
\documentclass{article}
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%TCIDATA{BibliographyScheme=Manual}
%TCIDATA{Created=Wednesday, May 31, 2017 18:45:40}
%TCIDATA{LastRevised=Wednesday, May 31, 2017 23:03:53}
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%TCIDATA{CSTFile=40 LaTeX article.cst}
%TCIDATA{ComputeDefs=
%1$a_{S}=2.390$
%1$a_{L}=6.008$
%$b=2.398$
%1$\rho _{f}=2780$
%1$r_{s}=2\ast a_{S}\ast b\ast \rho _{f}$
%$d=0.041$
%1$\nu _{f}=0.33$
%1$E_{f}=70\ast 10^{3}$
%1$t_{f}=0.001$
%1$G_{c}=20$
%1$r_{L}=2\ast a_{L}\ast b\ast \rho _{f}$
%$k=\frac{6080}{1533}$
%$l=\frac{17}{1533}$
%1$\nu _{s}=\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times
%10^{-2}\ast k\ast a_{S}\ast b^{3}}+\frac{l}{k\ast a_{S}\ast b\ast d}$
%1$d_{t}=0.041$
%1$c_{S}=\frac{2\left( 1-\nu _{f}^{2}\right) \ast b}{7.\,\allowbreak
%342\,4\times 10^{-2}\ast E_{f}\ast d^{2}\ast a_{S}\ast k}\ast
%4.\,\allowbreak 035\,2\times 10^{-3}$
%$t_{0}(D)=\frac{1}{\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak
%342\,4\times 10^{-2}\ast \frac{6080}{1533}\ast 2.390\ast 2.398^{3}}+\frac{%
%\frac{17}{1533}}{\frac{6080}{1533}\ast 2.390\ast 2.398\ast D}}\left( \sqrt[2]%
%{\frac{\left( 1-0.33^{2}\right) }{7.\,\allowbreak 342\,4\times 10^{-2}\ast
%70\ast 10^{3}\ast D^{2}\ast 2.390^{2}\ast 2780\ast \frac{6080}{1533}}\ast
%4.\,\allowbreak 035\,2\times 10^{-3}}+\frac{2\ast \left( 1-0.33^{2}\right)
%\ast 2.398}{7.\,\allowbreak 342\,4\times 10^{-2}\ast 70\ast 10^{3}\ast
%D^{2}\ast 2.390\ast \frac{6080}{1533}}\ast 4.\,\allowbreak 035\,2\times
%10^{-3}\right) $
%1$r_{S}=2\ast a_{S}\ast b\ast \rho _{f}$
%1$\nu _{S}=\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times
%10^{-2}\ast k\ast a_{S}\ast b^{3}}+\frac{l}{k\ast a_{S}\ast b\ast D}$
%$m\left( D\right) =2\ast 2.390\ast 2.398\ast 2780\ast t_{0}(D)+2.390\ast
%2.398\ast d\ast \rho \left( D\right) $
%$\rho \left( D\right) =\frac{1}{2.390\ast 2.398\ast D}\ast \left( \left( 
%\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times 10^{-2}\ast \frac{%
%6080}{1533}\ast 2.390\ast 2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}%
%\ast 2.390\ast 2.398\ast D}\right) -\frac{\frac{2\left( 1-0.33^{2}\right)
%\ast 2.398}{7.\,\allowbreak 342\,4\times 10^{-2}\ast 70\ast 10^{3}\ast
%D^{2}\ast 2.390\ast \frac{6080}{1533}}\ast 4.\,\allowbreak 035\,2\times
%10^{-3}}{t_{0}(D)}\right) ^{-1}$
%}


\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\input{tcilatex}
\begin{document}


$a_{S}=2.390$

$a_{L}=6.008$

$b=2.398$

$d_{t}=0.041$

$\rho _{f}=2780$

$\nu _{f}=0.33$

$E_{f}=70\ast 10^{3}$

$t_{f}=0.001$

$G_{c}=20$

\[
f\left( a_{S}/b\right) =\sum_{n=0}^{27}\sum_{m=0}^{27}\frac{16\left( \sin
\left( \frac{\left( 2m+1\right) \pi }{2}\right) \sin \left( \frac{\left(
2n+1\right) \pi }{2}\right) \right) }{\pi ^{6}\left( 2m+1\right) \left(
2n+1\right) \left( \left( \frac{2m+1}{\frac{a_{S}}{b}}\right) ^{2}+\left(
2n+1\right) ^{2}\right) ^{2}}=4.\,\allowbreak 035\,2\times 10^{-3} 
\]

\[
f\left( a_{L}/b\right) =\sum_{n=0}^{27}\sum_{m=0}^{27}\frac{16\left( \sin
\left( \frac{\left( 2m+1\right) \pi }{2}\right) \sin \left( \frac{\left(
2n+1\right) \pi }{2}\right) \right) }{\pi ^{6}\left( 2m+1\right) \left(
2n+1\right) \left( \left( \frac{2m+1}{\frac{a_{L}}{b}}\right) ^{2}+\left(
2n+1\right) ^{2}\right) ^{2}}=1.\,\allowbreak 150\,7\times 10^{-2} 
\]

\[
g\left( a_{S}/b\right) =\sum_{n=0}^{27}\sum_{m=0}^{27}\frac{16\left( \sin
\left( \frac{\left( 2m+1\right) \pi }{2}\right) \sin \left( \frac{\left(
2n+1\right) \pi }{2}\right) \right) }{\pi ^{4}\left( 2m+1\right) \left(
2n+1\right) \left( \left( \frac{2m+1}{\frac{a_{S}}{b}}\right) ^{2}+\left(
2n+1\right) ^{2}\right) }=7.\,\allowbreak 342\,4\times 10^{-2} 
\]

\[
g\left( a_{L}/b\right) =\sum_{n=0}^{27}\sum_{m=0}^{27}\frac{16\left( \sin
\left( \frac{\left( 2m+1\right) \pi }{2}\right) \sin \left( \frac{\left(
2n+1\right) \pi }{2}\right) \right) }{\pi ^{4}\left( 2m+1\right) \left(
2n+1\right) \left( \left( \frac{2m+1}{\frac{a_{L}}{b}}\right) ^{2}+\left(
2n+1\right) ^{2}\right) }=0.119\,96 
\]

\[
w_{s}/q=\frac{2\left( 1-\nu _{f}^{2}\right) b^{4}}{E_{f}\ast t_{f}\ast
d_{t}^{2}}\ast 4.\,\allowbreak 035\,2\times 10^{-3}+\frac{b^{2}}{G_{c}\ast
d_{t}}\ast 7.\,\allowbreak 342\,4\times 10^{-2}=2.\,\allowbreak 535\,8 
\]
\[
w_{L}/q=\frac{2\left( 1-\nu _{f}^{2}\right) b^{4}}{E_{f}\ast t_{f}\ast
d_{t}^{2}}\ast 1.\,\allowbreak 150\,7\times 10^{-2}+\frac{b^{2}}{G_{c}\ast
d_{t}}\ast 0.119\,96=6.\,\allowbreak 604\,3 
\]

$r_{S}=2\ast a_{S}\ast b\ast \rho _{f}$

$r_{L}=2\ast a_{L}\ast b\ast \rho _{f}$

$k=\frac{6080}{1533}$

$l=\frac{17}{1533}$

$\nu _{S}=\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times
10^{-2}\ast k\ast a_{S}\ast b^{3}}+\frac{l}{k\ast a_{S}\ast b\ast D}$

$\nu _{L}=\frac{6.\,\allowbreak 604\,3}{0.119\,96\ast k\ast a_{S}\ast b^{3}}+%
\frac{l}{k\ast a_{S}\ast b\ast D}$

$c_{S}=\frac{2\left( 1-\nu _{f}^{2}\right) \ast b}{7.\,\allowbreak
342\,4\times 10^{-2}\ast E_{f}\ast D^{2}\ast a_{S}\ast k}\ast
4.\,\allowbreak 035\,2\times 10^{-3}$%
\[
t_{0}(D)=\frac{1}{\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times
10^{-2}\ast \frac{6080}{1533}\ast 2.390\ast 2.398^{3}}+\frac{\frac{17}{1533}%
}{\frac{6080}{1533}\ast 2.390\ast 2.398\ast D}}\left( \sqrt[2]{\frac{\left(
1-0.33^{2}\right) }{7.\,\allowbreak 342\,4\times 10^{-2}\ast 70\ast
10^{3}\ast D^{2}\ast 2.390^{2}\ast 2780\ast \frac{6080}{1533}}\ast
4.\,\allowbreak 035\,2\times 10^{-3}}+\frac{2\ast \left( 1-0.33^{2}\right)
\ast 2.398}{7.\,\allowbreak 342\,4\times 10^{-2}\ast 70\ast 10^{3}\ast
D^{2}\ast 2.390\ast \frac{6080}{1533}}\ast 4.\,\allowbreak 035\,2\times
10^{-3}\right) 
\]

\[
t_{0}(H)=\frac{1}{\frac{6.\,\allowbreak 604\,3}{0.119\,96\ast \frac{6080}{%
1533}\ast 6.008\ast 2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}\ast
6.008\ast 2.398\ast H}}\left( \sqrt[2]{\frac{\left( 1-0.33^{2}\right) }{%
0.119\,96\ast 70\ast 10^{3}\ast H^{2}\ast 6.008^{2}\ast 2780\ast \frac{6080}{%
1533}}\ast 1.\,\allowbreak 150\,7\times 10^{-2}}+\frac{2\ast \left(
1-0.33^{2}\right) \ast 2.398}{0.119\,96\ast 70\ast 10^{3}\ast H^{2}\ast
6.008\ast \frac{6080}{1533}}\ast 1.\,\allowbreak 150\,7\times 10^{-2}\right) 
\]

\[
t_{0}(D) 
\]%
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\frac{6080}{1533}\ast 6.008\ast
2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}\ast 6.008\ast 2.398\ast
H}}\left( \root{2}\of{\frac{\left( 1-0.33^{2}\right) }{0.119\,96\ast 70\ast
10^{3}\ast H^{2}\ast 6.008^{2}\ast 2780\ast \frac{6080}{1533}}\ast
1.\,\allowbreak 150\,7\times 10^{-2}}+\frac{2\ast \left( 1-0.33^{2}\right)
\ast 2.398}{0.119\,96\ast 70\ast 10^{3}\ast H^{2}\ast 6.008\ast
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$\rho \left( D\right) =\frac{1}{2.390\ast 2.398\ast D}\ast \left( \left( 
\frac{2.\,\allowbreak 535\,8}{7.\,\allowbreak 342\,4\times 10^{-2}\ast \frac{%
6080}{1533}\ast 2.390\ast 2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}%
\ast 2.390\ast 2.398\ast D}\right) -\frac{\frac{2\left( 1-0.33^{2}\right)
\ast 2.398}{7.\,\allowbreak 342\,4\times 10^{-2}\ast 70\ast 10^{3}\ast
D^{2}\ast 2.390\ast \frac{6080}{1533}}\ast 4.\,\allowbreak 035\,2\times
10^{-3}}{t_{0}(D)}\right) ^{-1}$

\[
\rho \left( D\right) 
\]%
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\frac{6.\,\allowbreak 604\,3}{0.119\,96\ast \frac{6080}{1533}\ast 6.008\ast
2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}\ast 6.008\ast 2.398\ast
H}\right) -\frac{\frac{2\left( 1-0.33^{2}\right) \ast 2.398}{0.119\,96\ast
70\ast 10^{3}\ast H^{2}\ast 6.008\ast \frac{6080}{1533}}\ast 1.\,\allowbreak
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'OQU5380A.wmf';tempfile-properties "XPR";}}

\[
\rho \left( H\right) =\frac{1}{6.008\ast 2.398\ast H}\ast \left( \left( 
\frac{6.\,\allowbreak 604\,3}{0.119\,96\ast \frac{6080}{1533}\ast 6.008\ast
2.398^{3}}+\frac{\frac{17}{1533}}{\frac{6080}{1533}\ast 6.008\ast 2.398\ast H%
}\right) -\frac{\frac{2\left( 1-0.33^{2}\right) \ast 2.398}{0.119\,96\ast
70\ast 10^{3}\ast H^{2}\ast 6.008\ast \frac{6080}{1533}}\ast 1.\,\allowbreak
150\,7\times 10^{-2}}{t_{0}(H)}\right) ^{-1} 
\]

\[
\rho \left( H\right) 
\]

\[
m\left( D\right) =2\ast 2.390\ast 2.398\ast 2780\ast t_{0}(D)+2.390\ast
2.398\ast d\ast \rho \left( D\right) 
\]

\[
m\left( D\right) 
\]%
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\[
Q\left( H\right) =2\ast 6.008\ast 2.398\ast 2780\ast t_{0}(H)+6.008\ast
2.398\ast H\ast \rho \left( H\right) 
\]

\end{document}
