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diff --git a/Master/texmf-dist/doc/fonts/gfsbodoni/gfsbodoni.tex b/Master/texmf-dist/doc/fonts/gfsbodoni/gfsbodoni.tex deleted file mode 100644 index 9f0f82c6a22..00000000000 --- a/Master/texmf-dist/doc/fonts/gfsbodoni/gfsbodoni.tex +++ /dev/null @@ -1,372 +0,0 @@ -%% (c) copyright 2006, 2007 -%% Antonis Tsolomitis -%% Department of Mathematics, University of the Aegean -%% -%% This document can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN -%% archives in directory macros/latex/base/lppl.txt; either -%% version 1 of the License, or any later version. - -\documentclass{article} -\usepackage[polutonikogreek,english]{babel} -\usepackage[iso-8859-7]{inputenc} -\usepackage{txfonts} -\usepackage[default]{gfsbodoni} -\usepackage{latexsym,amsfonts} -%\renewcommand{\ttdefault}{hlst} - -%%%%% Theorems and friends -\newtheorem{theorem}{Θεώρημα}[section] -\newtheorem{lemma}[theorem]{Λήμμα} -\newtheorem{proposition}[theorem]{Πρόταση} -\newtheorem{corollary}[theorem]{Πόρισμα} -\newtheorem{definition}[theorem]{Ορισμός} -\newtheorem{remark}[theorem]{Παρατήρηση} -\newtheorem{axiom}[theorem]{Αξίωμα} -\newtheorem{exercise}[theorem]{Άσκηση} - - -%%%%% Environment ``proof'' -\newenvironment{proof}[1]{{\textit{Απόδειξη:}}}{\ \hfill$\Box$} -\newenvironment{hint}[1]{{\textit{Υπόδειξη:}}}{\ \hfill$\Box$} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - - - - - -\title{The \textsc{gfsbodoni} font family} -\author{Antonis Tsolomitis\\ -Laboratory of Digital Typography\\ and Mathematical Software\\ -Department of Mathematics\\ -University of the Aegean} -\date {\textsc{19} March \textsc{2006}} - - -\begin{document} -\maketitle - -\section{Introduction} -The Bodoni family of the Greek Font Society was made available for free -in autumn 2005. This font existed with a commercial license for many -years before. Support for LaTeX and the babel package was prepared -several years ago by the author and I.\ Vasilogiorgakis. With the -free availability of the fonts I have modified the original package -so that it reflects the changes occured in the latest releases by \textsc{gfs}. - -The package supports three encodings: OT1, T1 and LGR to the extend -that the font themselves cover these. OT1 and LGR should be -fairly complete. The greek part is to be used with the greek option of -the Babel package. - -The fonts are loaded with - -\verb|\usepackage{gfsdidot}| or \verb|\usepackage[default]{gfsdidot}|. - - -Tha latter one sets Bodoni as the default document font. The former -defines the environment \verb|bodoni| and the command -\verb|\textbodoni|. For example, while in Greek language - -\verb|\textbodoni{dokim'h}| - -produces - -\textgreek{\textbodoni{dokim'h}}. - -x-height is adjusted so that it matches with the x-height of the -\verb|txfonts| package. This is done to help with documents requiring -mathematics. In this case load \verb|txfonts| \textit{but before} \verb|gfsbodoni.sty|. - -\section{Installation} - -Copy the contents of the subdirectory afm in -texmf/fonts/afm/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory doc in -texmf/doc/latex/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory enc in -texmf/fonts/enc/dvips/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory map in -texmf/fonts/map/dvips/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory tex in -texmf/tex/latex/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory tfm in -texmf/fonts/tfm/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory type1 in -texmf/fonts/type1/GFS/Bodoni/ - -\medskip - -\noindent Copy the contents of the subdirectory vf in -texmf/fonts/vf/GFS/Bodoni/ - -\medskip - -\noindent In your installation's updmap.cfg file add the line - -\medskip - -\noindent Map gfsbodoni.map - -\medskip - -Refresh your filename database and the map file database (for example, on Unix systems -run mktexlsr and then run the updmap-sys (or updmap on older systems) script as root). - -You are now ready to use the fonts. - -\section{Usage} - -As said in the introduction the package covers both english and -greek. Greek covers polytonic too through babel (read the -documentation -of the babel package and its greek option). - -For example, the preample - -\begin{verbatim} -\documentclass{article} -\usepackage[english,greek]{babel} -\usepackage[iso-8859-7]{inputenc} -\usepackage[default]{gfsbodoni} -\end{verbatim} - -will be the correct setup for articles in Greek using Bodoni for the -main font. - -\bigskip - -\subsection{Transformations by \texttt{dvips}} - -Other than the shapes provided by the fonts themselves, this package -provides a slanted small caps shape -using the standard mechanism provided by dvips. Get slanted small caps with \verb|\scslshape|. -For example, the code -\begin{verbatim} -\textsc{small caps \textgreek{πεζοκεφαλαία} 0123456789} {\scslshape - \textgreek{πεζοκεφαλαία 0123456789}} -\end{verbatim} -will give - - -\textsc{small caps \textgreek{πεζοκεφαλαία} 0123456789} {\scslshape - \textgreek{πεζοκεφαλαία 0123456789}} - -\noindent The command \verb|\textscsl{}| are also provided. - - - - -\subsection{Tabular numbers} - -Tabular numbers (of fixed width) are accessed with the command -\verb|\tabnums{}|. Compare - -\begin{tabular}{ll} -\verb+|0|1|2|3|4|5|6|7|8|9|+ & |0|1|2|3|4|5|6|7|8|9|\\ -\verb+\tabnums{|0|1|2|3|4|5|6|7|8|9|}+ & \tabnums{|0|1|2|3|4|5|6|7|8|9|} -\end{tabular} - - -\subsection{Text fractions} - -Text fractions are composed using the lower and upper numerals -provided by the fonts, and are -accessed with the command \verb|\textfrac{}{}|. -For example, \verb|\textfrac{-22}{7}| gives \textfrac{-22}{7}. - -Precomposed fractions are provided too by \verb|\onehalf|, -\verb|\onethird|, etc. - - -\subsection{Additional characters} - -\begin{center} -\begin{tabular}{|c|c|}\hline -\verb|\textbullet| &\textbullet \\ \hline -\verb|\textparagraph| &\textparagraph \\ \hline -%\verb|\textparagraphalt| & \textparagraphalt\\ \hline -\verb|\careof| & \careof\\ \hline -\verb|\numero| & \numero\\ \hline -\verb|\estimated| & \estimated\\ \hline -%\verb|\whitebullet| & \whitebullet\\ \hline -\verb|\textlozenge| & \textlozenge\\ \hline -\verb|\eurocurrency| & \eurocurrency\\ \hline -%\verb|\interrobang| & \interrobang\\ \hline -\verb|\textdagger| & \textdagger\\ \hline -\verb|\textdaggerdbl| & \textdaggerdbl\\ \hline -\verb|\yencurrency| & \yencurrency\\ \hline -\end{tabular} -\end{center} - -Euro is also available in LGR enconding. \verb|\textgreek{\euro}| -gives \textgreek{\euro}. - - - -\section{Problems} - - - The -accents of the capital letters should hang in the left margin when such a letter starts a -line. \TeX\ and \LaTeX\ do not provide the tools for such a -feature. However, this seems to be possible with -\textlatin{pdf\TeX} -As this is work in progress, please be patient\ldots - - - - -\section{Samples} - -The next two pages provide samples in english and greek with math. - - -\newpage - -Adding up these inequalities with respect to $i$, we get -\begin{equation} \sum c_i d_i \leq \frac1{p} +\frac1{q} =1\label{10}\end{equation} -since $\sum c_i^p =\sum d_i^q =1$.\hfill$\Box$ - -In the case $p=q=2$ -the above inequality is also called the -\textit{Cauchy-Schwartz inequality}. - -Notice, also, that by formally defining $\left( \sum |b_k|^q\right)^{1/q}$ to be -$\sup |b_k|$ for $q=\infty$, we give sense to (9) for all -$1\leq p\leq\infty$. - - -A similar inequality is true for functions instead of sequences with the sums -being substituted by integrals. - -\medskip - -\textbf{Theorem} {\itshape Let $1<p<\infty$ and let $q$ be such that $1/p +1/q =1$. Then, -for all functions $f,g$ on an interval $[a,b]$ -such that the integrals $\int_a^b |f(t)|^p\,dt$, $\int_a^b |g(t)|^q\,dt$ and -$\int_a^b |f(t)g(t)|\,dt$ exist \textup{(}as Riemann integrals\textup{)}, -we have -\begin{equation} -\int_a^b |f(t)g(t)|\,dt\leq -\biggl(\int_a^b |f(t)|^p\,dt\biggr)^{1/p} -\biggl(\int_a^b |g(t)|^q\,dt\biggr)^{1/q} . -\end{equation} -} - -Notice that if the Riemann integral $\int_a^b f(t)g(t)\,dt$ also exists, then -from the inequality $\left|\int_a^b f(t)g(t)\,dt\right|\leq -\int_a^b |f(t)g(t)|\,dt$ follows that -\begin{equation} -\left|\int_a^b f(t)g(t)\,dt\right|\leq -\biggl(\int_a^b |f(t)|^p\,dt\biggr)^{1/p} -\biggl(\int_a^b |g(t)|^q\,dt\biggr)^{1/q} . -\end{equation} - - - -\textit{Proof:} Consider a partition of the interval $[a,b]$ in $n$ equal -subintervals with endpoints -$a=x_0<x_1<\cdots<x_n=b$. Let $\Delta x=(b-a)/n$. -We have -\begin{eqnarray} -\sum_{i=1}^n |f(x_i)g(x_i)|\Delta x &\leq& -\sum_{i=1}^n |f(x_i)g(x_i)|(\Delta x)^{\frac1{p}+\frac1{q}}\nonumber\\ -&=&\sum_{i=1}^n \left(|f(x_i)|^p \Delta x\right)^{1/p} \left(|g(x_i)|^q -\Delta x\right)^{1/q}.\label{functionalHolder1}\\ \nonumber -\end{eqnarray} - -\newpage\greektext - - -% $\bullet$ Μήκος τόξου καμπύλης - -% \begin{proposition}\label{chap2:sec1:prop 23} -% Έστω $\gamma$ καμπύλη με παραμετρική εξίσωση $x=g(t)$, $y=f(t)$, -% $t\in [a,\,b]$ αν $g'$, $f'$ συνεχείς στο $[a,\,b]$ τότε η -% $\gamma$ έχει μήκος $S=L(\gamma)=\int_a^b \sqrt{g'(t)^2+f'(t)^2} -% dt$. -% \end{proposition} - -\textbullet\ Εμβαδόν επιφάνειας από περιστροφή\\ - -\begin{proposition}\label{chap2:sec1:prop23-2} -Έστω $\gamma$ καμπύλη με παραμετρική εξίσωση $x=g(t)$, $y=f(t)$, -$t\in [a,\,b]$ αν $g'$, $f'$ συνεχείς στο $[a,\,b]$ τότε το -εμβαδόν από περιστροφή της $\gamma$ γύρω από τον $xx'$ δίνεται \\ -$Β=2\pi\int_a^b |f(t)| \sqrt{g'(t)^2+f^{\prime}(t^2)} dt$. \\ Αν η -$\gamma$ δίνεται από την $y=f(x)$, $x\in [a,\,b]$ τότε -$Β=2\pi\int_a^b |f(t)| \sqrt{1+f'(x)^2} dx$ -\end{proposition} - -\textbullet\ Όγκος στερεών από περιστροφή\\ Έστω $f : -[a,\,b]\rightarrow \mathbb{R}$ συνεχής και $R=\{f, Ox,x=a,x=b\}$ -είναι ο όγκος από περιστροφή του γραφήματος της $f$ γύρω από τον -$Ox$ μεταξύ των ευθειών $x=a$, και $x=b$, τότε $V=\pi\int_a^b f -(x)^2 dx$ - -\textbullet\ Αν $f,g : [a,\,b]\rightarrow \mathbb{R}$ και $0\leq -g(x)\leq f(x)$ τότε ο όγκος στερεού που παράγεται από περιστροφή -των γραφημάτων των $f$ και $g$, $R=\{f,g, Ox,x=a,x=b\}$ είναι \\ -$V=\pi\int_a^b\{ f (x)^2-g(x)^2\} dx$. - -\textbullet\ Αν $x=g(t)$, $y=f(t)$, $t=[t_1,\,t_2]$ τότε -$V=\pi\int_{t_1}^{t_2}\{ f (t)^2 g'(t)\} dt$ για $g(t_1)=a$, -$g(t_2)=b$. - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Ασκήσεις}\label{chap2:sec2} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{exercise}\label{chap2:ex1} -Να εκφραστεί το παρακάτω όριο ως ολοκλήρωμα $Riemann$ κατάλ\-ληλης -συνάρτησης\\ -$$\lim_{n\rightarrow\infty} \frac{1}{n}\sum_{k=1}^{n}\sqrt[n]{e^k} $$ -\end{exercise} -%%%%%%%%% -\textit{Υπόδειξη:} -Πρέπει να σκεφτούμε μια συνάρτηση της οποίας γνωρίζουμε ότι υπάρχει το ολοκλήρωμα. - Τότε παίρνουμε μια διαμέριση $P_n$ και δείχνουμε π.χ. ότι το $U(f,P_n)$ είναι η ζητούμενη σειρά. - -\bigskip - -%%%%%%%%%%%%%% -\textit{Λύση:} -Πρέπει να σκεφτούμε μια συνάρτηση της οποίας γνωρίζουμε ότι υπάρχει το ολοκλήρωμα. -Τότε παίρνουμε μια διαμέριση $P_n$ και δείχνουμε π.χ. ότι το $U(f,P_n)$ είναι η ζητούμενη σειρά.\\ -Έχουμε ότι -\begin{eqnarray}\frac{1}{n}\sum_{k=1}^{n}\sqrt[n]{e^k} = -\frac{1}{n}\sqrt[n]{e}+\frac{1}{n}\sqrt[n]{e^2}+\cdots + -\frac{1}{n}\sqrt[n]{e^n}\nonumber\\ -=\frac{1}{n}e^{\frac{1}{n}}+\frac{1}{n}e^{\frac{2}{n}}+\cdots+\frac{1}{n}e^{\frac{n}{n}}\nonumber -\end{eqnarray} - - - - -\end{document} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: |