# All Questions

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### Linearly constrained eigenvalue problem

Suppose I'd like to: \begin{align} \mathop{\text{min}}_\mathbf{x} && \mathbf{x}^T\mathbf{A}\mathbf{x} \\ \text{subject to:} && \mathbf{x}^T \mathbf{M} \mathbf{x} = 1\\ && ...
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### How to prove a relation holds almost surely? [on hold]

Let's assume x(t) and y(t) are to random processes. How should we prove a relation say x(t)>y(t) holds almost surely? Thanks in advance.
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### Isotropy of Apollonian disk-packing

Is there any sense in which the "epsilon-tail" of an Apollonian disk-packing (by which I mean the union of the disks of radius less than epsilon) exhibits more and more statistical isotropy as epsilon ...
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### Does the Gamma function preserve integers?

Does the Gamma function $\Gamma: \mathbb{C} \to \mathbb{C}$ preserve the Kummer ring $\mathbb{Z}[\exp(2\pi\imath/m)]$? And if not, then what about the Gaussian integers $\mathbb{Z}[\imath]$ or the ...
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### Conditions conformal mapping to be expansive

Let $\Omega' \subset \Omega$ be simply connected domains in the complex plane. The Riemann mapping theorem tells us that there a biholomorphism $f: \Omega' \to \Omega$. What conditions guarantee that ...
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### Coding for channels with concentrated error

A note: I accidentally over-simplified my first attempt at this question to the point of triviality - unfortunately, I didn't recognize this until after I had already placed a bounty to draw ...
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### Points with pairwise integer distances in the plane

Consider $n>3$ points with pairwise integer distances in the plane! What is the relationship between these $n(n-1)/2$ integers? Do we have a theorem or result about these points? Does there exist a ...
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### Is there any relationship between the Euler class and the Vandermonde determinant?

Several Wikipedia articles claim that the relationship between the Euler class $e(V)$ and the top Pontryagin class $p_k(V)$ of an oriented $2k$-dimensional real vector bundle $V$ corresponds, via the ...
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### $(LLP(Epi), Epi)$ is a WFS on any variety of algebras

This entry in the Joyal catlab claims without proof that in a category $\bf V$ which is a "variety of algebras" the two classes $(LLP(Epi), Epi)$ form a weak factorization system. I interpret this ...
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### Applying Lemma 2.12 of Deligne's/ Milne's “Tannakian Categories” on an irreducible representation

since this is my first question here, I'm not very certain whether I state it properly. I'm thankful for any helpful remarks. Currently I'm trying to understand the above-mentioned article which can ...
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### Question about non trivial zeros of Riemann zeta function [on hold]

I would like to know if is it true that $$-\frac{1}{2\pi i}\underset{n\geq1}{\sum}\frac{1}{n\rho^{n}}\in\mathbb{R}-\mathbb{Z}$$where $\rho$ is a non trivial zero of Riemann zeta function. How can I ...
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### Solution of parabolic PDE system [on hold]

For the following parabolic PDE system, $u(x,t)$ and $v(x,t)$ are functions of independent variables $x$ and $t$, $x\in[a,b]$. \begin{cases} \frac{\partial}{\partial ...
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### Can the Cohen forcing collapse cardinals?

Let $\kappa$ be a regular cardinal, and let $\mathbb{P} = Add(\kappa,1)$ be the standard forcing notion for adding a new subset of $\kappa$ using partial function from $\kappa$ to $2$ with domain of ...
Let $X$ and $X^\vee$ be a mirror pair, homological mirror symmetry relates the symplectic geometry of $X$ to the complex geometry of $X^\vee$ via the equivalence of triangulated categories ...