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Feb
9
accepted What general mobius transformation maps $|z-1|=1$ to itself and $|z+1|=1$ to $|w-3|=3$.
Feb
3
accepted If $f$ is analytic in $D$ and $|f(z)|<M$ everywhere on $|z|=1$, show for all $z:|z|<1$, $|f(z)| \leq M |\frac{z-a}{\bar a z - 1}|$
Feb
1
accepted Suppose $T$ is diagonalizable in $\mathbb{C}$. Show $e^T = \sum_{\lambda \in sp(T)} e^\lambda P_\lambda$ is the matrix exponential series.
Jan
18
accepted (Ahlfors, p198) Why is it clear we can write $G(z-1)=ze^{\gamma(z)}G(z)$ when deriving the Gamma function?
Jan
17
accepted Laurent expansion of $1/(1+z^n)$ for $n \in \mathbb{N}$.
Jan
13
accepted Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
Jan
2
accepted Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Dec
19
accepted What is the statistical steady state of this poisson process?
Dec
18
accepted Suppose $dX_t = a(X_t) dt + b(X_t) dW_t$ and $Y_s=X_t$ where $s=t^2$. What SDE does $Y_s$ satisfy in the weak sense?
Dec
13
accepted Suppose $X_t$ is a brownian motion with $X_0 \sim u_0$. What is the probability density of $X_t$? (heat equation)
Nov
20
accepted How to solve the following PDE for A and B?
Nov
4
accepted If $T^2=O$ where $O$ is $O(\vec{x})=\vec{0}$, prove that $T$ has no inverse
Nov
4
accepted If $A$ is a rank one linear transformation, show there is a unique scalar $\alpha$ such that $A^2 = \alpha A$
Nov
4
accepted Suppose $A$ is rank 1. If $A^2 = cA$ for some constant $c$, is it true that for a non-zero vector $x$, $Ax = cx$?
Oct
27
accepted Evaluate $\sum_{i=t'}^{s'-1} \delta (1-\delta)^{2(s'-1-i)}$ as $\delta \to 0$.
Aug
24
accepted Let $F$ be a vector field in $\mathbb{R}^3$. If $F$ is divergence free, we may deform the surface. Why?
Jul
18
accepted Describe the Riemann surface for $w=z^2-1$.
Jul
10
accepted Assume a die is rolled repeatedly. Find the markov matrix $P$ for the random variable of the time until the next $6$.
Jun
25
accepted Evaluate $\lim_{\alpha \to \infty} e^{-t\sqrt{\alpha}}(1-\frac{t}{\sqrt{\alpha}})^{-\alpha}$
May
6
accepted Evaluate $\int_0^1 \int_\sqrt{y}^1 \int_0^{x^2+y^2} dz dx dy$.