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diff --git a/Master/texmf-dist/doc/fonts/epigrafica/README b/Master/texmf-dist/doc/fonts/epigrafica/README index c3f5f9b056d..ea01cf080e7 100644 --- a/Master/texmf-dist/doc/fonts/epigrafica/README +++ b/Master/texmf-dist/doc/fonts/epigrafica/README @@ -1,4 +1,4 @@ -Epigrafica for LaTeX v1.0, 1 June 2006. +Epigrafica for LaTeX v1.01, 3 Oct 2009. Start by reading the files in the subdirectory doc/ diff --git a/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.pdf b/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.pdf Binary files differdeleted file mode 100644 index e1a41f9a8d0..00000000000 --- a/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.tex b/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.tex new file mode 100644 index 00000000000..ced8bd4a5be --- /dev/null +++ b/Master/texmf-dist/doc/fonts/epigrafica/epigrafica.tex @@ -0,0 +1,294 @@ +\documentclass{article} +\usepackage[polutonikogreek,english]{babel} +\usepackage[iso-8859-7]{inputenc} + +\usepackage{epigrafica} + + + +%%%%% 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{epigrafica} font family} +\author{Antonis Tsolomitis\\ +Laboratory of Digital Typography\\ and Mathematical Software\\ +Department of Mathematics\\ +University of the Aegean} +\date {\textsc{27} May \textsc{2006}} + + +\begin{document} +\maketitle + + + +\section{Introduction} +The Epigrafica family is a derivative work of the MgOpenCosmetica +fonts which has been made available by Magenta Ltd +(\texttt{http://www.magenta.gr}) +under the \textsc{gpl} license. + +This is the initial release of Epigrafica and supports only +monotonic Greek, and the OT1 and T1 partially. Polytonic and full OT1 +and T1 support is under development. However, basic latin is supported. + + + The greek part is to be used with the greek option of +the Babel package. + +The fonts are loaded with + +\verb|\usepackage{epigrafica}|. + +The package provides a true small caps font although not provided by +the source fonts from Magenta. However, the text figures are currently +under development. In addition to this there have been several +enhancements both to glyph coverage and to some buggy splines (for +example, +in O, Q and others) + + +Finally, the math symbols are taken from the pxfonts package. + + + +\section{Installation} + +Copy the contents of the subdirectory afm in +texmf/fonts/afm/source/public/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory doc in +texmf/doc/latex/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory enc in +texmf/fonts/enc/dvips/public/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory map in +texmf/fonts/map/dvips/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory tex in +texmf/tex/latex/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory tfm in +texmf/fonts/tfm/public/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory type1 in +texmf/fonts/type1/public/Epigrafica/ + +\medskip + +\noindent Copy the contents of the subdirectory vf in +texmf/fonts/vf/public/Epigrafica/ + +\medskip + +\noindent In your installations updmap.cfg file add the line + +\medskip + +\noindent Map epigrafica.map + +\medskip + +Refresh your filename database and the map file database (for example, on Unix systems +run mktexlsr and then run the updmap script as root). + +You are now ready to use the fonts provided that you have a relatively +modern installation that includes pxfonts. + +\section{Usage} + +As said in the introduction the package covers both english and +greek. Greek covers only monotonic for the moment. + +For example, the preample + +\begin{verbatim} +\documentclass{article} +\usepackage[english,greek]{babel} +\usepackage[iso-8859-7]{inputenc} +\usepackage{epigrafica} +\end{verbatim} + +will be the correct setup for articles in Greek. + +\bigskip + +\subsection{Transformations by \texttt{dvips}} + +Other than the shapes provided by the fonts themselves, this package +provides a slanted shape +using the standard mechanism provided by dvips. + + + +\subsection{Euro} + +Euro is also available in LGR enconding. \verb|\textgreek{\euro}| +gives \textgreek{\euro}. + + +\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 \textlatin{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: |