updated a lot intro control theory

Mathematics/5th/Introduction_to_nonlinear_elliptic_PDEs/Introduction_to_nonlinear_elliptic_PDEs.tex

@@ -282,7 +282,7 @@
     Let $H$ be an infinite-dimensional separable Hilbert space and $K:H\to H$ be a compact operator. Then:
     \begin{enumerate}
       \item $0\in \sigma(K)$.
-            \item\label{INEPDE:item2_spectrum} If $\lambda\in \sigma(K)\setminus\{0\}$, then $\lambda$ is an eigenvalue of $K$.
+      \item\label{INEPDE:item2_spectrum} If $\lambda\in \sigma(K)\setminus\{0\}$, then $\lambda$ is an eigenvalue of $K$.
       \item $\sigma(K)$ is closed and at most countable.
       \item If $\sigma(K)\cap\RR$ is infinite, then $\sigma(K)\setminus\{0\}$ is of the form $\{\lambda_n\}_{n\in \NN}$ with $\lambda_n\to 0$.
       \item If $\lambda\in \sigma(K)\setminus\{0\}$, then:

Mathematics/5th/Stochastic_calculus/Stochastic_calculus.tex

@@ -808,7 +808,7 @@
     $$
   \end{definition}
   \subsubsection{Existence and uniqueness of solutions}
-  \begin{lemma}[Gronwall's lemma]\label{SC:gronwall}
+  \begin{lemma}[Grönwall's lemma]\label{SC:gronwall}
     Let ${(x_t)}_{t\in[0,T]}$ be a non-negative function in $L^1([0,T])$ satisfying that $\forall t\in[0,T]$:
     $$
       x_t\leq \alpha+\beta\int_0^t x_s\dd{s}