diff options
Diffstat (limited to 'fvc/n4.lyx')
| -rw-r--r-- | fvc/n4.lyx | 50 |
1 files changed, 25 insertions, 25 deletions
@@ -108,7 +108,7 @@ Toda curva Demostración: \series default Sean -\begin_inset Formula $\rho:=\min_{t\in[a,b]}|\gamma(t)|>0$ +\begin_inset Formula $\rho\coloneqq \min_{t\in[a,b]}|\gamma(t)|>0$ \end_inset , @@ -140,7 +140,7 @@ Demostración: \end_inset y -\begin_inset Formula $D_{k}:=D(\gamma(t_{k}),\rho)$ +\begin_inset Formula $D_{k}\coloneqq D(\gamma(t_{k}),\rho)$ \end_inset . @@ -180,11 +180,11 @@ Demostración: . Sean ahora -\begin_inset Formula $\theta_{k}(t):=A_{k}(\gamma(t))\in\text{Arg}(\gamma(t))$ +\begin_inset Formula $\theta_{k}(t)\coloneqq A_{k}(\gamma(t))\in\text{Arg}(\gamma(t))$ \end_inset y -\begin_inset Formula $m_{k}:=\theta_{k}(t_{k})-\theta_{k+1}(t_{k})$ +\begin_inset Formula $m_{k}\coloneqq \theta_{k}(t_{k})-\theta_{k+1}(t_{k})$ \end_inset , y definimos @@ -192,7 +192,7 @@ Demostración: \end_inset como -\begin_inset Formula $\theta(t):=\theta_{k}(t)+\sum_{i=0}^{k-1}m_{k}$ +\begin_inset Formula $\theta(t)\coloneqq \theta_{k}(t)+\sum_{i=0}^{k-1}m_{k}$ \end_inset para @@ -334,7 +334,7 @@ Sean \end_inset , -\begin_inset Formula $\rho:=\min_{t\in[a,b]}|\gamma(t)-z_{0}|>0$ +\begin_inset Formula $\rho\coloneqq \min_{t\in[a,b]}|\gamma(t)-z_{0}|>0$ \end_inset y @@ -371,7 +371,7 @@ Sean \end_inset , tenemos que -\begin_inset Formula $\theta(t):=\theta_{0}(t)+\arg\frac{\gamma(t)-z}{\gamma(t)-z_{0}}$ +\begin_inset Formula $\theta(t)\coloneqq \theta_{0}(t)+\arg\frac{\gamma(t)-z}{\gamma(t)-z_{0}}$ \end_inset es un argumento continuo de @@ -499,7 +499,7 @@ Demostración: \end_inset , entonces -\begin_inset Formula $\varphi(t):=\log|\gamma(t)-z|+i\theta(t)$ +\begin_inset Formula $\varphi(t)\coloneqq \log|\gamma(t)-z|+i\theta(t)$ \end_inset es un logaritmo continuo de @@ -525,7 +525,7 @@ Demostración: es derivable. Entonces -\begin_inset Formula $\varphi_{k}:=\varphi|_{[t_{k-1},t_{k}]}$ +\begin_inset Formula $\varphi_{k}\coloneqq \varphi|_{[t_{k-1},t_{k}]}$ \end_inset también lo es y @@ -560,7 +560,7 @@ Una cadena \series default es una expresión de la forma -\begin_inset Formula $\Gamma:=m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}$ +\begin_inset Formula $\Gamma\coloneqq m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}$ \end_inset donde los @@ -581,7 +581,7 @@ soporte \end_inset a -\begin_inset Formula $\Gamma^{*}:=\bigcup_{k}\gamma_{k}^{*}$ +\begin_inset Formula $\Gamma^{*}\coloneqq \bigcup_{k}\gamma_{k}^{*}$ \end_inset y @@ -593,16 +593,16 @@ longitud \end_inset a -\begin_inset Formula $\ell(\Gamma):=\sum_{k}|m_{k}|\ell(\gamma_{k})$ +\begin_inset Formula $\ell(\Gamma)\coloneqq \sum_{k}|m_{k}|\ell(\gamma_{k})$ \end_inset . Si -\begin_inset Formula $\Sigma:=n_{1}\sigma_{1}+\dots+n_{p}\sigma_{p}$ +\begin_inset Formula $\Sigma\coloneqq n_{1}\sigma_{1}+\dots+n_{p}\sigma_{p}$ \end_inset es otra cadena, llamamos -\begin_inset Formula $\Gamma+\Sigma:=m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}+k_{1}\sigma_{1}+\dots+k_{p}\sigma_{p}$ +\begin_inset Formula $\Gamma+\Sigma\coloneqq m_{1}\gamma_{1}+\dots+m_{q}\gamma_{q}+k_{1}\sigma_{1}+\dots+k_{p}\sigma_{p}$ \end_inset . @@ -647,7 +647,7 @@ ciclo \end_inset a -\begin_inset Formula $\text{Ind}_{\Gamma}(z):=\sum_{k}m_{k}\text{Ind}_{\gamma_{k}}(z)$ +\begin_inset Formula $\text{Ind}_{\Gamma}(z)\coloneqq \sum_{k}m_{k}\text{Ind}_{\gamma_{k}}(z)$ \end_inset . @@ -806,7 +806,7 @@ es continua en \end_inset Como -\begin_inset Formula $K:=\{\{z_{n}\}_{n}\cup\{a\}\}\times\Gamma^{*}$ +\begin_inset Formula $K\coloneqq \{\{z_{n}\}_{n}\cup\{a\}\}\times\Gamma^{*}$ \end_inset es compacto por ser producto de compactos, @@ -889,7 +889,7 @@ Si además, para \end_inset dada por -\begin_inset Formula $F_{w}(z):=F(z,w)$ +\begin_inset Formula $F_{w}(z)\coloneqq F(z,w)$ \end_inset es holomorfa en @@ -1059,7 +1059,7 @@ Ahora bien, fijado \end_inset , sea -\begin_inset Formula $F_{w}(z):=F(w,z)$ +\begin_inset Formula $F_{w}(z)\coloneqq F(w,z)$ \end_inset , es claro que @@ -1083,7 +1083,7 @@ Ahora bien, fijado \begin_layout Standard Sea -\begin_inset Formula $\Omega_{0}:=\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)=0\}$ +\begin_inset Formula $\Omega_{0}\coloneqq \{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)=0\}$ \end_inset , que es abierto por ser unión de componentes conexas de @@ -1123,7 +1123,7 @@ status open \end_inset dada por -\begin_inset Formula $F_{0}(z,w):=\frac{f(w)}{w-z}$ +\begin_inset Formula $F_{0}(z,w)\coloneqq \frac{f(w)}{w-z}$ \end_inset . @@ -1302,7 +1302,7 @@ forma general del teorema de Cauchy \end_inset , aplicando la fórmula integral de Cauchy a -\begin_inset Formula $g(z):=(z-a)f(z)$ +\begin_inset Formula $g(z)\coloneqq (z-a)f(z)$ \end_inset , como @@ -1886,7 +1886,7 @@ status open . Sea -\begin_inset Formula $K:=\mathbb{C}\setminus\Omega_{0}=\Gamma^{*}\cup\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)\neq0\}$ +\begin_inset Formula $K\coloneqq \mathbb{C}\setminus\Omega_{0}=\Gamma^{*}\cup\{z\in\mathbb{C}\setminus\Gamma^{*}\mid \text{Ind}_{\Gamma}(z)\neq0\}$ \end_inset , que es cerrado por ser complementario de un abierto y acotado porque no @@ -1934,15 +1934,15 @@ Sean \end_inset , -\begin_inset Formula $m_{k}:=\text{Ind}_{\Gamma}(a_{k})$ +\begin_inset Formula $m_{k}\coloneqq \text{Ind}_{\Gamma}(a_{k})$ \end_inset , -\begin_inset Formula $\gamma_{k}:=C(a_{k},\rho)$ +\begin_inset Formula $\gamma_{k}\coloneqq C(a_{k},\rho)$ \end_inset y -\begin_inset Formula $\Sigma:=\sum_{k=1}^{q}m_{k}\gamma_{k}$ +\begin_inset Formula $\Sigma\coloneqq \sum_{k=1}^{q}m_{k}\gamma_{k}$ \end_inset . |