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Power series ring $\Theta[[X_1,\ldots,X_d]]$ and prime ideals

Let $\Theta$ be a domain. We shall choose $d$ elements $\theta_1,\ldots,\theta_d \in \Theta$ such that any chosen $j$ elements $\theta_{i_1},\ldots,\theta_{i_j}$ form a prime ideal $(\theta_{i_1},\...
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6 views

Look for a suitable cut-function: from Pierre Grisvard “Elliptic Problems in Nonsmooth Domains”: (Theorem 1.4.2.4)

From Pierre Grisvard "Elliptic Problems in Nonsmooth Domains": Theorem[Theorem 1.4.2.1] Let $\Omega$ be an open subset of $\mathbb{R}^d$ with a continuous boundary, then $C_c^\infty(\overline{\...
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16 views

Local question and $\it descent$ category for a quasi-coherent sheaf on $\mathbb{G}_m$-gerbe

I initially asked the question on MathStackExchange but it might be more appropriate on this website. Context: Suppose I have a $\mathbb{G}_m$-gerbe $\mathcal{G}$ over a scheme $X$ with the fppf (or ...
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20 views

Holomorphic functions to complex torus

Let $X$ be a complex algebraic variety and $T$ a complex torus (not necessarily algebraic). Let $f:X \to T$ be an holomorphic map. Assume $X$ is not complete and $\bar{X}$ is a completion. Is it ...
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23 views

Correctly defining a grah problem

I would like to solve a graph theory problem but I am struggling finding the most efficient Algo to solve it because I'm not correctly defining it. Here is my problem: I have two sets of data: A={A1,...
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0answers
52 views

$G_1$ a subquotient of $G_2$ and $G_2$ a subquotient of $G_1$, is $G_1 \cong G_2$?

Sorry for a presumably noobish group theory question. I would like an example of the following: $G_1,G_2$ are finitely presented groups such that there exists finitely presented groups $C_1,C_2$ ...
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17 views

Enhanced dissipation for Kolmogorov flow

My problem is $$\frac{\partial u}{\partial t}+\ sin(y)\frac{\partial u}{\partial x}=\nu(\frac{\partial^2 u}{\partial x^2} +\frac{\partial^2 u}{\partial y^2})$$ with periodic boundary conditions and ...
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17 views

Gamble Game-Maximum value

BALL GAME Your friend will put 100 balls with 5 different colors in a bag and tell you the number of balls for each color. Then you will randomly choose a ball and guess its color. If your guess is ...
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1answer
21 views

The number of hamiltonian circuits on a convex polytope embedded in $\mathbb{R}^N$

Recently I wondered whether there might be a natural topological complexity measure for convex polytopes embedded in $\mathbb{R}^N$. After some reflection it occurred to me that the number of distinct ...
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18 views

Implementing Continous Restricted Boltzmann Machine

Okay, so I want to impletent a CRBM in python, which is modeling a simple function, for example $f(x, y) = 5\cdot x + y$. Its training data is random $[x_i, y_i, f(x_i, y_i)]$, $i=0,\dots,N-1$. I know ...
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2answers
130 views

A conjectural trigonometric identity

Recently, I formulated the following conjecture which seems novel. Conjecture. For any positive odd integer $n$, we have the identity $$\sum_{j,k=0}^{n-1}\frac1{\cos 2\pi j/n+\cos 2\pi k/n}=\frac{n^2}...
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26 views

Pseudoisometry in Mostow's rigidity theorem for non-compact manifolds

The first step of all proofs of Mostow's Rigidity theorem for closed manifolds is to show that given a homotopy equivalence $M\rightarrow N$ between two closed hyperbolic manifolds, having the same ...
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32 views

Stable splitting of products

This question concerns the well-known homotopy equivalence $$ \Sigma (X\times Y) \simeq \Sigma (X \vee \ Y) \vee \Sigma (X\wedge Y) $$ (I'm happy to use only CW complexes). I can see that there is ...
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1answer
106 views

Texts on moduli of elliptic curves

I want to study FLT, and now I'm studying moduli of elliptic curves. I've heard that Deligne-Rapoport, Katz-Mazur, Mazur's "Modular curves...", and Katz's "p-adic..." are very good for this topic. ...
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26 views

Parallel hyperplane to a hyperbolic isometry of a CAT(0)-cube complex

Consider a finite-dimensional geodesically complete CAT(0) cube complex $X$. A hyperplane of $X$ is a convex subspace of $X$ that intersects the mid-point of edges of $X$ such that $X - H$ has two ...

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