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136 lines
4.6 KiB
TeX
136 lines
4.6 KiB
TeX
%% BEGIN poster1.tex
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%% Sample for poster.tex/poster.sty.
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\documentstyle{article}
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\input poster % Input here in case poster.sty not installed.
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\mag\magstep5 % Magnification of 1.2^5 (roughly 2.5)
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\begin{document}
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%% Add paperwidth=210mm,paperheight=297mm if using A4 paper:
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\begin{Poster}[vcenter=true,hcenter=true]
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\setlength{\fboxsep}{.8truein}%
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\setlength{\fboxrule}{.1truein}%
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\fbox{\begin{minipage}{11.1truein}
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\begin{center}
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\bf ON SOME \boldmath$\Pi$-HEDRAL SURFACES IN QUASI-QUASI SPACE
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\end{center}
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\begin{center}
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CLAUDE HOPPER, Omnius University
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\end{center}
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There is at present a school of mathematicians which holds that the
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explosive growth of jargon within mathematics is a deplorable trend. It
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is our purpose in this note to continue the work of
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Redheffer~\cite{redheffer} in showing how terminology itself can lead to
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results of great elegance.
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I first consolidate some results of Baker~\cite{baker} and
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McLelland~\cite{mclelland}. We define a class of connected snarfs as
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follows: $S_\alpha=\Omega(\gamma_\beta)$. Then if
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$B=(\otimes,\rightarrow,\theta)$ is a Boolean left subideal, we have:
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$$
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\nabla S_\alpha=\int\int\int_{E(\Omega)}
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B(\gamma_{\beta_0},\gamma_{\beta_0})\,d\sigma d\phi d\rho
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-\frac{19}{51}\Omega.
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$$
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Rearranging, transposing, and collecting terms, we have:
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$\Omega=\Omega_0$.
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The significance of this is obvious, for if $\{S_\alpha\}$ be a class of
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connected snarfs, our result shows that its union is an utterly
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disjoint subset of a $\pi$-hedral surface in quasi-quasi space.
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We next use a result of Spyrpt~\cite{spyrpt} to derive a property of
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wild cells in door topologies. Let $\xi$ be the null operator on a door
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topology, $\Box$, which is a super-linear space. Let $\{P_\gamma\}$ be
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the collection of all nonvoid, closed, convex, bounded, compact,
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circled, symmetric, connected, central, $Z$-directed, meager sets in
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$\Box$. Then $P=\cup P_\gamma$ is perfect. Moreover, if $P\neq\phi$,
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then $P$ is superb.
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\smallskip
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{\it Proof.} The proof uses a lemma due to
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Sriniswamiramanathan~\cite{srinis}. This states that any unbounded
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fantastic set it closed. Hence we have
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$$
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\Rightarrow P\sim\xi(P_\gamma)-\textstyle\frac{1}{3}.
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$$
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After some manipulation we obtain
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$$
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\textstyle\frac{1}{3}=\frac{1}{3}
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$$
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I have reason to believe~\cite{russell} that this implies $P$ is perfect.
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If $P\neq\phi$, $P$ is superb. Moreover, if $\Box$ is a $T_2$ space, $P$
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is simply superb. This completes the proof.
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Our final result is a generalization of a theorem of Tz, and
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encompasses some comments on the work of Beaman~\cite{beaman} on the
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Jolly function.
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Let $\Omega$ be any $\pi$-hedral surface in a semi-quasi space. Define
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a nonnegative, nonnegatively homogeneous subadditive linear functional
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$f$ on $X\supset\Omega$ such that $f$ violently suppresses $\Omega$.
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Then $f$ is the Jolly function.
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\smallskip
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{\it Proof.} Suppose $f$ is not the Jolly function. Then
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$\{\Lambda,\mbox{@},\xi\}\cap\{\Delta,\Omega,\Rightarrow\}$ is void. Hence
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$f$ is morbid. This is a contradiction, of course. Therefore, $f$ is
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the Jolly function. Moreover, if $\Omega$ is a circled husk, and
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$\Delta$ is a pointed spear, then $f$ is uproarious.
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\small
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\begin{center}
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\bf References
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\end{center}
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\def\thebibliography#1{%
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\list
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{\bf\arabic{enumi}.}{\settowidth\labelwidth{\bf #1.}\leftmargin\labelwidth
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\advance\leftmargin\labelsep
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\usecounter{enumi}}
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\def\newblock{\hskip .11em plus .33em minus .07em}
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\sloppy\clubpenalty4000\widowpenalty4000
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\sfcode`\.=1000\relax}
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\begin{thebibliography}{9}
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\bibitem{redheffer}
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R. M. Redheffer, A real-life application of mathematical symbolism,
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this {\it Magazine}, 38 (1965) 103--4.
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\bibitem{baker}
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J. A. Baker, Locally pulsating manifolds, East Overshoe Math. J., 19
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(1962) 5280--1.
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\bibitem{mclelland}
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J. McLelland, De-ringed pistons in cylindric algebras,
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Vereinigtermathematischerzeitung f\"ur Zilch, 10 (1962) 333--7.
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\bibitem{spyrpt}
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Mrowclaw Spyrpt, A matrix is a matrix is a matrix, Mat. Zburp., 91
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(1959) 28--35.
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\bibitem{srinis}
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Rajagopalachari Sriniswamiramanathan, Some expansions on the Flausgloten
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Theorem on locally congested lutches, J. Math. Soc., North Bombay, 13
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(1964) 72--6.
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\bibitem{russell}
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A. N. Whitehead and B. Russell, Principia Mathematica, Cambridge
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University Press, 1925.
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\bibitem{beaman}
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J. Beaman, Morbidity of the Jolly function, Mathematica Absurdica, 117
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(1965) 338--9.
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\end{thebibliography}
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\end{minipage}}%
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\end{Poster}
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\end{document}
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%% END poster1.tex
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