# All Questions

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### Convergent's numerators of the continued fraction for $\pi$

Call $C_{\pi} = \{ 1,3,22,333,355,… \}$, it´s the sequence of the numerators of convergents of the continued fraction for $\pi$, its OEIS' A002485, http://oeis.org/A002485. Let $n \in C_{\pi}$, such ...
1answer
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### Analog of eigenvalue bound for a general bounded operator

It's known that for a matrix, $\max|λ|≤\sqrt{tr(A^*A)}=\sqrt{∑_{i,j=1}^n|A_{i,j}|^2}$ where $\lambda$ denotes its eigenvalue. I'm wondering whether there's an analog of this inequality for a general ...
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### Travelling round a circle

A and B start running from the same point to run in opposite directions round a circular race course 4324 meters in circumference, A not starting till B has run 716 meters. They pass each other when A ...
1answer
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### On the confinement to $[0;1]$ of the solution of $dX_{t}=(1-X_{t})X_{t}dB_{t}$

One considers the stochastic differential equation $$dX_{t}=(1-X_{t})X_{t}dB_{t},$$ with $B$ Brownian motion, and one assumes that $0\leq X_{0}\leq1$. One wants to show that \$\textbf{P}(X_{t}\in[0;1]...

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