Newest Questions
162,007 questions
2
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views
$\text{div}(\mathbf {A}\nabla u)=0$ with bounded $\mathbf A$: least Holder continuity of $u$?
Let $u\in H^1(B_1)$ be a weak solution to $$\text{div}(\mathbf {A}\nabla u)=0 \qquad\text{in }B_1$$ where $\lambda \mathbf I\le\mathbf A\le\Lambda\mathbf{I}$. What is the least Holder continuity of $u$...
- 41
0
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0
answers
53
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Sharpness of $L^1 - L^2$ inequality on Gauss space
Talagrand's $L^1-L^2$ inequality states that if $f \colon \mathbb{R}^n \to \mathbb{R}$ is a smooth enough function, we have for the canonical basis $\{e_i\}$ that
$$
\mathrm{Var}(f) \leq C_1 \,
\sum_{...
- 396
2
votes
0
answers
105
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Homotopy class of certain loops in $\mathit{SO}(n)$
I'm wondering if there's any known formula or algorithm for computing the class of a loop in $\pi_1(\mathit{SO}(n))$ (say, for a sufficiently large $n$). In particular, I have a family of such loops ...
- 21
2
votes
0
answers
85
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Finite and faithfully flat morphisms of Huber Rings
I am currently studying the notes of Kiran Kedlaya for Arizona Winter School 2017 on Perfectoid Spaces.
Link : https://swc-math.github.io/aws/2017/2017KedlayaNotes.pdf
I am stuck at Exercise $1.1.6$, ...
3
votes
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answers
57
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Does a monoidal "reflective" adjunction induce adjunctions on module categories?
Let $F\colon (\mathcal{D},\otimes_{\mathcal{D}},1_{\mathcal{D}})\to (\mathcal{C},\otimes_{\mathcal{C}},1_{\mathcal{C}})$ be a (strong) monoidal functor and let $G$ be right adjoint to $F$. Then $G$ ...
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-1
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1
answer
133
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Can we have a downshifting elementary embedding in stratified ZF?
If we work in Stratified $\sf ZF$ (i.e. $\sf ZF$-$\sf Reg.$ but Separation and Replacement replaced by their stratified instances, and infinity written in a stratified manner), then:
is it ...
- 12.4k
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votes
0
answers
41
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Estimate on asymptotics of coefficients in BCH formula
I am interested in quantitative estimates on the possible decay of coefficients in the Baker–Campbell–Hausdorff (BCH) formula for matrix Lie groups/Lie algebras. I haven't been able to find anything ...
- 449
1
vote
0
answers
117
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Explicit constants in exponentially weak ABC conjecture
The ABC conjecture states that for any $\epsilon >0$, there is a constant $K_\epsilon$ such that if $a$, $b$, and $c$ are relatively prime integers such that $a+b=c$, then $$c \leq K_e(\...
- 7,766
2
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0
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28
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Separation in perfect compactifications
I refer to the book Isbell, Uniform spaces, 1970.
p.97. Definition. A set $C$ separates $A$ and $B$ in a space $X$ if $X\setminus C=M\cup N$ where $M,N$ are separated sets containing $A,B$. And $M,N$ ...
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3
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78
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Is there a universal LCCB (locally compact, countably based) sober space?
By LC, I mean that every neighbourhood (of a point, or compact subspace) contains a compact neighbourhood.
Every locally-closed (open $\cap$ closed) subspace of a LC space is LC. Similarly for locally-...
- 3,652
2
votes
0
answers
27
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Path-wise uniqueness of SDE driven by Poisson process (or more generally by Lévy process)
Consider the SDE for the right-continuous process $(X_t)$ taking values in $\mathbb R^n$ :
$$dX_t=b(X_{t-})dt+\int_{|z|<1}a\big(X_{t-},z\big)\tilde{N}(dt,dz),$$
where $b:\mathbb{R}^n\longrightarrow ...
- 1,673
-3
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83
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Aubin-Lions lemma: Can I replace the interval $[0,T]$ with the interval $[-T,T]$? [closed]
Let $X_0$, $X$, and $X_1$ be three Banach spaces such that
$
X_0 \subset X \subset X_1,
$
and suppose that:
$X_0$ is compactly embedded in $X$,
$X$ is continuously embedded in $X_1$.
For $1 \leq p, q \...
2
votes
0
answers
104
views
Lifting automorphic forms on Shimura subvarieties to automorphic forms on the Shimura variety
Forgive my ignorance, I am new to the subject. I have a need for determining the existence of certain lifts of elliptic modular forms to Hilbert modular forms (over a real quadratic field). The ...
- 51
2
votes
0
answers
71
views
Name for integral representation of Riesz potential
Let $\phi:\mathbb{R}^d \rightarrow \mathbb{R}$ be a sufficiently nice (e.g. Schwartz) radial function . Then it is classical by scaling that the Riesz potential $|x|^{-s}$, for $s>0$, may be ...
- 893
1
vote
0
answers
23
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Relation between local-to-global principle in stratification and topology of the Balmer spectrum
The context of my question is the theory of stratification of a tensor triangulated category via Balmer-Favi support recently developed by Barthel, Heard and Sanders in their paper "...
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