# All Questions

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154 views

### Weight spaces of representations of finite dimensional simple Lie algebras

This question has probably been asked before on this website, but I could not find any solution and neither can I solve this question. So again I am asking the following question: Let $\mathfrak{g}$ ...
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### Stationary sets and $\kappa$-complete normal ultrafilters

Let $\kappa$ be a measurable cardinal, and let $u$ be a normal $\kappa$-complete ultrafilter over $\kappa$. It is a standard easy fact that every closed unbounded set must belong to $u$ (notice that ...
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### Blowing up vector bundles in the zero section

Assume we are given a scheme $X$ (feel free to add all the needed hypotheses, at this point I’m working with smooth schemes, but the fewer is needed, the better) and a vector bundle $E$ over $X$. I ...
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### Is there a classification of finite simple groups of perfect power order?

The finite simple group $\operatorname{PSp}(4,7)$ has order $138297600 = 11760^2$. There also seems to be a description of the $q$ such that $\operatorname{PSp}(4,q)$ has square order, see for ...
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### What work can be done to study the solutions of $\varphi\left(x^{\sigma(x)}\sigma(x)^x\right)=2^{x-1} x^{3x-1}\varphi(x)$?

For integers $n\geq 1$ I denote the Euler's totient function as $\varphi(n)$ and the divisor function $\sum_{1\leq d\mid n}d$ as $\sigma(n)$, that are two well-known mulitplicative functions. We ...
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### Regular triangulations of star-convex polyhedra with given boundary

Given an $n$-dimensional star-convex polyhedron $P\subset \mathbb{R}^n$ with simplicial facets, is it always possible to construct a regular triangulation $K$ of $P$ which does not subdivide the ...
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### Characterization of Besov space with Lp-modulus of continuity

When reading the characterization of Besov space with $L_p$-modulus of continuity in the 7th chapter “Fractional Order Space” of Sobolev space written by Adams(Page 243), I encounter some small ...
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### Existence of topologically mixing (discrete) dynamical system on manifold

If $M$ is a connected $(d\geq 2)$-dimensional smooth closed manifold, then does there exist a class $C^1$-diffeomorphism $\phi$ from $M$ onto itself, such that $(M,\phi)$ is a topologically mixing (...
98 views

### Cohomology and base change theorem for non-noetherian schemes

Let $Y$ be a locally noetherian scheme, $f : X \to Y$ proper morphism, $\mathscr{F}$ a coherent module on $X$ which is flat over $Y$. Then we have many theorems about the cohomology of $\mathscr{F}$ ...
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### A generalization of $p$-groups

I was wondering if there is a reference studying groups with order $m^k$ where $m,k$ are integers and $m$ is not supposed to be a prime, as a generalization of $p$-groups?
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### Real orthogonal and sign [on hold]

I came across the following conjecture, reading a recent paper in the Monthly, an orthogonal matrix of order $n\neq 0 \pmod 4$ has a nonnegative (up to a scalar) row vector. It should be straight in ...
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### Petries exotic circle action

In the paper "S^1-actions on homotopy complex projective spaces" by Petrie (Bulletin of the AMS, 1972), Petrie constructs a smooth circle action on $\mathbb{CP}^{3}$ (page 148). The fixed point set ...
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### How to sort differential equation list? [on hold]

Which sorting related with famous sequence for example  sorting differential equation in a list then access the list with famous sequence as index such as using https://oeis.org/ after access with ...
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### Question about the Invariance of Domain Theorem [on hold]

Dear fellow mathematicians, As you know, the Invariance of Domain Theorem states the followiing: "Let f be an injective continuous mapping from Euclidean space R^n to Euclidean space R^n. Let U be ...
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### Topological properties of a subset of $\mathbb R^n$ [on hold]

Consider $\mathbb R^n \quad (n>1)$. A point of $\mathbb R^n$ is a a $n$-uple written $(x_1,\ldots,x_n)$. Consider a set of indices $\{i_1,i_2,\ldots,i_{2p}\}$ of even cardinal $2p$ $(2p\leq n)$ ...
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### Prove that this expression is greater than 1/2

Let $0<x < y < 1$ be given. Prove $$4x^{2}+4y^{2}-4xy-4y+1 + \frac{4}{\pi^2}\Big[ \sin^{2}(\pi x)+ \sin^{2}(\pi y) + \sin^{2}[\pi(y-x)] \Big] \geq \frac{1}{2}$$ I have been working on this ...
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### Probability distributions on algebraic varieties [on hold]

Is there a notion of (algebraic) probability distribution on algebraic varieties? If there is, where can I find it? If not, why not?
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### Is there a weak homotopy equivalence between Sp(2n,ℂ)/U(n) and SU(n)?

This question, Is there a weak homotopy equivalence between Sp(2n,ℂ)/U(n) and SU(n)?, is at the end of a long string of my comments in https://math.stackexchange.com/questions/3296373/is-sp2n-mathbbc-...
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### Equivalence between Gibbs measures and conformal measures

I was reading an article about Gibbs measures, but the author defines Gibbs measures in a different way than the usual (which is done by using conditional expectations). The way that he defines I have ...
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