[OS X TeX] Font problem

George Gratzer gratzer at ms.umanitoba.ca
Sat Dec 17 17:07:18 EST 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


> 	• 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/ 
Map urwvn.map

None are listed.

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


% Introductory sample article: intrart.tex


\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}
    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.

In this note, we prove the following result:

There exists an infinite complete distributive lattice~$K$
with only the two trivial complete congruence relations.

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

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.

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 $0$.

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

Next we verify the following result:

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 $d \leq c < 1_{i}$,
    \langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
    \langle \ldots, c, \ldots, 0, \ldots \rangle
then $\Theta = \iota$.

\langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
\langle \ldots, c, \ldots, 0, \ldots \rangle
and $\Theta$ is a complete congruence relation,
it follows from condition~(J) that
\langle \ldots, d, \ldots, 0, \ldots \rangle \equiv
\bigvee ( \langle \ldots, c, \ldots, 0, \ldots \rangle
\mid d \leq c < 1 ) \pmod{\Theta}.

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
    0 = \langle \ldots, a, \ldots, 0, \ldots \rangle
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 $\Theta = \iota$.


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

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

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

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.



Log file:

This is pdfeTeX, Version 3.141592-1.30.4-2.2 (Web2C 7.5.5)
\write18 enabled.
entering extended mode
LaTeX2e <2003/12/01>
Babel <v3.8d> and hyphenation patterns for american, french, german,  
ngerman, d
utch, italian, norsk, portuges, spanish, swedish, nohyphenation, loaded.
Document Class: amsart 2004/08/06 v2.20
For additional information on amsmath, use the `?' option.
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/latexsym.sty) (./ 
) (/usr/local/teTeX/share/texmf.tetex/tex/latex/amsfonts/umsa.fd)
(/usr/local/teTeX/share/texmf.tetex/tex/latex/base/ulasy.fd) [1{/usr/ 
X/share/texmf.local/fonts/map/pdftex/updmap/pdftex.map}] [2] (./ 
intrart.aux) )<
Output written on intrart.pdf (2 pages, 88477 bytes).
Transcript written on intrart.log.

I hope this helps.


> --
> 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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