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$ Life$%
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$ HighLife$%
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$ S_{min}=2$%
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$ 1000101$%
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$\displaystyle \varphi({\mathbf{x}_{0}},{\mathbf{x}_{1}},\ldots,{\mathbf{x}_{8}}) = \left\{ \begin{array}{ll}                                                                 1 & si \qquad \left\{ \begin{array}{lll}           {\mathbf{x}_{0}} = 0 & y & 3 \leq \overset{8}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 3 \\\\{\mathbf{x}_{0}} = 1 & y & 2 \leq \overset{8}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 3                                                                                              \end{array} \right. \\\\0 & \mbox{en otro caso}                                                                \end{array} \right.$%
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p_{t+2} & = & 84(84p_{t+1}^{3}(1-p_{t+1})^{6}+56p_{t+1}^{4}(1-p_{t+1})^{5})^{3}(1-(84p_{t+1}^{3}(1-p_{t+1})^{6}+56p_{t+1}^{4}(1-p_{t+1})^{5}))^{6}+ \\
   &     & 56(84p_{t+1}^{3}(1-p_{t+1})^{6}+56p_{t+1}^{4}(1-p_{t+1})^{5})^{4}(1-(84p_{t+1}^{3}(1-p_{t+1})^{6}+56p_{t+1}^{4}(1-p_{t+1})^{5}))^{5}
\end{array} 
\end{displaymath}%
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$ p_{1}$%
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$ p_{2}$%
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$\displaystyle p_{t+1}=28p_{t}^{3}q_{t}^{6}+56p_{t}^{3}q_{t}^{6}+56p_{t}^{4}q_{t}^{5}+28p_{t}^{6}q_{t}^{3}$%
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$ (x_{i},y_{i},0)$%
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$ z$%
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$ (x_{i},y_{i},1)$%
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$ R(5767)$%
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$ R(5777)$%
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$ R(5566)$%
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$ R(5755)$%
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$ R(4656)$%
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$ R(4655)$%
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{\newpage\clearpage
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$ R(6767)$%
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$ R(4567)$%
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{\newpage\clearpage
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$ R(6766)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13410}%
$ R(5655)$%
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{\newpage\clearpage
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$ R(5877)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13414}%
$ R(4666)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13416}%
$ R(4566)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13418}%
$ R(3455)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13420}%
$ R(3566)$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay13443}%
$\displaystyle \varphi({\mathbf{x}_{0}},{\mathbf{x}_{1}},\ldots,{\mathbf{x}_{26}}) = \left\{ \begin{array}{ll}                                                                 1 & si \qquad \left\{ \begin{array}{lll}           {\mathbf{x}_{0}} = 0 & y & 6 \leq \overset{26}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 6 \\\\{\mathbf{x}_{0}} = 1 & y & 5 \leq \overset{26}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 7                                                                                              \end{array} \right. \\\\0 & \mbox{en otro caso}                                                                \end{array} \right.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13465}%
$\displaystyle \varphi({\mathbf{x}_{0}},{\mathbf{x}_{1}},\ldots,{\mathbf{x}_{26}}) = \left\{ \begin{array}{ll}                                                                 1 & si \qquad \left\{ \begin{array}{lll}           {\mathbf{x}_{0}} = 0 & y & 5 \leq \overset{26}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 5 \\\\{\mathbf{x}_{0}} = 1 & y & 4 \leq \overset{26}{\underset{i=1}{\sum}} {\mathbf{x}_{i}} \leq 5                                                                                              \end{array} \right. \\\\0 & \mbox{en otro caso}                                                                \end{array} \right.$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13469}%
$ z^{-}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13471}%
$ z^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13475}%
$ y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13477}%
$ R(2+2,3+2,3+2,3+2)=R(4,5,5,5)$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13487}%
$ S_{min}=5$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13489}%
$ S_{max}=7$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13491}%
$ N_{min}=6$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13496}%
$\displaystyle p_{t+1}=65780p_{t}^{6}q_{t}^{21}+657800p_{t}^{8}q_{t}^{19}+230230p_{t}^{6}q_{t}^{21}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13499}%
$\displaystyle p_{t+1}=296010p_{t}^{6}q_{t}^{21}+657800p_{t}^{8}q_{t}^{19}.$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13505}%
$ v=6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13507}%
$ n-v=27-6=21$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13511}%
$ v=8$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13513}%
$ n-v=27-8=19$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13526}%
\includegraphics[width= 3.1in]{imagenes/capitulo3/curva_5766.eps}%
\lthtmlpictureZ
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13538}%
\includegraphics[width= 5.5in]{imagenes/capitulo3/curva_5766a.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13552}%
$ R(5,6,7,7)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13560}%
$ R(2+2,3+2,3+2,3+2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13572}%
$ S_{min}=4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13574}%
$ S_{max}=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13576}%
$ N_{min}=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13578}%
$ N_{max}=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13581}%
$\displaystyle p_{t+1}=14950p_{t}^{5}q_{t}^{22}+65780p_{t}^{6}q_{t}^{21}+65780p_{t}^{5}q_{t}^{22}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13584}%
$\displaystyle p_{t+1}=80730p_{t}^{5}q_{t}^{22}+65780p_{t}^{6}q_{t}^{21}.$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13585}%
\includegraphics[width= 3.1in]{imagenes/capitulo3/curva_4555.eps}%
\lthtmlpictureZ
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13607}%
\includegraphics[width= 6.3in]{imagenes/capitulo3/curva_4555a.eps}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13635}%
$ \varphi(0,0,0) \rightarrow 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13637}%
$ \varphi(1,0,0) \rightarrow 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13639}%
$ \varphi(0,0,1) \rightarrow 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13641}%
$ \varphi(1,0,1) \rightarrow 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13643}%
$ \varphi(0,1,0) \rightarrow 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13645}%
$ \varphi(1,1,0) \rightarrow 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13647}%
$ \varphi(0,1,1) \rightarrow 1$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13649}%
$ \varphi(1,1,1) \rightarrow 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13668}%
$ x_{i+1}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13676}%
$ x_{i-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13690}%
\includegraphics[width= 6.5in]{imagenes/capitulo4/evolucion_110.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13695}%
$ 0011$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13697}%
$ 0110$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13700}%
$\displaystyle M_{i,j} = \left\{\begin{array}{lllll} 			         1&si&j&=&  \left\{\begin{array}{lll} 		       		 		                ki \\ki+1 \\\vdots & (mod&k^{2r}) \\ki+k-1   					                         \end{array}  				                         \right.\  \\\\0& \mbox{en otro caso} \\\end{array}  			 \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13708}%
$\displaystyle M_{i,j} = \left [\begin{array}{cccc}
1 & 1 & 0 & 0 \\
0 & 0 & 1 & 1 \\
1 & 1 & 0 & 0 \\
0 & 0 & 1 & 1
\end{array} \right ].
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13710}%
$ i=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13712}%
$ j=ki=2*0=0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13714}%
$ j=(2*0)+1=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13716}%
$ M_{0,0}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13718}%
$ M_{0,1}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13720}%
$ i=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13722}%
$ j=ki=2*1=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13724}%
$ j=(2*1)+1=3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13726}%
$ M_{1,2}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13728}%
$ M_{1,3}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13730}%
$ i=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13732}%
$ j=ki=2*2=4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13734}%
$ j=(2*2)+1=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13736}%
$ M_{2,0}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13738}%
$ M_{2,1}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13740}%
$ i=3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13742}%
$ j=ki=2*3=6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13744}%
$ j=(2*3)+1=7$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13746}%
$ M_{3,2}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13748}%
$ M_{3,3}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13750}%
$ M_{i,j}=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13755}%
\includegraphics[width= 2.5in]{imagenes/capitulo4/deBruijn_generico.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13764}%
$ k^{2r}=2^{2}=4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13766}%
$ j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13768}%
$ k*i=2i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13770}%
$ (k*i)+k-1=(2*i)+2-1=2i-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline13811}%
$ \{0,1,2,3\}$%
\lthtmlinlinemathZ
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\end{document}
