This Document<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowThis document lists symbols <strong>in</strong> standard LATEX, AMS-LATEXand a few additional packages.The document is optimized for view<strong>in</strong>g on a computer. Irecommend us<strong>in</strong>g it full screen (Ctrl+L for Acrobat) and<strong>the</strong>n navigat<strong>in</strong>g by click<strong>in</strong>g <strong>the</strong> sidebar.This document uses <strong>the</strong> Txfonts package, which redef<strong>in</strong>esmany symbols. There’s ano<strong>the</strong>r, standard version.You may reach <strong>the</strong> latest version <strong>of</strong> both files atacademic.cankaya.edu.tr/˜sermutlu.Copyright NoticeYou may download, upload, post, use and distribute this pdf filefreely, provided that you do not add or delete material, split,merge or <strong>in</strong> any o<strong>the</strong>r way modify <strong>the</strong> file.This file is provided as is, with no warranties implied.


STABILITY OF CERTAIN OSCILLATORY INTEGRALS 3<strong>in</strong> particular, we can embed N as a subgroup <strong>of</strong> ˜G via n ↦→ (n, 1). Consider <strong>the</strong> spaceΩ gen (N\ ˜G, ψ N ) <strong>of</strong> smooth genu<strong>in</strong>e functions W on ˜G such that W ((n, 1)g) = ψ N (n)W (g)for all n ∈ N, g ∈ ˜G. Theorems 1 and 2 are also valid for Ω gen (N\ ˜G, ψ N ). In a forthcom<strong>in</strong>gpaper we will use <strong>the</strong>se results to analyze <strong>the</strong> Whittaker coefficients <strong>of</strong> cusp forms on <strong>the</strong>metaplectic group [LM].Acknowledgement. We thank <strong>the</strong> referee for useful suggestions.2. Notation and prelim<strong>in</strong>ariesWe first fix some more notation. Throughout F will be a p-adic field with r<strong>in</strong>g <strong>of</strong> <strong>in</strong>tegersO, normalized absolute value ∣ ∣·∣∣and valuation v. Let G be a semisimple split group overF <strong>of</strong> rank r. (Theorems 1 and 2 easily reduce to <strong>the</strong> semisimple case.) Let B be a Borelsubgroup <strong>of</strong> G, A a maximal F -split torus conta<strong>in</strong>ed <strong>in</strong> B and N <strong>the</strong> unipotent radical <strong>of</strong>B so that B = AN. Let B = AN be <strong>the</strong> opposite Borel subgroup with respect to A. LetK be a hyperspecial maximal compact subgroup <strong>of</strong> G <strong>in</strong> good position with respect to B.We have Iwasawa decomposition G = ANK. Let X ∗ (A) (resp. X ∗ (A)) be <strong>the</strong> lattice <strong>of</strong>rational characters (resp. co-characters) <strong>of</strong> A.2.1. Roots and weights. Let Φ ⊆ X ∗ (A) be <strong>the</strong> set <strong>of</strong> roots <strong>of</strong> A <strong>in</strong> Lie(G), Φ + <strong>the</strong>subset <strong>of</strong> positive roots and ∆ 0 <strong>the</strong> subset <strong>of</strong> simple roots with respect to B. Similarly,let ∆ ∨ 0 ⊆ Φ ∨ + ⊆ Φ ∨ ⊆ X ∗ (A) be <strong>the</strong> sets <strong>of</strong> (simple, or positive) co-roots. We denote byα ↔ α ∨ <strong>the</strong> canonical bijection between Φ and Φ ∨ (resp., Φ + ↔ Φ ∨ +, ∆ 0 ↔ ∆ ∨ 0 ).For any α ∈ Φ let N α be <strong>the</strong> one-parameter subgroup correspond<strong>in</strong>g to α and choose aparametrization n α : G a → N α def<strong>in</strong>ed over F such that n α (O) = N α ∩ K. For any α ∈ ∆ 0we write N α for <strong>the</strong> unipotent radical <strong>of</strong> <strong>the</strong> (semisimple) rank one parabolic subgroupB ∪ Bs α B. Thus, N = N α ⋉ N α . We also have(3) N ∩ K = (N α ∩ K) ⋉ (N α ∩ K).Let a ∗ 0 = X ∗ (A) ⊗ R and a 0 = X ∗ (A) ⊗ R. These are r-dimensional R-vector spaces and∆ 0 (resp., ∆ ∨ 0 ) is a basis for a ∗ 0 (resp., a 0 ). The canonical pair<strong>in</strong>g 〈·, ·〉 : X ∗ (A)×X ∗ (A) → Zextends to a par<strong>in</strong>g a ∗ 0 × a 0 → R. Any λ = ∑ ∣ α∈∆ 0r α α ∈ a ∗ 0 def<strong>in</strong>es a positive character∣ λ : A → R+ given by∣ ∏ ∣ ∣∣ λ∣(t) = ∣α(t) r α.α∈∆ 0By Iwasawa decomposition we extend ∣ ∣ λ to a left-N and right-K <strong>in</strong>variant function on G.For any compact subset C ⊆ G <strong>the</strong>re exists a constant κ C > 0 (depend<strong>in</strong>g also on λ) suchthat∣ ∣ ∣ ∣ ∣(4) κ −1 ∣ λ∣(g) ≤ ∣λ∣(gh) ≤ κC∣λ∣(g)Cfor all g ∈ G, h ∈ C.Let H : A → a 0 be <strong>the</strong> homomorphism def<strong>in</strong>ed by q −〈χ,H(t)〉 = ∣ ∣ χ(t)∣ ∣ for all t ∈ A,χ ∈ X ∗ (A). Thus, H(χ ∨ (r)) = v(r)χ ∨ for any χ ∨ ∈ X ∗ (A).


TEXT <strong>Symbols</strong> I<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifont$ \$& \&# \#% \%{ \{} \}\- \P§ \S† \dag‡ \ddagı \ij \jBB \t{BB}Ü \"{U}İ \.{I}˜G \˜{G}˝A \H{A}Ò \‘{O}Ĉ \ˆ{C}Č \v{C}˚T \r{T}Ṕ \’{P}˘M \u{M}¯N \={N}Ē \b{E}Ş \c{S}F. \d{F}© \copyrightR \circledRa \textcircled{a} \texttrademarǩ \checkmark£ \pounds✠ \maltese• \textbullet\ \textbackslash| \textbar\_– \textendash— \textemdash< \textless> \textgreaterChemarrow


TEXT <strong>Symbols</strong> II<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow. . . \dotsł \lŁ \Lø \oØ \Oå \aaÅ \AAß \ssSS \SSæ \aeÆ \AEœ \oeŒ \OE˜ \textasciitildeˆ \textasciicircum¡ \textexclamdown¿ \textquestiondown‘ \textquoteleft’ \textquoteright“ \textquotedblleft” \textquotedblright\textvisiblespaceº \textordmascul<strong>in</strong>eª \textordfem<strong>in</strong><strong>in</strong>e* \textasteriskcentered· \textperiodcentered


Common Math <strong>Symbols</strong>Some <strong>of</strong> <strong>the</strong>se symbols may appear at o<strong>the</strong>r tables for user convenience<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow≈≡≃∂∞∇ℵl∨∧∀∃\neq\leqslant\geqslant\approx\equiv\cong\simeq\partial\<strong>in</strong>fty\nabla\aleph\ell\vee\wedge\forall\exists± \pm∓ \mp× \times÷ \div∪ \cup∩ \cap∈ \<strong>in</strong> \not<strong>in</strong>\ \setm<strong>in</strong>us∅ \varnoth<strong>in</strong>g⊂ \subset⊃ \supset· \cdot \centerdot© \copyright✠ \maltese→ \to⇐⇒ \iff$ \$£ \pounds% \%& \&{ \{} \}\_ \P§ \S∗ \ast† \dag‡ \ddag• \bullet≀ \wr


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowGreek Lettersα\alphaβ\betaγ\gammaδ\deltaλ\lambdaω\omegaψ\psiχ\chiρ\rhoɛ\epsilonκ\kappaπ\piφ\phiσ\sigmaθ\<strong>the</strong>taυ\upsilonξ\xiτ\tauι\iotaη\etaζ\zetaµ \muν\nuϱ\varrhoε\varepsilonκ\varkappaϖ\varpiϕ\varphiς\varsigmaϑ\var<strong>the</strong>ta


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowB<strong>in</strong>ary Relations I\cong\preccurlyeq\curlyeqprec≺\prec≼\preceq\precapprox\precsim≻\succ≽\succeq\succapprox\succsim\ncong\succcurlyeq\curlyeqsucc⊀\nprec\npreceq\precnapprox\precnsim⊁\nsucc\nsucceq\succnapprox\succnsim


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowB<strong>in</strong>ary Relations II| \mid\shortmid‖\parallel\shortparallel∼\sim∼\thicksim≃\simeq∽\backsim⋍\backsimeq≈\approx≈\thickapprox≅\approxeq≡\equiv∝\propto∝\varpropto⊸\multimap∤\nmid\nshortmid∦\nparallel\nshortparallel\nsim≐\doteq\doteqdot≬\between≍\asymp\fall<strong>in</strong>gdotseq\ris<strong>in</strong>gdotseq≏\bumpeq≎\Bumpeq⊜\circeq≖\eqcirc⊥\perp


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowSubset Relations⊂\subset⊆\subseteq\subseteqq⊏\sqsubset⊑\sqsubseteq⋐\Subset\nsubseteq\subsetneq\varsubsetneq\nsubseteqq\subsetneqq\varsubsetneqq⊃\supset⊇\supseteq\supseteqq⊐\sqsupset⊒\sqsupseteq⋑\Supset\nsupseteq\supsetneq\varsupsetneq\nsupseteqq\supsetneqq\varsupsetneqq


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowInequalities I< >\leqslant\geqslant≤\leq≥\geq≦\leqq≧\geqq\eqslantless\eqslantgtr≨\lneq≩\gneq≮\nless≯\ngtr\nleqslant\ngeqslant≰\nleq≱\ngeq\nleqq\ngeqq\lneqq\gneqq\lvertneqq\gvertneqq


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowInequalities II≪\ll≫\gg\lesssim\gtrsim\lessapprox\gtrapprox≶\lessgtr≷\gtrless⋚\lesseqgtr\gtreqless≪\lll≫\ggg\lnsim\gnsim≨\lnapprox≩\gnapprox⋖\lessdot⋗\gtrdot\lesseqqgtr\gtreqqless


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowTriangular RelationsHarpoons△\bigtriangleup⊲\triangleright⋫\ntriangleright⊲\vartriangleright⊲\rhd\unrhd\trianglerighteq\ntrianglerighteq◮\blacktriangleright\triangleq▽\bigtriangledown⊳\triangleleft⋪\ntriangleleft⊳\vartriangleleft⊳\lhd\unlhd\trianglelefteq\ntrianglelefteq◭\blacktriangleleft⇀\rightharpoonup⇁\rightharpoondown⇋\rightleftharpoons↾\upharpoonright⇂\downharpoonright↼\leftharpoonup↽\leftharpoondown⇌\leftrightharpoons↿\upharpoonleft⇃\downharpoonleft


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowArrows I→\rightarrow⇒\Rightarrow−→\longrightarrow=⇒ \Longrightarrow↑\uparrow⇑\Uparrow↛\nrightarrow\nRightarrow↕\updownarrow⇕\Updownarrow↗\nearrow↖\nwarrow↙\swarrow↘\searrow⇐⇒\iff←\leftarrow⇐\Leftarrow←−\longleftarrow⇐= \Longleftarrow↓\downarrow⇓\Downarrow↚\nleftarrow\nLeftarrow↮\nleftrightarrow\nLeftrightarrow↔\leftrightarrow⇔\Leftrightarrow←→\longleftrightarrow⇐⇒\Longleftrightarrow\leftrightsquigarrow


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowArrows II⇒\rightrightarrows⇄\rightleftarrows⇛\Rrightarrow↩→\hookrightarrow↣\rightarrowtail\looparrowright↠\twoheadrightarrow\curvearrowright\circlearrowright\dashrightarrow\Rsh⇈\upuparrows↦→\mapsto↦−→\longmapsto⇔\leftleftarrows⇆\leftrightarrows⇚\Lleftarrow←↪\hookleftarrow↢\leftarrowtail\looparrowleft↞\twoheadleftarrow\curvearrowleft\circlearrowleft\dashleftarrow\Lsh\downdownarrows\rightsquigarrow\leadsto


Ma<strong>the</strong>matical OperatorsThe follow<strong>in</strong>g operators have two different sizes<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow∏ ∐ ∏ ∐\prod\coprod∑⋃ ∑ ⋃\sum\bigcup⋂∫⋂∫\bigcap\<strong>in</strong>t ⊎ ⊎∮\biguplus∮⊔\o<strong>in</strong>t⊔ \bigsqcup∨ ∨\i<strong>in</strong>t\bigvee∧ ∧ \bigwedge\ii<strong>in</strong>t ⊕ ⊕ \bigoplus ⊗ \iii<strong>in</strong>t⊗\bigotimes ⊙ ⊙\idots<strong>in</strong>t \bigodot


Ma<strong>the</strong>matical Functions I<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTPure FunctionsPlease note that s<strong>in</strong>x (s<strong>in</strong> x) and s<strong>in</strong> x (\s<strong>in</strong> x) look totallydifferent.MATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifonts<strong>in</strong>costancotseccsclndimdeg\s<strong>in</strong>\cos\tan\cot\sec\csc\ln\dim\degarcs<strong>in</strong>arccosarctanargm mod nm mod nm (mod n)m (n)\arcs<strong>in</strong>\arccos\arctan\argm\mod nm\bmod nm\pmod nm\pod ns<strong>in</strong>hcoshtanhcothlglogexphomker\s<strong>in</strong>h\cosh\tanh\coth\lg\log\exp\hom\kerChemarrow


Ma<strong>the</strong>matical Functions II<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowFunctions with LimitsThe follow<strong>in</strong>g functions may take limits below: limx→0This is written as: \lim_{x \to 0}m<strong>in</strong>max<strong>in</strong>fsupdetgcdPrlim\m<strong>in</strong>\max\<strong>in</strong>f\sup\det\gcd\Pr\limlim <strong>in</strong>flimlim suplim<strong>in</strong>j limlim−→proj limlim←−\lim<strong>in</strong>f\varlim<strong>in</strong>f\limsup\varlimsup\<strong>in</strong>jlim\var<strong>in</strong>jlim\projlim\varprojlim


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowMiscellaneous <strong>Symbols</strong> II\ImR\Re℘\wp⊤\top⊥\bot∀\forall∃\exists∄\nexists¬ \neg∈\<strong>in</strong>\not<strong>in</strong>∋\ni∁\complement\hbarħ\hslashl\ell∂\partialð\ethı\imathj\jmathk\BbbkℲ\F<strong>in</strong>v\Game∞\<strong>in</strong>fty∅\emptyset∅\varnoth<strong>in</strong>g∠\angle∡\measuredangle∢\sphericalangle∫\small<strong>in</strong>t


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowMiscellaneous <strong>Symbols</strong> II∇\nabla\mho□\square□\Box△\triangle△\vartriangle▽\triangledown♦\lozenge√\surď\checkmark♯\sharp♮\natural♭\flat′ \prime\backprime↦\mapstochar\ \backslash\diagdown\diagup\blacksquare⋄\Diamond\blacktriangle\blacktriangledown\blacklozenge♥\heartsuit♦\diamondsuit♠\spadesuit♣\clubsuit⋆\star⋆\bigstarR\circledRS\circledS


Ma<strong>the</strong>matical Alphabets I<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowABCDEFGHIJKLMNOPQRS TUVWXYZabcde f ghi jklmnopqrstuvwxyz1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890\mathnormal{...}\mathrm{...}\mathsf{...}


Ma<strong>the</strong>matical Alphabets II<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890A BC DE F G H I J K L M NOPQRS T U V W X Y Z(Include \usepackage{mathrsfs}before \beg<strong>in</strong>{document})ABCDEF GHIJKLMNOPQRST UVWXYZ\mathbf{...}\mathscr{...}\mathcal{...}


Ma<strong>the</strong>matical Alphabets III<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz1234567890αβπθΦΨΩ . . .∈ ∂∇ ← ∞∅□ . . .\mathfrak{...}\boldsymbol{...}


Ma<strong>the</strong>matical Alphabets IV<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbb{...}\varmathbb{...}


BracketsThese are variable sized<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow( ([ [| \vert{ \{〈 \langle⌈ \lceil⌊ \lfloor⎩ \lgroup| \lvert‖ \lVert{ \lmoustache| \arrowvert\ \backslash) )] ]‖ \Vert} \}〉 \rangle⌉ \rceil⌋ \rfloor⎭ \rgroup| \rvert‖ \rVert{ \rmoustache‖ \Arrowvert⎪ \bracevert


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowBrackets - Math Accents\ulcorner\llcorner↑\uparrow↓\downarrow↕\updownarrow\urcorner\lrcorner⇑\Uparrow⇓\Downarrow⇕\Updownarrowã\tilde{a}â\hat{a}ǎ\check{a}⃗a\vec{a}ā\bar{a}á\acute{a}à\grave{a}ă\breve{a}ȧ\dot{a}ä\ddot{a}...a\dddot{a}....a\ddddot{a}å\mathr<strong>in</strong>g{a}


Dots<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow. . . \ldots lower dots· · · \cdots center dots. .. \ddots diagonal dots. \vdots vertical dots. . . . . . . \dotfill fill with dots. . . \dots lower or center· · · \dotsm multiplication· · · \dotsi dots for <strong>in</strong>tegrals· · · \dotsb dots for b<strong>in</strong>ary op.. . . \dotsc dots after commas. . . \dotso o<strong>the</strong>r dots. \ldotp· \cdotp: \colon


<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrowVariable Size Constructions{}}{abc\overbrace{abc}abc}{{}\underbrace{abc}abc←−−\xleftarrow{abc}abc−−→\xrightarrow{abc}√ abc\sqrt{abc}ãbc\widetilde{abc}âbc\widehat{abc}abc\overl<strong>in</strong>e{abc}abc\underl<strong>in</strong>e{abc}−→abc\overrightarrow{abc}←−abc\overleftarrow{abc}←→abc\overleftrightarrow{abc}abc−→\underrightarrow{abc}abc←−\underleftarrow{abc}abc←→\underleftrightarrow{abc}


Txfonts IInclude \usepackage{txfonts} before \beg<strong>in</strong>{document}<strong>TX</strong>FONTSEmre SermutluIntroductionTEXTMATHCommonGreekB<strong>in</strong>arySubsetsInequalitiesTrianglesArrowsOperatorsFunctionsMiscel.AlphabetBracketsDotsVar. SizeEXTRATxfontsTextcompMarvosymPifontChemarrow\bigsqcapplus\bigsqcupplus\i<strong>in</strong>t\ii<strong>in</strong>t\iii<strong>in</strong>t\sq<strong>in</strong>t\sqi<strong>in</strong>t\sqii<strong>in</strong>t\idots<strong>in</strong>t\f<strong>in</strong>t\oi<strong>in</strong>t \oii<strong>in</strong>t\o<strong>in</strong>tclockwise\o<strong>in</strong>tctrclockwise\oi<strong>in</strong>tclockwise\oi<strong>in</strong>tctrclockwise\oii<strong>in</strong>tclockwise\oii<strong>in</strong>tctrclockwise\varo<strong>in</strong>tclockwise\varo<strong>in</strong>tctrclockwise\varoi<strong>in</strong>tclockwise\varoi<strong>in</strong>tctrclockwise\varoii<strong>in</strong>tclockwise\varoii<strong>in</strong>tctrclockwise


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