# All Questions

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### n-dimensional polyhedron with special properties

I'd like to know if there exists a convex face transitive n-dimensional polyhedron with all dihedral angles equal to $\frac{2\pi}{3}$. For n = 2,3,4 an example can be a regular hexagon, a rhombic ...
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### Uniform position for multiple components

(Modified from https://math.stackexchange.com/questions/3730261/uniform-position-theorem-for-reducible-varieties/3730457#3730457) The uniform position theorem states (roughly) that a general ...
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### How can construct three circles in a given triangle such that three internal tangent form an equilateral triangle

How can construct three circles in a given triangle such that three internal tangent form an equilateral triangle? See also: Malfatti circles
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### Why can't we embed Tarski's truth in PA?

I recently learned that ZFC can prove $Con(PA)$ because it can give a model of PA, but I'm not given the technical details. (My teacher thinks it is too obvious to even mention.) What plagues me is ...
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### Braided category inside braided 2-category

Let $\mathcal{C}$ be a semistrict braided monoidal $2$-category in the sense of [BN] (so in particular a strict $2$-category). Let $\mathcal{C}_1$ be the category of $1$-morphisms (objects) and $2$-...
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### Properties of the total variation norm on space of totally finite measure (from Bogachev)

Let $(X,d)$ be a metric space, $\mathcal{B}$ the Borel $\sigma$-algebra on $X$, and $\mathcal{M}(X)$ the space of totally finite measures on $\mathcal{B}$. Let $\|\mu\|_{TV}$ be the total variation ...
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### Infinitely many $n$ such that $\gcd(\lfloor n\sqrt{2}\rfloor, \lfloor n\sqrt{3}\rfloor)=m$

Is it true that for any positive integer $m$ there are infinitely many positive integers $n$ such that $\gcd(\lfloor n\sqrt{2}\rfloor, \lfloor n\sqrt{3}\rfloor)=m$? $\lfloor x \rfloor$ is the floor ...
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### Fast way to generate random points in 2D according to a density function

I'm looking for a fast way to generate random points in 2D according to a given 2D density function. For instance something like this: Right now I'm using a modified version of "Poisson disc&...
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### Invertible bimodule for hereditary algebras

Let $A=kQ$ be a path algebra over a field $k$ for a finite acyclic quiver with enveloping algebra $A^e$. Question: When is it true that $\tau_{A^e}(A) \cong A$ as a left and as a right $A$-modules? (...
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### Permutation and combination [closed]

Problem Statement : Given input x,y,a,b where x is the number of 0's a binary string has , y is the number of 1's, a is the number of possible sub-sequence "01" while b the number of ...
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### Fourier transform of a function of bounded variation

I know if $f\in L^2(\mathbb R)$ is two times continuously differentiable, then we must have that the Fourier transform is integrable. Is there any more relaxed condition than this? For example if $f$ ...
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### Conjugate point to spacelike hypersurface

Suppose you have a smooth spacelike hypersurface $\Sigma$ in some spacetime (four-dimensional Lorentzian manifold). Let $\gamma$ be a timelike geodesic meeting $\Sigma$ orthogonally and let $p$ be a ...
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### “Well-known fact” that every irreducible 3-manifold with non-empty boundary has an incompressible surface

I have seen in several sources that this results holds, however none of them included the proof. Does anyone know where I can find one? Also, it would be great if someone could provide me with a ...
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### why can't i integration and differentiation? [closed]

Please kindly help solve this question for me. I need it quite urgent
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### Are “large enough” finite etale covers arithmetic?

Let $X$ be a variety over a number field $K$. Then it is known that for any topological covering $X' \to X(\mathbb{C})$, the topological space $X'$ can be given the structure of a $\overline{K}$-...
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### Dense generator whose closure under finite colimits takes several steps to form?

Let $\mathcal C$ be a locally finitely presentable category, and let $\mathcal C_0 \subseteq \mathcal C$ be a dense generator of finitely-presentable objects. Then Every object $C \in \mathcal C$ is ...
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### If a Markov semigroup is eventually contractive, can we conclude that it admits a unique invariant measure?

Let $E$ be a separable $\mathbb R$-Banach space, $\rho$ be a complete separable metric on $E$, $\operatorname W_\rho$ denote the Wasserstein metric of order $1$ associated to $\rho$, $\mathcal M_1(E)$ ...
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### Rings or algebras with many nilpotent elements and efficient computation

Crossposted from quantum.SE where comment appears to suggest that solving modulo 2 might be possible. Searching the web for '"quantum computer" nilpotent' returns many results, so maybe the ...
Is it consistent with $ZF$ to have a set $S$ and a function $F: P(S) \to S$ such that: $\forall X,Y \in P(S): X \subsetneq Y \implies F(X) \neq F(Y)$