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-rw-r--r--graf/n6.lyx74
1 files changed, 37 insertions, 37 deletions
diff --git a/graf/n6.lyx b/graf/n6.lyx
index 6bf574a..c3d6148 100644
--- a/graf/n6.lyx
+++ b/graf/n6.lyx
@@ -158,7 +158,7 @@ Si
\end_inset
, llamamos
-\begin_inset Formula $[x,y]:=(x_{1},\dots,x_{m},y_{1},\dots,y_{n})\in\mathbb{R}^{n+m}$
+\begin_inset Formula $[x,y]\coloneqq (x_{1},\dots,x_{m},y_{1},\dots,y_{n})\in\mathbb{R}^{n+m}$
\end_inset
; si
@@ -170,11 +170,11 @@ Si
\end_inset
, llamamos
-\begin_inset Formula $[A,B]:=(c_{ij})\in{\cal M}_{n\times(p+q)}(\mathbb{R})$
+\begin_inset Formula $[A,B]\coloneqq (c_{ij})\in{\cal M}_{n\times(p+q)}(\mathbb{R})$
\end_inset
dada por
-\begin_inset Formula $c_{ij}:=a_{ij}$
+\begin_inset Formula $c_{ij}\coloneqq a_{ij}$
\end_inset
para
@@ -182,7 +182,7 @@ Si
\end_inset
y
-\begin_inset Formula $c_{ij}:=b_{i(j-p)}$
+\begin_inset Formula $c_{ij}\coloneqq b_{i(j-p)}$
\end_inset
para
@@ -190,7 +190,7 @@ Si
\end_inset
, y escribimos
-\begin_inset Formula $[x_{1},\dots,x_{n}]:=[x_{1},[x_{2},\dots,x_{n}]]$
+\begin_inset Formula $[x_{1},\dots,x_{n}]\coloneqq [x_{1},[x_{2},\dots,x_{n}]]$
\end_inset
para
@@ -198,7 +198,7 @@ Si
\end_inset
y
-\begin_inset Formula $[x_{1}]:=x_{1}$
+\begin_inset Formula $[x_{1}]\coloneqq x_{1}$
\end_inset
.
@@ -222,11 +222,11 @@ teorema
\end_inset
,
-\begin_inset Formula $P:=\{[x,y]\in\mathbb{R}^{p+q}\mid Ax+Gy\leq b\}$
+\begin_inset Formula $P\coloneqq \{[x,y]\in\mathbb{R}^{p+q}\mid Ax+Gy\leq b\}$
\end_inset
y
-\begin_inset Formula $S:=\{[x,y]\in P\mid x\in\mathbb{Z}^{p}\}$
+\begin_inset Formula $S\coloneqq \{[x,y]\in P\mid x\in\mathbb{Z}^{p}\}$
\end_inset
, existen
@@ -253,11 +253,11 @@ teorema
Demostración:
\series default
Sean
-\begin_inset Formula $S:=\{(x,y)\in\mathbb{Z}^{2}\mid y\leq\sqrt{2}x,x\geq0,y\geq0\}$
+\begin_inset Formula $S\coloneqq \{(x,y)\in\mathbb{Z}^{2}\mid y\leq\sqrt{2}x,x\geq0,y\geq0\}$
\end_inset
y
-\begin_inset Formula $C:=\{(x,y)\mid y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$
+\begin_inset Formula $C\coloneqq \{(x,y)\mid y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$
\end_inset
.
@@ -283,7 +283,7 @@ Demostración:
\end_inset
y
-\begin_inset Formula $p:=(1-t)a+tb$
+\begin_inset Formula $p\coloneqq (1-t)a+tb$
\end_inset
, si uno de
@@ -406,11 +406,11 @@ Sean
\end_inset
y
-\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid Ax\leq b\}$
+\begin_inset Formula $P\coloneqq \{x\in\mathbb{R}^{n}\mid Ax\leq b\}$
\end_inset
, si
-\begin_inset Formula $P_{I}:=\text{ec}(P\cap\mathbb{Z}^{n})\neq\emptyset$
+\begin_inset Formula $P_{I}\coloneqq \text{ec}(P\cap\mathbb{Z}^{n})\neq\emptyset$
\end_inset
, para
@@ -552,11 +552,11 @@ variable básica
\end_inset
, llamamos
-\begin_inset Formula $x_{B}:=(x_{s_{1}},\dots,x_{s_{m}})$
+\begin_inset Formula $x_{B}\coloneqq (x_{s_{1}},\dots,x_{s_{m}})$
\end_inset
,
-\begin_inset Formula $x_{N}:=(x_{t_{1}},\dots,x_{t_{n-m}})$
+\begin_inset Formula $x_{N}\coloneqq (x_{t_{1}},\dots,x_{t_{n-m}})$
\end_inset
,
@@ -564,7 +564,7 @@ variable básica
\end_inset
y
-\begin_inset Formula $\mathbf{n}(x_{1},\dots,x_{n-m}):=\sum_{k}e_{t_{k}}x_{k}$
+\begin_inset Formula $\mathbf{n}(x_{1},\dots,x_{n-m})\coloneqq \sum_{k}e_{t_{k}}x_{k}$
\end_inset
,
@@ -609,7 +609,7 @@ factible
\begin_layout Standard
Dado
-\begin_inset Formula $F:=\{Ax=b,x\geq0\}$
+\begin_inset Formula $F\coloneqq \{Ax=b,x\geq0\}$
\end_inset
,
@@ -706,7 +706,7 @@ Lema de Veinott-Dantzig:
\end_inset
,
-\begin_inset Formula $Q:=\{x\in\mathbb{R}^{n}\mid Ax=b,x\geq0\}$
+\begin_inset Formula $Q\coloneqq \{x\in\mathbb{R}^{n}\mid Ax=b,x\geq0\}$
\end_inset
es entero.
@@ -804,11 +804,11 @@ Sea
\end_inset
tal que
-\begin_inset Formula $z:=y+(B^{-1})_{i}\geq0$
+\begin_inset Formula $z\coloneqq y+(B^{-1})_{i}\geq0$
\end_inset
y
-\begin_inset Formula $b:=Bz=By+e_{i}$
+\begin_inset Formula $b\coloneqq Bz=By+e_{i}$
\end_inset
,
@@ -828,11 +828,11 @@ Sea
\end_inset
todos los coeficientes enteros, luego
-\begin_inset Formula $Q:=\{Ax=b,x\geq0\}$
+\begin_inset Formula $Q\coloneqq \{Ax=b,x\geq0\}$
\end_inset
es entero y
-\begin_inset Formula $x:=\mathbf{b}z=\mathbf{b}B^{-1}b$
+\begin_inset Formula $x\coloneqq \mathbf{b}z=\mathbf{b}B^{-1}b$
\end_inset
es una solución básica factible de
@@ -978,7 +978,7 @@ Dada una submatriz
\end_inset
es unimodular, con lo que
-\begin_inset Formula $Q:=\{[x,y]\in\mathbb{R}^{n+m}\mid Ax+Iy=b,[x,y]\geq0\}$
+\begin_inset Formula $Q\coloneqq \{[x,y]\in\mathbb{R}^{n+m}\mid Ax+Iy=b,[x,y]\geq0\}$
\end_inset
es entero.
@@ -1003,7 +1003,7 @@ Dada una submatriz
\end_inset
es
-\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$
+\begin_inset Formula $P\coloneqq \{x\in\mathbb{R}^{n}\mid b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$
\end_inset
.
@@ -1016,7 +1016,7 @@ Dada una submatriz
\end_inset
es un punto extremo, pues si no lo fuera existirían
-\begin_inset Formula $U:=[u,b-Au],V:=[v,b-Av]\in Q$
+\begin_inset Formula $U\coloneqq [u,b-Au],V\coloneqq [v,b-Av]\in Q$
\end_inset
distintos y
@@ -1069,11 +1069,11 @@ Sean
\end_inset
,
-\begin_inset Formula $P:=\{x\mid Ax\leq b,x\geq0\}$
+\begin_inset Formula $P\coloneqq \{x\mid Ax\leq b,x\geq0\}$
\end_inset
,
-\begin_inset Formula $Q:=\{[x,y]\mid Ax+y=b,[x,y]\geq0\}$
+\begin_inset Formula $Q\coloneqq \{[x,y]\mid Ax+y=b,[x,y]\geq0\}$
\end_inset
y
@@ -1293,7 +1293,7 @@ teorema
\end_inset
tal que, si
-\begin_inset Formula $F_{2}:=F\setminus F_{1}$
+\begin_inset Formula $F_{2}\coloneqq F\setminus F_{1}$
\end_inset
, para
@@ -1496,7 +1496,7 @@ Si las tareas se pueden hacer a la vez, lo que queremos minimizar es
\begin_layout Standard
Sean ahora
-\begin_inset Formula $R:=(V:=\{1,\dots,n\},E,\omega)$
+\begin_inset Formula $R\coloneqq (V\coloneqq \{1,\dots,n\},E,\omega)$
\end_inset
una red y
@@ -1595,7 +1595,7 @@ Para obtener el árbol generador minimal de
\end_inset
, llamamos
-\begin_inset Formula $x_{ij}:=\chi_{E_{T}}(i,j)$
+\begin_inset Formula $x_{ij}\coloneqq \chi_{E_{T}}(i,j)$
\end_inset
para
@@ -1643,7 +1643,7 @@ Otra posible formulación, con las mismas variables resulta de cambiar la
\begin_layout Standard
Para el problema del viajante de comercio sobre una red completa
-\begin_inset Formula $R:=(V:=\{0,\dots,n-1\},E\mid =\{\{i,j\}\}_{i,j\in V,i\neq j},d)$
+\begin_inset Formula $R\coloneqq (V\coloneqq \{0,\dots,n-1\},E\coloneqq \{\{i,j\}\}_{i,j\in V,i\neq j},d)$
\end_inset
, existen varias formulaciones:
@@ -1774,7 +1774,7 @@ es
.
Llamando
-\begin_inset Formula $n:=|V|$
+\begin_inset Formula $n\coloneqq |V|$
\end_inset
:
@@ -1783,7 +1783,7 @@ es
& \min & {\textstyle \sum}_{ij}d_{ij}x_{ij}\\
& & {\textstyle \sum_{(i,j)\in E}}x_{ij} & =1 & & \forall i\\
& & {\textstyle \sum_{(k,i)\in E}}x_{ki} & =1 & & \forall i\\
- & & u_{i}-u_{j}+nx_{ij} & \leq n-1 & & \forall i,j\in\{1,\dots,n-1\}\mid (i,j)\in E\\
+ & & u_{i}-u_{j}+nx_{ij} & \leq n-1 & & \forall i,j\in\{1,\dots,n-1\}:(i,j)\in E\\
& & x_{ij} & \in\{0,1\} & & \forall i,j\\
& & u_{i} & \in\mathbb{R}^{>0} & & \forall i
\end{alignat*}
@@ -1830,7 +1830,7 @@ Sea
\end_inset
la representación por variables de un ciclo hamiltoniano, llamamos
-\begin_inset Formula $u_{i}:=t$
+\begin_inset Formula $u_{i}\coloneqq t$
\end_inset
si
@@ -1928,7 +1928,7 @@ Dadas dos variables
\end_inset
, para definir una variable
-\begin_inset Formula $y:=[x_{1}>x_{2}]$
+\begin_inset Formula $y\coloneqq [x_{1}>x_{2}]$
\end_inset
(
@@ -2053,7 +2053,7 @@ Si
\end_inset
, para definir
-\begin_inset Formula $y:=\min\{x_{1},x_{2}\}$
+\begin_inset Formula $y\coloneqq \min\{x_{1},x_{2}\}$
\end_inset
añadimos
@@ -2073,7 +2073,7 @@ Si
\end_inset
, y para definir
-\begin_inset Formula $y:=\max\{x_{1},x_{2}\}$
+\begin_inset Formula $y\coloneqq \max\{x_{1},x_{2}\}$
\end_inset
añadimos
generated by cgit v1.2.3 (git 2.46.0) at 2025-10-30 22:40:40 +0000