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authorJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
committerJuan Marin Noguera <juan@mnpi.eu>2022-12-04 22:49:17 +0100
commitc34b47089a133e58032fe4ea52f61efacaf5f548 (patch)
tree4242772e26a9e7b6f7e02b1d1e00dfbe68981345 /ggs/n9.lyx
parent214b20d1614b09cd5c18e111df0f0d392af2e721 (diff)
Oops
Diffstat (limited to 'ggs/n9.lyx')
-rw-r--r--ggs/n9.lyx20
1 files changed, 10 insertions, 10 deletions
diff --git a/ggs/n9.lyx b/ggs/n9.lyx
index 5d0cf43..3f506e8 100644
--- a/ggs/n9.lyx
+++ b/ggs/n9.lyx
@@ -161,7 +161,7 @@ Demostración:
\end_inset
dada por
-\begin_inset Formula $h(t):=(f(t)-\cos\theta(t))^{2}+(g(t)-\sin\theta(t))^{2}$
+\begin_inset Formula $h(t)\coloneqq (f(t)-\cos\theta(t))^{2}+(g(t)-\sin\theta(t))^{2}$
\end_inset
, entonces
@@ -345,7 +345,7 @@ Teorema de Liouville:
\end_inset
,
-\begin_inset Formula $\tilde{\alpha}:=(u,v):=X^{-1}\circ\alpha:I\to U$
+\begin_inset Formula $\tilde{\alpha}\coloneqq (u,v)\coloneqq X^{-1}\circ\alpha:I\to U$
\end_inset
,
@@ -373,7 +373,7 @@ e_{1}(s):=\frac{1}{\sqrt{E(\tilde{\alpha}(s))}}X_{u}(\tilde{\alpha}(s)),
\end_inset
,
-\begin_inset Formula $\alpha_{v}(u):=\beta_{u}(v):=X(u,v)$
+\begin_inset Formula $\alpha_{v}(u)\coloneqq \beta_{u}(v)\coloneqq X(u,v)$
\end_inset
,
@@ -425,7 +425,7 @@ e_{1}(s) & =\frac{X_{u}}{\Vert X_{u}\Vert}(\tilde{\alpha}(s)).
\end_inset
Entonces
-\begin_inset Formula $e_{2}(s):=Je_{1}(s)$
+\begin_inset Formula $e_{2}(s)\coloneqq Je_{1}(s)$
\end_inset
es también tangente y unitario y ortogonal a
@@ -451,7 +451,7 @@ Con esto,
\end_inset
luego si
-\begin_inset Formula $\omega:=\langle e_{1}',e_{2}\rangle=-\langle e_{1},e_{2}'\rangle$
+\begin_inset Formula $\omega\coloneqq \langle e_{1}',e_{2}\rangle=-\langle e_{1},e_{2}'\rangle$
\end_inset
@@ -709,7 +709,7 @@ velocidad que llega
\end_inset
es
-\begin_inset Formula $\alpha'_{-}(\ell):=\lim_{s\to\ell^{-}}\alpha'(s)$
+\begin_inset Formula $\alpha'_{-}(\ell)\coloneqq \lim_{s\to\ell^{-}}\alpha'(s)$
\end_inset
, y la
@@ -814,11 +814,11 @@ Teorema de rotación de las tangentes:
\end_inset
el ángulo de rotación de la velocidad de
-\begin_inset Formula $\alpha_{i}:=\alpha|_{[s_{i-1},s_{i}]}$
+\begin_inset Formula $\alpha_{i}\coloneqq \alpha|_{[s_{i-1},s_{i}]}$
\end_inset
respecto a
-\begin_inset Formula $e_{1}(s):=X_{u}(X^{-1}(\alpha(s)))/\sqrt{E(s)}$
+\begin_inset Formula $e_{1}(s)\coloneqq X_{u}(X^{-1}(\alpha(s)))/\sqrt{E(s)}$
\end_inset
, entonces
@@ -842,7 +842,7 @@ Teorema de Gauss-Bonnet
Teorema de Green:
\series default
Sea
-\begin_inset Formula $\tilde{\alpha}:=(u,v):[0,\ell]\to\mathbb{R}^{2}$
+\begin_inset Formula $\tilde{\alpha}\coloneqq (u,v):[0,\ell]\to\mathbb{R}^{2}$
\end_inset
una parametrización positivamente orientada de la frontera de un
@@ -987,7 +987,7 @@ característica de Euler
\end_inset
es
-\begin_inset Formula $\chi(T):=i_{0}-i_{1}+\dots+(-1)^{n}i_{n}$
+\begin_inset Formula $\chi(T)\coloneqq i_{0}-i_{1}+\dots+(-1)^{n}i_{n}$
\end_inset
.