# All Questions

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### What characterizations of relative information are known?

Given two probability distributions $p,q$ on a finite set $X$, the quantity variously known as relative information, relative entropy, information gain or Kullback–Leibler divergence is defined ...
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### Equivariant form of Nagata's compactification theorem?

Given a finite group $G$ acting on an algebraic variety $X$ (let's say over $\mathbb C$, if that helps), is there always a proper variety $\bar X$ with a $G$ action such that $X \to \bar X$ is a ...
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### Simple question: different definitions of Bousfield localization

I am not an expert on model categories and I am getting lost with two different definitions I have found on Bousfield localizations. I don't see the link between them. First definition: Let ...
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### Prove or disprove a monotonicity property of a certain convex optimization problem

Let $R = (r_{ij})$ be an $n\times k$ real matrix with only positive entries, and consider the convex optimization problem $\max f(x) = \sum_{i=1}^n \log \sum_{j=1}^k r_{ij} x_j$ such that ...
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### Has every Lusin vector space a stronger Polish vector space topology?

Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger ...
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### Why are these two gamma functions equal? [on hold]

$\gamma_{1}(s)=\pi^{\frac{1}{2}-s}\frac{\Gamma(\frac{s}{2})}{\Gamma(\frac{1}{2}(1-s))}$ $\gamma_{2}(s)=(\frac{b}{2\pi})^{\frac{1}{2}-a} e^{-2i\theta(b)}$ ,where $s=a+bi$ I calculated ...
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### Okounkov-Vershik approach to representation theory of $S_n$

This is a rather soft question. I was wondering if someone could explain on a fundamental and intuitive level, what the Okounkov-Vershik approach to representation theory of $S_n$ is all about. It's ...
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### Implicit feature space of Power Kernel

For the polynomial kernel, $K(x,y) = (x^Ty+c)^d$, the implicit feature space $\phi$ for which $K(x,y) = \phi(x)^T \phi(y)$ is of finite dimension and well known [1][2]. It is also well known that the ...
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### A new result on the Diophantine equation $x^3 + y^3 +z^3 = 3$ [on hold]

The above Diophantine equation is unknown to have any further integer solutions other than $(x, y, z) = (1, 1, 1)$ and $(4, 4, -5)$. I am a prospective undergraduate mathematics student in Zimbabwe ...
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### Does the nearby cycle functor commute with the Verdier duality?

I would be interested to know the answer to the above question for the constructible bounded derived category on complex analytic or complex algebraic manifolds (or some other context). A reference ...
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### Monotonicity per dimension of multivariate scattered data

For my thesis, I am working on interpolation using the RBF method (Radial Basis Functions). Before interpolating, I want some a priori insight into the data, for example check in which dimensions it ...
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### expressing in terms of sum of (double) schubert polynomial

It is well known that Schubert polynomials form a basis for the polynomial ring $\mathbb{Z}[x_1,x_2,x_3,...]$. I am interested in knowing how to express a particular polynomial into sum of Schubert ...
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### find a formula for a vector using a cartesian equation of a sphere [on hold]

I've this exercise and i'm stuck, I'l appreciate any help. ...
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### Reference on the classification of (low rank) Gorenstein rings over $\mathbb{C}$

I am interested in the question of the classification of (low rank) Gorenstein rings over $\mathbb{C}$. The socle of a local algebra is the annihilator of its maximal ideal. A commutative local ring ...
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### Uniqueness of $\partial_t u -u\Delta u=0$ with $u(0,\cdot)=1$

Is there anything known about uniqueness of classical solutions to $$\partial_t u -u\Delta u=0\quad u(0,\cdot)=1$$ on smooth domains $[0,T]\times D$ without boundary conditions? I know that ...
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### Integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of varieties of general type is a rational numbers?

It is known that the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of Calabi-Yau varieties is a rational numbers My question is on moduli space of varieties of ...
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### How to prove the Hölder continuity of a function $u$ by evaluating $\int_{B_{\rho}(x_0)}\frac{|Du(x)|^{2}}{|x-x_0|^{n-2}} dx$?

I'm looking at a video on thin obstacle problem given by Arshak Petrosyan. In his lecture, he uses the following results: Let $0<\alpha<1$, and $B_1$ be the unit ball centered at origin in ...
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### Regularity on Neumann problem on polygonal domain

I asked a similar question before but didn't get any responses. So I will attempt again (the prior question was regarding Holder continuity). Let $\Omega$ denote a cube in $R^n$ and consider ...
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### family of polynomials with square discriminant

The title pretty much sums it up: do people know of nice parametrized families of polynomials (with integer coefficients) with square discriminant. I should say that one such family consists of ...
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### Compact embedding and fractional Sobolev spaces in unbounded domain

It is known that there exists a compactness results involving fractional sobolev spaces in bounded domain. What about unbounded domain? More precisely, Under which conditions, we can extend the ...
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### Information and intuition packed in the Chern character for coherent sheaves

even after quite some time learning it, I still get somehow puzzled by the Chern character. Let me recall some stuff to get notation and setting. Let us consider a smooth projective algebraic variety ...