# All Questions

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### Chances for a cosine polynomial to be positive at a point

Let $k_1,\ldots,k_n$ be distinct integers. Let $s_n(t)=\cos (k_1t)+\cdots+\cos (k_nt)$ be a trigonometric sum. Consider any interval $I\subset [-\pi,\pi)$ of length $\delta=\delta(n)$. Let $\,U$ be a ...
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### A curious Gauss-Sum type identity

Let $q=e^{2\pi i/m}$, $a\in\mathbb{R}$ and $1\leq j\leq m-1$. I would like to prove that: $$(a-1)\sum_{n=0}^{m-1} q^n\frac{\prod_{k=0}^{j-2} (q^{n+k+1}-a)}{\prod_{k=0}^{j} (aq^{n+k}-1)}=0.$$ For ...
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### Is there a site where I should post questions about mathematics for which I seek a solution? [on hold]

Is there a site where I should post questions about mathematics for which I seek a solution, without risk that it will be closed for not being "research level"?
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### Is there effective algorithm for finding “minimal discovery time” for large graphs?

Consider a large, probably sparse graph with Markovian random walkers on it. Define discovery time as time to first reach a vertex by random walk from uniform start. Are there effective ways to find ...
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### Isotropic correlation function for a vector valued random field

I'm having trouble with some of the implications of the following theorem. Let $\mathbf{T} (\mathbf{x})$ be a mean-square continuous vector valued random field on $\mathbb{R}^3$ satisfying conditions ...
For a set of points in $\mathbb{R}^d$ with minimum distance $a$, the minimum-distance graph connect two points iff they are at distance $a$. We can also view it as the tangency graph for a set of ...
### Which univariate function satisfies $e^{g(x)} + e^{-g(x)} = \alpha x$ for $x>0$ and some constant $\alpha>0$? [on hold]
Which univariate function $x \mapsto g(x)$ satisfies $$e^{g(x)} + e^{-g(x)} = \alpha x$$ for $x>0$ and some constant $\alpha>0$? How can it be computed? What does it look like? How can it be ...