1%% BEGIN poster1.tex
2%%
3%% Sample for poster.tex/poster.sty.
4%% Run with LaTeX, with or without the NFSS.
5%% You might have problems with missing fonts.
6%%
7%% See below if using A4 paper.
8
9\documentstyle{article}
10
11\input poster  % Input here in case poster.sty not installed.
12
13\mag\magstep5  % Magnification of 1.2^5 (roughly 2.5)
14               % Use "true" dimensions below for magnified values.
15
16\begin{document}
17
18%% Add  paperwidth=210mm,paperheight=297mm  if using A4 paper:
19
20\begin{Poster}[vcenter=true,hcenter=true]
21\setlength{\fboxsep}{.8truein}%
22\setlength{\fboxrule}{.1truein}%
23\fbox{\begin{minipage}{11.1truein}
24
25\begin{center}
26  \bf ON SOME \boldmath$\Pi$-HEDRAL SURFACES IN QUASI-QUASI SPACE
27\end{center}
28\begin{center}
29  CLAUDE HOPPER, Omnius University
30\end{center}
31
32There is at present a school of mathematicians which holds that the
33explosive growth of jargon within mathematics is a deplorable trend.  It
34is our purpose in this note to continue the work of
35Redheffer~\cite{redheffer} in showing how terminology itself can lead to
36results of great elegance.
37
38I first consolidate some results of Baker~\cite{baker} and
39McLelland~\cite{mclelland}.  We define a class of connected snarfs as
40follows: $S_\alpha=\Omega(\gamma_\beta)$.  Then if
41$B=(\otimes,\rightarrow,\theta)$ is a Boolean left subideal, we have:
42$$
43\nabla S_\alpha=\int\int\int_{E(\Omega)}
44B(\gamma_{\beta_0},\gamma_{\beta_0})\,d\sigma d\phi d\rho
45-\frac{19}{51}\Omega.
46$$
47Rearranging, transposing, and collecting terms, we have:
48$\Omega=\Omega_0$.
49
50The significance of this is obvious, for if $\{S_\alpha\}$ be a class of
51connected snarfs, our result shows that its union is an utterly
52disjoint subset of a $\pi$-hedral surface in quasi-quasi space.
53
54We next use a result of Spyrpt~\cite{spyrpt} to derive a property of
55wild cells in door topologies.  Let $\xi$ be the null operator on a door
56topology, $\Box$, which is a super-linear space.  Let $\{P_\gamma\}$ be
57the collection of all nonvoid, closed, convex, bounded, compact,
58circled, symmetric, connected, central, $Z$-directed, meager sets in
59$\Box$.  Then $P=\cup P_\gamma$ is perfect.  Moreover, if $P\neq\phi$,
60then $P$ is superb.
61
62\smallskip
63{\it Proof.}  The proof uses a lemma due to
64Sriniswamiramanathan~\cite{srinis}.  This states that any unbounded
65fantastic set it closed.  Hence we have
66$$
67\Rightarrow P\sim\xi(P_\gamma)-\textstyle\frac{1}{3}.
68$$
69
70After some manipulation we obtain
71$$
72\textstyle\frac{1}{3}=\frac{1}{3}
73$$
74I have reason to believe~\cite{russell} that this implies $P$ is perfect.
75If $P\neq\phi$, $P$ is superb.  Moreover, if $\Box$ is a $T_2$ space, $P$
76is simply superb.  This completes the proof.
77
78Our final result is a generalization of a theorem of Tz, and
79encompasses some comments on the work of Beaman~\cite{beaman} on the
80Jolly function.
81
82Let $\Omega$ be any $\pi$-hedral surface in a semi-quasi space.  Define
83a nonnegative, nonnegatively homogeneous subadditive linear functional
84$f$ on $X\supset\Omega$ such that $f$ violently suppresses $\Omega$.
85Then $f$ is the Jolly function.
86
87\smallskip
88{\it Proof.}  Suppose $f$ is not the Jolly function.  Then
89$\{\Lambda,\mbox{@},\xi\}\cap\{\Delta,\Omega,\Rightarrow\}$ is void.  Hence
90$f$ is morbid.  This is a contradiction, of course.  Therefore, $f$ is
91the Jolly function.  Moreover, if $\Omega$ is a circled husk, and
92$\Delta$ is a pointed spear, then $f$ is uproarious.
93
94\small
95\begin{center}
96\bf References
97\end{center}
98\def\thebibliography#1{%
99  \list
100 {\bf\arabic{enumi}.}{\settowidth\labelwidth{\bf #1.}\leftmargin\labelwidth
101 \advance\leftmargin\labelsep
102 \usecounter{enumi}}
103 \def\newblock{\hskip .11em plus .33em minus .07em}
104 \sloppy\clubpenalty4000\widowpenalty4000
105 \sfcode`\.=1000\relax}
106\begin{thebibliography}{9}
107\bibitem{redheffer}
108R. M. Redheffer, A real-life application of mathematical symbolism,
109this {\it Magazine}, 38 (1965) 103--4.
110\bibitem{baker}
111J. A. Baker, Locally pulsating manifolds, East Overshoe Math. J., 19
112(1962) 5280--1.
113\bibitem{mclelland}
114J. McLelland, De-ringed pistons in cylindric algebras,
115Vereinigtermathematischerzeitung f\"ur Zilch, 10 (1962) 333--7.
116\bibitem{spyrpt}
117Mrowclaw Spyrpt, A matrix is a matrix is a matrix, Mat. Zburp., 91
118(1959) 28--35.
119\bibitem{srinis}
120Rajagopalachari Sriniswamiramanathan, Some expansions on the Flausgloten
121Theorem on locally congested lutches, J. Math. Soc., North Bombay, 13
122(1964) 72--6.
123\bibitem{russell}
124A. N. Whitehead and B. Russell, Principia Mathematica, Cambridge
125University Press, 1925.
126\bibitem{beaman}
127J. Beaman, Morbidity of the Jolly function, Mathematica Absurdica, 117
128(1965) 338--9.
129\end{thebibliography}
130\end{minipage}}%
131\end{Poster}
132
133\end{document}
134%% END poster1.tex
135
136