# All Questions

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### Vector fields whose divergence are proper maps

Let $X$ be a polynomial vector field of degree $2$ on $\mathbb{R}^{2}$. Does there exist a nonvanishing smooth function $g$ such that $Div(gX)$ is a proper map?Or at least the zero locus of ...
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### Least supersingular prime

Given an elliptic curve over the rationals, what can one say about the size of the smallest supersingular prime?
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### A subgroup of outer automorphisms group of a free product

I would like to ask a question about automorphisms of free products of groups. More specifically, let $G = G_1 \ast ... \ G_n \ast F_r$ where $F_r$ is free group on r generators. We can define the ...
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### Schoenberg correspondence on $L^p$

Schoenberg correspondence states that $\psi: \mathbb R^d\longrightarrow \mathbb C$ is conditionally positive definite and hermitian if and only if $e^{t\psi}$ is positive definite for each $t>0$. ...
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### convergence and divergence using a root test [on hold]

why does infinity sigma n^7 / 7^n n=1 converge using a root test? I'm a bit confused on this series..
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### Moser's iteration for non homogeneous quasilinear elliptic PDE

I want to know some reference of Moser's iteration for non homogeneous quasilinear uniformly elliptic PDE, in particular, $u_{ij}(\delta_{ij}+u_iu_j|\nabla u|^2)=0$. I want to know how to deal with ...
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### textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks? ...
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### Combining Pearson correlations [on hold]

I have variables a, b, c, x I know sample values A, B, C, but not X I know Pearson correlations pairwise: ax, bx, cx (and ab, ac, bc too if it helps) Now what is the most likely value for X? ...
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### Odd-cycle inequality [closed]

Consider the stable set problem. An odd hole is a cycle with an odd number if nodes and no edges between nonadjacent nodes of the cycle. Show that if H is the node set of an odd hole, the following ...
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### Rademacher type of a Banach space is always less than or equal to 2

Before I ask my question I will provide a brief introduction. I came across the notion of Rademacher type while reading Assaf Naor's article An introduction to the Ribe program, which can be found ...
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### A surface on which all regular curves have nowhere vanishing curvature

Let $S$ be a surface in $\mathbb{R}^{3}$ such that every regular curve $\gamma\subset S$ has nowhere vanishing curvature, that is $\kappa(z)\neq 0$ for all $z\in \gamma$. Does this imply that ...
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### Groups arising as direct limits of a stationary system of primitive matrices over the integers

I am interested in the kinds of groups of the form $\displaystyle\lim_{\longrightarrow}(\mathbf{Z}^k,M)$ where $M$ is a primitive (some power of $M$ has strictly positive components) $k\times k$ ...
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### Maths to take a user chosen number to a predictable number [closed]

As part of simple card trick, I want to allow a user to choose a number between 1 and 100 and then ask them to do various maths to lead them to the same number so their choice becomes irrelevant. One ...
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### Contractibility of a poset-indexed colimit

Let $(X,\leq)$ be a poset with distinguished element $p$, and let $P'$ be the poset of "finite chains which weakly descend to $p$" given by all $\sigma = (x_0 \geq x_1 \geq \cdots \geq x_k \geq p)$ ...
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### Boolean algebra 1´=0 ; 0´=1 ; x+1=1 [closed]

Hi I have a problem to solve, in Boolean algebra. I have to prove that 1´=0 ; 0´=1 ; x+1=1 I solve the first problem x*0=0 -> x*0=x*0+0=x*0+x* x´=x*(0+x´)=x*x´=0 previous 3 problems ...