Newest Questions
162,010 questions
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The number of words of finite group [closed]
Let $G=\langle g_{1},\cdots,g_{d}\rangle$. Set $n\in\mathrm{N}_{+}$. Denote $S=\{g_{1},\cdots,g_{d}\}$. Set $S^{n}$ is Cartesian Product of $n$ copies of $S$. If there exists $m\leq n$ such that $x_{1}...
- 389
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Extend the monotonicity of $W^2(\mu_{\alpha},\nu_{\alpha})$ from the Dirac case to finite mixtures
I'm having trouble completing a proof and would appreciate your insight. I’d like to share what I’ve done so far and hope you can help me move forward.
My current result: Suppose that $\widehat{P} = \...
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3
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2
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124
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Representing elements of Tate-Shafarevich group of $E$ as translates of $E$ in abelian variety
Let $E$ be an elliptic curve over a number field $K$ (I’m more generally interested in global fields). Cremona and Mazur in section 3 of these notes explain that any element $C$ of the Tate-...
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Does the statement that every sequentially compact metric space is compact imply the axiom of countable choice?
I know that the statement that every sequentially compact pseudometric space is compact implies the axiom of countable choice (H. Herrlich, Axiom of Choice, 2006). How about in the realm of metric ...
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Closed form for A072170
Let
$a(n)$ be A018819 (i.e., binary partition function: number of partitions of $n$ into powers of $2$), whose ordinary generating function is $$ A(x) = \frac{1}{\prod\limits_{j=0}^{\infty} (1-x^{2^j}...
- 5,890
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Bad approximate unit in the Fourier algebra
Let $G$ be a locally compact group and denote by $A(G)$ its Fourier algebra.
There are various properties on $G$ or on various algebras associated to $G$ which are characterized by the existence of ...
- 457
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Can the set of non-differentiability of a Lipschitz function be of arbitrary Hausdorff dimension?
Let $n$ be a positive integer, and $s \leq n$ a positive real number.
Does there exist a Lipschitz function $f: \mathbb R^n \to \mathbb R$ such that the set on which $f$ is not differentiable has ...
- 8,175
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161
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Deformation theoretic meaning of Deligne's conjecture
Deligne's conjecture says that the Hochschild cochains $\text{HC}(A)$ of an associative algebra acts on $A$, specifically that it forms an algebra for the Swiss cheese operad. There are lots of proofs ...
- 5,973
2
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A question about weighted spaces
Let $1<p<\infty$ and $w\in A_p$ a weight in the Muckenhoupt class. In [Lemma 2.2] Fröhlich, A. The Stokes Operator in Weighted
-Spaces I: Weighted Estimates for the Stokes Resolvent Problem in a ...
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Characterization of the probability density induced by an antisymmetric wave function
Suppose real-valued wave function $\psi(r_1,\dots,r_N)\in L^2$ (or $H^1$) is unnormalized and antisymmetric, that is:
$$\psi(r_{\sigma(1)},\dots,r_{\sigma(N)}) = \text{sgn}(\sigma)\psi(r_1,\dots,r_N),\...
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2
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285
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The strong Mersenne conjecture
The strong twin conjecture:
For every number $a≥0$, there exist two prime numbers $p$ and $p+2$ such that $$a+4<p<2^{a+4}$$
and it was believed that this conjecture implies the twin conjecture.
...
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zeros of trigonometric polynomials
Pólya and Szegö showed that for
\begin{eqnarray}
&&u(\theta)= a_0 + a_1{\rm cos}\theta +a_2{\rm cos}(2\theta) + \cdots + a_n{\rm cos}(n\theta), \\
&&v(\theta)= a_1{\rm sin}\theta + a_2{...
- 113
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Questions about $\epsilon$-completeness, equivalent definitions of nontrivial $\epsilon$
Shelah discusses $\epsilon$-completeness in his book Proper and Improper Forcing, p196. But my question is just about the definition of nontrivial there.
For $\epsilon$ a family of subsets of $S_{\...
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The Chow ring with rational coefficients is generated multiplicatively by Picard group?
I see Kiritchenko's Intersection theory note claims that the Chow ring with rational coefficients of a smooth scheme $X$ is generated multiplicatively by Picard group (page 18). Is this claim true ? ...
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Sobolev extension: "we can arrange for the support of $\bar u$ to lie within $V\supset\supset U$". How, exactly?
My questions: Is this sort of what Evans was referring to when he claims we can "arrange" for the support of $Eu$ to be compact? If not, what did he mean? How can I easily see that we can &...
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