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\noindent
Das Fib-Multimediaformat dient zum Speichern von Multimediainformationen in strukturierter, funktionaler und hierarchischer Form. Die Struktur des Fib-Multi\-media\-for\-mats unterst"utzt die Objektsicht auf Dinge. Das Fib-Multimediaformat ist sehr m"achtig, da Ausdr"ucke kombiniert und verschachtelt werden k"onnen (Baukastensystem).
\textbf{Mit Fib ist die Frage nicht mehr, ob Sie etwas machen k"onnen, sondern nur noch wie Sie etwas machen k"onnen.}
Der Speicheraufwand eines Multimediobjekts in Fib ist vielmehr von dessen Komplexit"at abh"angig als von dessen Gr"o"se (im Sinne von Ausdehnung in den Dimensionen, also beispielsweise die H"ohe und Breite bei Bildern), wie bei "ublichen Speicherformaten.
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Die einzige Einschr"ankung bez"uglich der Multimediadaten, die im Fib-Multi\-media\-format darstellbar sind, ist, dass sie als Eigenschaften von Punkten eines endlichen, euklidischen und diskreten (es gibt kleinste Einheiten) Raumes darstellbar sind. Daher k"onnen nicht nur Bilder und T"one mit Fib abgespeichert werden, sondern beispielsweise auch Ger"uche oder wie weich etwas ist.
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Die zweite wichtige Komponente des Fib-Systems ist der genetische Algorithmus zum Kodieren in und Komprimieren von Fib-Multi\-media\-objekten. Der gro"se Vorteil dessen ist, dass die Kodierung und Komprimierung nicht mehr an einem bestimmten Algorithmus gebunden ist, sondern dass die eigentlichen Kodierungs- und Komprimierungsalgorithmen im genetischen Algorithmus als Operationen eingebunden werden, welche leicht hinzugef"ugt und ge"andert werden k"onnen. Dadurch ist es leicht, neue Kodierungs- und Komprimierungsideen einzubringen und eine Vielzahl von diesen auf ein Multimediaobjekt anzuwenden.
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In diesem Sinne ist der genetische Algorithmus f"ur Fib ein transgenialer Algorithmus, der darauf angelegt ist, die Ideen von Menschen zur Kodierung von Multimediadaten aus deren K"opfe herauszuholen und in einem Topf zu transportieren bzw. zu sammeln. Damit sollen diese Ideen / Algorithmen mehr leisten k"onnen, als sie es einzeln k"onnten.
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$0{,}5$%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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$x=y/3$%
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{\newpage\clearpage
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{\newpage\clearpage
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$x=4*(y/z)$%
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{\newpage\clearpage
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$fun(x, div( 4, 0 ), Obj)$%
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{\newpage\clearpage
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$x=4/0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1924}%
$fun(x, div( 335, 113 ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1926}%
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\lthtmlcheckvsize\clearpage}

\stepcounter{paragraph}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1928}%
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{\newpage\clearpage
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$int$%
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{\newpage\clearpage
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$UF=mod( UF_1, UF_2 )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1934}%
$fun(x, mod( -12.3, 3 ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1936}%
$-0.3$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1938}%
$fun(x, mod( 6.5, 0.5 ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1942}%
$fun(x, mod( -4.687, -3 ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1944}%
$-1.687$%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1948}%
$fun(x, exp( 2, 3), Obj)$%
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{\newpage\clearpage
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$x=2^3$%
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{\newpage\clearpage
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$fun(x, exp( y, 3), Obj)$%
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{\newpage\clearpage
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$x=y^3$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1956}%
$fun(x, exp( 4, div(y,z) ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1958}%
$x=4^{y/z}$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{paragraph}
{\newpage\clearpage
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$UF=min( UF_1, UF_2 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1962}%
$fun(x, min( 0, 12 ), Obj)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1966}%
$fun(x, min( add( -2, 7 ), 4 ), Obj)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1968}%
$add( -2, 7 )= -2+7 = 5$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1970}%
$4$%
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\stepcounter{paragraph}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1972}%
$UF=max( UF_1, UF_2 )$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1974}%
$fun(x, max( 0, 12 ), Obj)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1976}%
$12$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1978}%
$fun(x, max( add( -2, 7 ), 4 ), Obj)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{paragraph}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1984}%
$e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1986}%
$UF=ln(UF_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1988}%
$fun(x, ln(2), Obj)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1990}%
$x=\ln{(2)} \simeq 0{,}6931$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1992}%
$fun(x, ln(-2), Obj)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1996}%
$x=\ln{(-2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{paragraph}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1998}%
$UF=sin(UF_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2000}%
$\pi/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2002}%
$cos{(x)}=sin{(x+\pi/2)}$%
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$\tan{(x)}=sin{(x)}/sin{(x+\pi/2)}$%
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$fun(x, sin(0), Obj)$%
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{\newpage\clearpage
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$x=\sin{0}=0$%
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{\newpage\clearpage
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$fun(x, sin(1.57), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2012}%
$x=\sin{1.57}=\sin{3.14/2} \simeq 1$%
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\lthtmlinlinemathA{tex2html_wrap_inline2014}%
$fun(x, sin(y), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2016}%
$x=\sin{y}$%
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{\newpage\clearpage
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$fun(x, sin( add(y, 1.57) ), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2020}%
$x=\sin{(y + 1.57 )} \simeq \cos{y}$%
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\lthtmlinlinemathA{tex2html_wrap_inline2022}%
$UF=arcsin( UF_1 )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2024}%
$fun(x, arcsin(0), Obj)$%
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{\newpage\clearpage
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$-1$%
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\lthtmlinlinemathA{tex2html_wrap_inline2030}%
$UF=abs( UF_1 )$%
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{\newpage\clearpage
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$fun(x, abs(-124), Obj)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2034}%
$x=|-124|=124$%
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$UF=round( UF_1 )$%
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{\newpage\clearpage
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$fun(x, round(-12.3), Obj)$%
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$fun(x, round(6.5), Obj)$%
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{\newpage\clearpage
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$fun(x, round(-4.687), Obj)$%
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$UF=delay( X, UF_1, UF_2 )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2066}%
$a$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2068}%
$W_a$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2076}%
$W_{n-UF_1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2078}%
$n-UF_1$%
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{\newpage\clearpage
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$delay(x, 1, 3)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2096}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2108}%
$if( lo(x, 7), 1, sin(x) )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2114}%
$7$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2116}%
$sin(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2118}%
$Obj=if( Condition, Obj_1, Obj_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2124}%
$Obj_2$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2126}%
$Conditions$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2128}%
$UF_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2130}%
$true$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2132}%
$false$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2134}%
$not(Condition_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2136}%
$Condition_1$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2138}%
$or( Condition_1, Condition_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2142}%
$Condition_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2144}%
$and( Condition_1, Condition_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2150}%
$xor( Condition_1, Condition_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2156}%
$eqInt(UF_1,UF_2)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2162}%
$lo(UF_1,UF_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2168}%
$UF_1<UF_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2170}%
$gr(UF_1,UF_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2176}%
$UF_1>UF_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2180}%
$Obj=if( lo(x, 7), Obj_1, Obj_2)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2190}%
$Obj=if( and( gr( add(x, 2), 3), lo(x, 7) ), Obj_1, Obj_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2212}%
$root$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar1053}%
\begin{eqnarray*}
Obj &=& obj( Identifier , ( V_1 , \ldots , V_n ) , ( OutVar_{1}, \ldots  \\
  && ,OutVar_{v_1}, Obj_1), \ldots , ( OutVar_{1}, \ldots ,OutVar_{v_m}, Obj_m) )
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2214}%
$Identifier$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2220}%
$root_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2234}%
$( V_1 , \ldots , V_n )$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2236}%
$V_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2240}%
$Obj_o$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2244}%
$OutVar_{g_o}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2252}%
$obj( -3 , (x, y) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2256}%
$-3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2260}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2262}%
$obj( 5 , ( x_1, y_1, 3 ) , ( x_2, y_2, r, pr( (r, 0, 0)_{colorRGB}, p((x_2;y_2)) ) ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2268}%
$pr( (r, 0, 0)_{colorRGB}, p((x_2;y_2))$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2270}%
$r$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2272}%
$x_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2274}%
$y_2$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2278}%
$Obj = sub( Number , ( V_1 , \ldots , V_n ) )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2280}%
$Number$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2290}%
$OutVar_{i_Number}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2298}%
$sub( 1 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2300}%
$sub( 1, ( x, y, 7 ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2308}%
$(x, y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2312}%
$Obj = domainProperty( Variable , Type[.Element]*, Mode, Obj_1 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2314}%
$Obj = dp( Variable , Type[.Element]*, Mode, Obj_1 )$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2320}%
$Type$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2322}%
$Element$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2332}%
$Mode$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2338}%
$Maximum-Minimum$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2342}%
$(unskaliertes\ Maximum)-(unskaliertes\ Minimum)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2344}%
$dp( x , dim.1, min, Obj_1 )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2348}%
$dp( x , property( colorRGB).2, max, Obj_1 )$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2352}%
$dp( x , property( colorGrayscale).1, size, Obj_1 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2358}%
$dp( x , matrix.3.2, null, Obj_1 )$%
\lthtmlinlinemathZ
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2362}%
$Obj = set( (Variable_1, \ldots, Variable_n), [DomainNr,]( (W_{1.1}, \ldots, W_{n.1}),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2364}%
$ \ldots, (W_{1.k}, \ldots, W_{n.k}) ), Obj_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2370}%
$k$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2372}%
$k \geq 1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2374}%
$Variable_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2376}%
$DomainNr$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2378}%
$W_{i.g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2382}%
$(g = 1 \ldots k)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2384}%
$(W_{1.g}, \ldots, W_{n.g})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2390}%
$(Variable_1, \ldots, Variable_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2398}%
$g=1, \ldots k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2404}%
$W_{i.1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2406}%
$W_{i.2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2414}%
$set( (x, y),( (1, 2), (3, 8), (3, -8) ), Obj)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2422}%
$(x=1, y=2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2424}%
$(x=3, y=8)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2426}%
$(x=3, y=-8)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2428}%
$set( (x, y, z), 3,( (1, 2, 3), (3, 8, 15), (3,-8,-1) ), Obj)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2434}%
$z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2438}%
$(x=1, y=2, z=3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2440}%
$(x=3, y=8, z=15)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2442}%
$(x=3, y=-8, z=-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{eqnarraystar1142}%
\begin{eqnarray*}
Obj &=& matrix( (Variable_1, \ldots, Variable_d, Variable_{d+1}, \ldots, Variable_{d+i}),\\
&& [DomainNr,] ( (Startvalue_1, Endvalue_1), \ldots, (Startvalue_d, Endvalue_d) ),\\
&& ( (W_{1.1}, \ldots, W_{i.1}), \ldots, (W_{1.k}, \ldots, W_{i.k}) ), Obj_1)
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2444}%
$d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2446}%
$d \geq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2450}%
$i \geq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2454}%
$k \geq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2456}%
$Variable_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2460}%
$(Startvalue_h, Endvalue_h)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2462}%
$h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2464}%
$Startvalue_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2468}%
$Endvalue_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2472}%
$W_{a.b}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2474}%
$(a = 1 \ldots i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2476}%
$(b = 1 \ldots k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2478}%
$(W_{1.b}, \ldots, W_{n.b})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2488}%
$(Variable_1, \ldots, Variable_d)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2494}%
$Variable_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2496}%
$Variable_{h-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2500}%
$(Variable_{d+1}, \ldots, Variable_{d+i})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2502}%
$(W_{1.b}, \ldots, W_{i.b})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2506}%
$(W_{1.k+1}, \ldots, W_{i.k+1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2510}%
$Variable_{d+a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2514}%
$i=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{lstlisting1166}%
\begin{lstlisting}[language=C, numbers=left, frame=single, caption={Pseudoalgorithmus des Matrixelements}, label={lstMatrixCode}, breaklines, basicstyle=\footnotesize\ttfamily , numberstyle=\tiny ]
void evalue( matrix ){
   a = 1;
   for ( int Variable_d = Startvalue_d; Variable_d <= Endvalue_d; Variable_d += 1 ){
      ...
         for ( int Variable_1 = Startvalue_1; Variable_1 <= Endvalue_1; Variable_1 += 1 ){
            Variable_{d+1} = W_{1.a};
            ...
            Variable_{d+i} = W_{i.a};
\par
obj_1( Variable_1, ..., Variable_{d+i} );
\par
a++;
            if ( (k < a) && (0 < i) ){
               return;
            }
         }
      ...
   }
}
\end{lstlisting}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2518}%
$matrix( (x, y, w), (1, 1), ( 3, 3), ( (11), (12), (13),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2520}%
$ (21), (22), (23), (31),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2522}%
$(32),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2524}%
$(33) ), Obj_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2530}%
$w$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2532}%
$( x=1, y=1, w=11)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2534}%
$( x=2, y=1, w=12)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2536}%
$( x=3, y=1, w=13)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2538}%
$( x=1, y=2, w=21)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2540}%
$( x=2, y=2, w=22)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2542}%
$( x=3, y=2, w=23)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2544}%
$( x=1, y=3, w=31)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2546}%
$( x=2, y=3, w=23)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2548}%
$( x=3, y=3, w=33)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2550}%
$matrix( (x, w), (1), (5), ( (1), (2), (3) ), Obj_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2556}%
$( x=1, w=1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2558}%
$( x=2, w=2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2560}%
$( x=3, w=3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2564}%
$matrix( (x, w), (1), (2), ( (1), (2), (3), (4) ), Obj_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2576}%
$matrix( (x, y), (2, 3), (4, 4), ( ), Obj_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2582}%
$( x=2, y=3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2584}%
$( x=3, y=3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2586}%
$( x=4, y=3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2588}%
$( x=2, y=4)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2590}%
$( x=3, y=4)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2592}%
$( x=4, y=4)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{eqnarraystar1182}%
\begin{eqnarray*}
Rootobj &=& root( [Multimediainformation], [Domains], \\
&& [DomainsValues], [((InVar_1, S_1), \ldots , (InVar_v, S_v) )],  Obj ,\\
&& [((Identifier_1, Rootobj_1) , \ldots , (Identifier_n, Rootobj_n))],\\
&& [( DB\_Identifier_1, \ldots , DB\_Identifier_d)], [Optionalpart] )
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2598}%
$(Identifier_i, Rootobj_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2600}%
$Identifier_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2602}%
$obj$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2604}%
$Rootobj_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2614}%
$Multimediainformation$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2618}%
$Domains$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2620}%
$DomainsValues$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2622}%
$InVar_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2632}%
$integerB(16)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2636}%
$S_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2652}%
$DB\_Identifier_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2656}%
$Optionalpart$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2660}%
$Multimediainformation = ( Fib\_Version, Db\_Version )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2662}%
$Fib\_Version$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2664}%
$Db\_Version$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2668}%
$Domains=( (Name_1, Dom_1), \ldots , (Name_k, Dom_k) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2670}%
$DomainsValues=( (Name_1, Dom_1), \ldots , (Name_k, Dom_k) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2676}%
$Name_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2678}%
$Dom_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2682}%
$dim$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2684}%
$IntegerB$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2708}%
$Scale_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2716}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2718}%
$mm$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2720}%
$*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2724}%
$integerB(16) * 2^{-16}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2726}%
$2^{-16}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2736}%
$F=1/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2738}%
$\{$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2740}%
$0*1/2=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2742}%
$1*1/2=0{,}5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2744}%
$2*1/2=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2746}%
$3*1/2=1{,}5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2748}%
$\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2756}%
$Dimmap_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2758}%
$\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2760}%
$Dimmap_{Dim}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2764}%
$Dimmap_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2780}%
$vector( 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2784}%
$integerB(16) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2790}%
$B_{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2794}%
$naturalNumberB(8),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2796}%
$vector( 2,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2798}%
$integerB(16),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2800}%
$integerB(16) ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2806}%
$vector( 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2810}%
$naturalNumberB(32),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2812}%
$vectorOpenEnd($%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2814}%
$integerB(32) ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2826}%
$vector( 4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2832}%
$vector( 2, integerB(8),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2834}%
$integerB(8) ),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2856}%
$vector( 0 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2858}%
$Name$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2868}%
$,integerB(8),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2870}%
$integerB(8),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2872}%
$integerB(8) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2874}%
$vector( 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2880}%
$integerB(4) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2894}%
$vector( 1 )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2906}%
$integerB(32)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2910}%
$integerB(32) * 2^{-8}  )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2930}%
$vector( 3 + Dim$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2938}%
$integerB(32) * 2^{-8},$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2940}%
$[integerB(16) * 2^{-16}]^{Dim-1}  )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2948}%
$integerB(32)*2^{-16}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2950}%
$integerB(0) * 1/44100$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2952}%
$integerB(8) * 2^{-16}  )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2962}%
$integerB(16) * 2^{-16} )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2970}%
$integerB(16) * 2^{-4} )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2992}%
$integerB(64)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2994}%
$integerB(64) * 2^{-16}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3006}%
$integerB(24) * 2^{-8} )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3016}%
$integerB(24) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3020}%
$integerB(4)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3022}%
$integerB(8)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3030}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3032}%
$0 \ldots S*(2^X-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3038}%
$S*-(2^{X-1}) \ldots S*(2^{X-1}-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3042}%
$0 \ldots 4294967295$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3044}%
$-2147483648 \ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3046}%
$ 2147483647$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3054}%
$0 \ldots S*X$%
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\\
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\begin{lstlisting}[language=C, numbers=left, frame=single, caption={Algorithmus zur Erzeugung eines korrekten Fib-Objekts aus einer Bildmatrix}, label={alleBild}, breaklines, basicstyle=\footnotesize\ttfamily , numberstyle=\tiny ]
void translate( matrix ){
\par
int xmax = Anzahl der Spalten der Matrix;
   int ymax = Anzahl der Zeilen der Matrix;
   Fib_Objekt_Pointer obj=new root();
\par
//Eigenschaften der Rastergrafik setzen
   obj->setBild( xmax, ymax, Farbschema);
\par
list hauptliste=new list()
\par
obj->insertMainObject( hauptliste )
\par
for( int x = 0; x == xmax; x = x + 1 ){
\par
for( int y = 0; y == xmax; y = y + 1 ){
         hauptliste->insertObject( property( getColorVector( matrix[x,y] ) , p( (x,y) ) ) );
      };
   };
};
\end{lstlisting}%
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$Fib\_max_{min}$%
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{\newpage\clearpage
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$* [$%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4475}%
$256 (Pixel) * 3 Bytes = 768 Bytes$%
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{\newpage\clearpage
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$W_{min}$%
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{\newpage\clearpage
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$(0, 0 ,0 )_{colorRGB}$%
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\graphicspath{{/home/biokom/projekte/fib_git/docu/docu_V1_ger\/beispiele/}}


\graphicspath{{/home/biokom/projekte/fib_git/docu/docu_V1_ger\/beispiele/}{../beispiele}}

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{\newpage\clearpage
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$(255;255;255)_{colorRGB}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4695}%
$7857$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4697}%
$7294$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4699}%
$9500$%
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{\newpage\clearpage
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$25$%
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$<_{Fib}$%
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$[B_1, \ldots ,B_{j-1}, B_j, \ldots , B_k, B_{k+1}, \ldots ,B_n]$%
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{\newpage\clearpage
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$[(a;b)]$%
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$Obj_{1}$%
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{\newpage\clearpage
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$Obj_1'$%
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$Obj_1''$%
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$(a; b)$%
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$[a,b]$%
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{\newpage\clearpage
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$b$%
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{\newpage\clearpage
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$Obj\_e_1$%
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{\newpage\clearpage
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$Obj\_e_2$%
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{\newpage\clearpage
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$Obj'$%
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{\newpage\clearpage
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$Obj <_{Fib} Obj'$%
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{\newpage\clearpage
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{\newpage\clearpage
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$* 8$%
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{\newpage\clearpage
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$ = 80.000$%
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\graphicspath{{/home/biokom/projekte/fib_git/docu/docu_V1_ger\/material_enviroment/}}


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{\newpage\clearpage
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$=16+64+64$%
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\par
int xmax = Anzahl der Spalten der Matrix;
   int ymax = Anzahl der Zeilen der Matrix;
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\par
//Eigenschaften der Rastergrafik setzen
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};
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25020}%
$1.51$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25024}%
$2.49$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25032}%
$n'-1 < x' < n'+1$%
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{\newpage\clearpage
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$U_i$%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25270}%
$s \leq n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\begin{eqnarray*}
U_1: y_1 &\leq&  a_1 * x_{1.1} + a_2 * x_{1.2} + \ldots + a_d * x_{1.d}\\
U_2: y_2 &\leq&  a_1 * x_{2.1} + a_2 * x_{2.2} + \ldots + a_d * x_{2.d}\\
\vdots & & \\
U_n: y_n &\leq&  a_1 * x_{n.1} + a_2 * x_{n.2} + \ldots + a_d * x_{n.d}\\
\end{eqnarray*}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25272}%
$y_i$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25274}%
$x_{i.k}$%
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\lthtmlcheckvsize\clearpage}

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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25288}%
$y_{i.k}$%
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\lthtmlcheckvsize\clearpage}

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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25294}%
$-y_u \leq -a_0 - a_1 * x^{1} - a_2 * x^{2} - \ldots - a_d * x^{d}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25298}%
$2p$%
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\lthtmlcheckvsize\clearpage}

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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25304}%
$k < l$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25306}%
$k+1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25308}%
$g-1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25322}%
$v_{max}$%
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\lthtmlcheckvsize\clearpage}

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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25330}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25332}%
$dim+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25336}%
$E_k$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25338}%
$LS_g$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25342}%
$g$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25344}%
$H$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25370}%
$U_i=U[i]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25376}%
$y_i \leq  a_1 * x_{i.1} + a_2 * x_{i.2} + \ldots + a_d * x_{i.d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25378}%
$ \vec{x_i} \cdot \vec{a} - y_i = 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25380}%
$\vec{x_i} = (x_{i.1}, \ldots, x_{i.d})^T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25382}%
$\vec{a} = (a_{1}, \ldots, a_{d})^T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25412}%
$H_e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25414}%
$n-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25418}%
$n-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25454}%
$LS_{n-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25462}%
$d_s={n-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25464}%
$d_s={1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25466}%
$d_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25470}%
$LS_{d_s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25474}%
$HS$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25478}%
$HU$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25486}%
$SU$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25488}%
$d_s-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25528}%
$LS_{d_s-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25562}%
$LS_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25566}%
$G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25578}%
$PM$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25582}%
$P_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25584}%
$P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25600}%
$N_e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25610}%
$P_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25626}%
$E \neq P_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25632}%
$d_h = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25634}%
$d_h = (n-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25636}%
$d_h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25638}%
$d_h-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25640}%
$i < n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25654}%
$M = 1 / \sharp E * \sum_{i=1}^{\sharp E} E_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25660}%
$d-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25662}%
$3 \leq d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25726}%
$L_z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25730}%
$E_o$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25734}%
$E_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25736}%
$E_{ho}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25742}%
$E_{hn}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25748}%
$E_{h1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25752}%
$\{E_{h1}\} = \{E_{h2}\} = \{E_{ho}\} \cup \{E_{hn}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25754}%
$E_{h2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25758}%
$d-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25760}%
$H_a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25762}%
$H \neq H_a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25778}%
$H_l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25824}%
$y(x)_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25826}%
$y(x)_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25836}%
$for( x, (x_1,x_2),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25838}%
$fun( y_1, ...,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25840}%
$fun( y_2, ...,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25842}%
$for( y, (y_1, y_2),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25844}%
$p(x,y) ) ) ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25848}%
$(y_1, y_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25850}%
$y_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25864}%
$f(x)=y$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25872}%
$(y-0.5, y+0.5)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25874}%
$for($%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25876}%
$x, [1, 20],$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25878}%
$fun( y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25880}%
$,mult(x,0.5),$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25882}%
$pr($%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25884}%
$(y)_{colorGrayscale},$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25886}%
$p(x,1) ) ) )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25888}%
$P_1( x_1, (yu_1,yo_1 )), \ldots,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25890}%
$P_p( x_p, y_p \in (yu_p,yo_p ))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25894}%
$n < p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25896}%
$f(x) = \sum_{i=0}^{n} (a_i( x )^i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25900}%
$i=0, \ldots, n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25902}%
$a_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25904}%
$-inf$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25906}%
$+inf$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar25188}%
\begin{eqnarray*}
yu_1 &<=  a_0 + a_1( x_1 ) + \ldots + a_n( x_1 )^n &<= yo_1\\
yu_2 &<=  a_0 + a_1( x_2 ) + \ldots + a_n( x_2 )^n &<= yo_2\\
\ldots & & \\
yu_p &<=  a_0 + a_1( x_p ) + \ldots + a_n( x_p )^n &<= yo_p\\
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25908}%
$<?>$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25912}%
$a_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25918}%
$as_{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar25193}%
\begin{eqnarray*}
&&yu_1 <= a_0 + a_1( x_1 ) + \ldots + a_n( x_1 )^n <= yo_1\\
&&(yu_2 - yu_1)/x_2 <?> a_1 + \ldots + 2* a_n( x_2 )^{n-1} <?> (yo_2-yo_1)/x_2\\
&&yu_3 /x_3 - yu_2/x_2 + yu_1*(1/x_2-1/x_3) <?> a_2 + \ldots + 3 * a_n( x_3 )^{n-2} \\
&&  <?> yo_3/x_3 - yo_2/x_2 + yo_1*(1/x_2-1/x_3) \ldots \\
&&  yu_n / x_n^n + g_n( yu_1,\ldots, yu_{n-1}, x_1, \ldots, x_{n-1}) <?>  k*(k-1)/2 * a_k + as_{k}\\
&&  <?> yo_n / x_n^n - g_n( yo_1, \ldots yo_{n-1}, x_1, \ldots, x_{n-1}) \\
&&yu_{n+1} / x_{n+1}^n + g_{n+1}( yu_1, \ldots, yu_{n}, x_1,\ldots, x_n, x_{n+1})\\
&&  <?> k*(k-1)/2 * a_{k} + as_{k+1} \\
&&  <?> yo_{n+1} / x_{n+1}^n + g_{n+1}( yo_1, \ldots, yo_{n}, x_1, \ldots, x_n, x_{n+1})\\
&&\ldots\\
&&yu_p / x_p^n + g_p( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p) \\
&&  <?> k*(k-1)/2 *  a_k  + as_{p} \\
&&  <?> yo_p / x_p^n + g_p( yo_1, \ldots, yo_{n}, x_1, \ldots, x_n, x_p)\\
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25926}%
$b_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar25217}%
\begin{eqnarray*}
&& g_0( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p) <?>  b_0 * a_0 + as_{0} <?> g_0( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p)\\
&& g_1( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p) <?>  b_1 * a_1 + as_{1} <?> g_1( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p)\\
&& g_2( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p) <?>  b_2 * a_2 + as_{2} <?> g_2( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p)\\
&& \ldots\\
&& yu_n / x_n^n + g_n( yu_1, \ldots, yu_{n-1}, x_1, \ldots, x_{n-1}) \\
&&   <?>  k*(k-1)/2 * a_k + as_{k} <?> yo_n / x_n^n - g_n( yo_1, \ldots, yo_{n-1}, x_1, \ldots, x_{n-1})\\
&& yu_{n+1} / x_{n+1}^n + g_{n+1}( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_{n+1})\\
&&   <?> k*(k-1)/2 * a_{k} + as_{k+1} <?> yo_{n+1} / x_{n+1}^n +\\
&&   + g_{n+1}( yo_1, \ldots, yo_{n}, x_1, \ldots, x_n, x_{n+1})\\
&& \ldots\\
&& yu_p / x_p^n + g_p( yu_1, \ldots, yu_{n}, x_1, \ldots, x_n, x_p)\\
&&   <?> k*(k-1)/2 *  a_k  + as_{p} <?> yo_p / x_p^n + g_p( yo_1, \ldots, yo_{n}, x_1, \ldots, x_n, x_p)\\
\end{eqnarray*}%
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