Mathematics
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27 $ I(r) = \int_0^{2\pi}\frac{\cos(t) - r}{1 - 2r\cos t + r^2}\,dt$ is always zero for $r\in[0,1)$. Why? Jan 26
10 If $f : [a,b]\to\Bbb R$ is continuous, are there $x_1,x_2\in (a,b)$ such that $\tfrac{f(b)-f(a)}{b-a} = \tfrac{f(x_1)-f(x_2)}{x_1-x_2}$? Sep 14 '18
8 How to find the limit of series? (What should I know?) Oct 29 '17
8 Show that $A^{-1} + B^{-1}$ is invertible when $A,B$ and $A+B$ are invertible Mar 27
7 Given $A\in\Bbb R^{n\times n}$, is $C_A := \{SAS^{-1} : S\in GL(n,\mathbb R)\}$ connected? Jul 20 '18
6 Inverse of an “anti-Jordan” matrix Jul 18 '18
6 $X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$. Mar 28
5 Showing that given matrix does not have negative eigenvalues without using the knowledge that it is positive definite. Sep 14 '18
5 Given real angles $\phi_1,\ldots,\phi_N$, there exist infinitely many integers $n$ such that $\cos(n\phi_k) > 0$ for all $k$. Sep 8 '18
5 How to see that group of unitary operators with strong operator topology is connected? Oct 14 '17
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