[OS X TeX] Font problem

George Gratzer gratzer at ms.umanitoba.ca
Sat Dec 17 23:07:18 CET 2005 

On Dec 17, 2005, at 3:47 PM, Peter Dyballa wrote:

>
> Am 17.12.2005 um 20:05 schrieb George Gratzer:
>
>> I am beginning to understand. Apparently, two fonts are missing  
>> and are substituted: NimbusMonL and NimbusRomNo9L. Where did these  
>> comes from? Why are they used?
>>
>
> Three possible sources:
>
> 	• you use them in your TeX file

No.

> 	• you load a STY or CLS file that uses them

No. I use amsart.

> 	• you have URW++ map file fragments chosen and think you're using  
> Times and Courier
>
> Try in Terminal:	updmap --listmaps | grep -v '^#' | grep urw
>
> Then disable with 'sudo -H updmap-sys --nohash --disable <MAP  
> name>' any urw name listed.

gratzer% updmap --listmaps | grep -v '^#' | grep urw
updmap: This is updmap, version 1122009795
updmap: using transcript file `/Users/gratzer/Library/texmf/web2c/ 
updmap.log'
Map urwvn.map

None are listed.

>
> If this still fails you will need to publish your TeX and LOG  
> files ...

Source:

% Introductory sample article: intrart.tex

\documentclass{amsart}
\usepackage{amssymb,latexsym}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}{Definition}
\newtheorem{notation}{Notation}

\begin{document}
\title{A construction of complete-simple\\
        distributive lattices}
\author{George~A. Menuhin}
\address{Computer Science Department\\
          University of Winnebago\\
          Winnebago, MN 53714}
\date{March 15, 2006}
\begin{abstract}
    In this note, we prove that there exist
    \emph{complete-simple distributive lattices,}
    that is, complete distributive lattices
   in which there are only two complete congruences.
\end{abstract}
\maketitle


\section{Introduction}\label{S:intro}
In this note, we prove the following result:

\begin{theorem}
There exists an infinite complete distributive lattice~$K$
with only the two trivial complete congruence relations.
\end{theorem}

\section{The $\Pi^{*}$ construction}\label{S:P*}
The following construction is crucial in the proof
of our Theorem:

\begin{definition}\label{D:P*}
Let $D_{i}$, for $i \in I$, be complete distributive
lattices satisfying condition~\textup{(J)}.  Their
$\Pi^{*}$ product is defined as follows:
\[
    \Pi^{*} ( D_{i} \mid i \in I ) =
    \Pi ( D_{i}^{-} \mid i \in I ) + 1;
\]
that is, $\Pi^{*} ( D_{i} \mid i \in I )$ is
$\Pi ( D_{i}^{-} \mid i \in I )$ with a new
unit element.
\end{definition}

\begin{notation}
If $i \in I$ and $d \in D_{i}^{-}$, then
\[
   \langle \ldots, 0, \ldots, d, \ldots, 0, \ldots \rangle
\]
is the element of $\Pi^{*} ( D_{i} \mid i \in I )$ whose
$i$-th component is $d$ and all the other components
are $0$.
\end{notation}

See also Ernest~T. Moynahan~\cite{eM57a}.

Next we verify the following result:

\begin{theorem}\label{T:P*}
Let $D_{i}$, $i \in I$, be complete distributive
lattices satisfying condition~\textup{(J)}.  Let $\Theta$
be a complete congruence relation on
$\Pi^{*} ( D_{i} \mid i \in I )$.
If there exist $i \in I$ and $d \in D_{i}$ with
$d < 1_{i}$ such that, for all $d \leq c < 1_{i}$,
\begin{equation}\label{E:cong1}
    \langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
    \langle \ldots, c, \ldots, 0, \ldots \rangle
    \pmod{\Theta},
\end{equation}
then $\Theta = \iota$.
\end{theorem}

\begin{proof}
Since
\begin{equation}\label{E:cong2}
\langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
\langle \ldots, c, \ldots, 0, \ldots \rangle
\pmod{\Theta},
\end{equation}
and $\Theta$ is a complete congruence relation,
it follows from condition~(J) that
\begin{equation}\label{E:cong}
\langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
\bigvee ( \langle \ldots, c, \ldots, 0, \ldots \rangle
\mid d \leq c < 1 ) \pmod{\Theta}.
\end{equation}

Let $j \in I$, $j \neq i$, and let $a \in D_{j}^{-}$.
Meeting both sides of the congruence (\ref{E:cong2}) with
$\langle \ldots, a, \ldots, 0, \ldots \rangle$,
we obtain that
\begin{equation}\label{E:comp}
    0 = \langle \ldots, a, \ldots, 0, \ldots \rangle
    \pmod{\Theta},
\end{equation}
Using the completeness of $\Theta$ and (\ref{E:comp}),
we get:
\[
    0 \equiv \bigvee ( \langle \ldots, a, \ldots, 0, \ldots
    \rangle \mid a \in D_{j}^{-} ) = 1 \pmod{\Theta},
\]
hence $\Theta = \iota$.
\end{proof}

\begin{thebibliography}{9}

\bibitem{sF90}
Soo-Key Foo,
\emph{Lattice Constructions},
Ph.D. thesis,
University of Winnebago, Winnebago, MN, December, 1990.

\bibitem{gM68}
George~A. Menuhin,
\emph{Universal Algebra},
D.~van Nostrand, Princeton, 1968.

\bibitem{eM57}
Ernest~T. Moynahan,
\emph{On a problem of M. Stone},
Acta Math. Acad. Sci. Hungar. \textbf{8} (1957),
455--460.

\bibitem{eM57a}
Ernest~T. Moynahan,
\emph{Ideals and congruence relations in lattices.} II,
Magyar Tud. Akad. Mat. Fiz. Oszt. K\"{o}zl. \textbf{9}
(1957), 417--434.

\end{thebibliography}

\end{document}

Log file:

This is pdfeTeX, Version 3.141592-1.30.4-2.2 (Web2C 7.5.5)
\write18 enabled.
entering extended mode
(./intrart.tex
LaTeX2e <2003/12/01>
Babel <v3.8d> and hyphenation patterns for american, french, german,  
ngerman, d
utch, italian, norsk, portuges, spanish, swedish, nohyphenation, loaded.
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amscls/amsart.cls
Document Class: amsart 2004/08/06 v2.20
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amstext.sty
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsgen.sty))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsbsy.sty)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsmath/amsopn.sty))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amsfonts.sty))
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/amssymb.sty)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/latexsym.sty) (./ 
intrart.aux
) (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsb.fd)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/ulasy.fd) [1{/usr/ 
local/teTe
X/share/texmf.local/fonts/map/pdftex/updmap/pdftex.map}] [2] (./ 
intrart.aux) )<
/usr/local/teTeX/share/texmf.tetex/fonts/type1/bluesky/cm/cmbx8.pfb></ 
usr/local
/teTeX/share/texmf.tetex/fonts/type1/bluesky/symbols/msam10.pfb></usr/ 
local/teT
eX/share/texmf.tetex/fonts/type1/bluesky/cm/cmr7.pfb></usr/local/ 
teTeX/share/te
xmf.tetex/fonts/type1/bluesky/cm/cmex10.pfb></usr/local/teTeX/share/ 
texmf.tetex
/fonts/type1/bluesky/cm/cmsy10.pfb></usr/local/teTeX/share/ 
texmf.tetex/fonts/ty
pe1/bluesky/cm/cmmi7.pfb></usr/local/teTeX/share/texmf.tetex/fonts/ 
type1/bluesk
y/cm/cmsy7.pfb></usr/local/teTeX/share/texmf.tetex/fonts/type1/ 
bluesky/cm/cmmi1
0.pfb></usr/local/teTeX/share/texmf.tetex/fonts/type1/bluesky/cm/ 
cmti10.pfb></u
sr/local/teTeX/share/texmf.tetex/fonts/type1/bluesky/cm/cmr10.pfb></ 
usr/local/t
eTeX/share/texmf.tetex/fonts/type1/bluesky/cm/cmti8.pfb></usr/local/ 
teTeX/share
/texmf.tetex/fonts/type1/bluesky/cm/cmcsc10.pfb></usr/local/teTeX/ 
share/texmf.t
etex/fonts/type1/bluesky/cm/cmr8.pfb></usr/local/teTeX/share/ 
texmf.tetex/fonts/
type1/bluesky/cm/cmbx10.pfb>
Output written on intrart.pdf (2 pages, 88477 bytes).
Transcript written on intrart.log.

I hope this helps.

GG

>
> --
> Greetings
>
>   Pete
>
> Our enemies are innovative and resourceful, and so are we. They never
> stop thinking about new ways to harm our country and our people, and
> neither do we. -- Georges W. Bush
>
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