Newest Questions
162,007 questions
6
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Convergence of mollifiers of a Lipschitz function on a codimension 1 subspace
Let $f:\mathbb{R}^2\to \mathbb{R}$ be $L$-Lipschitz. Let
$f_\varepsilon:=f*\eta_\varepsilon$ be its smooth $\varepsilon$-mollification, where
$\eta_\varepsilon(x)=\frac{1}{C\varepsilon^2}\eta(|x|/\...
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0
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47
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Index of singular point for 2nd order ODE
There exists classification of equilibrium points for 2nd order ODEs like
$$
\ddot x = f(x, \dot x), \quad \text{where} \quad x \in \mathbb{R}.
$$
The classification includes stable/unstable nodes, ...
- 141
4
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0
answers
78
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On Schuricht and Schönherr approach for proving the divergence theorem on general Borel sets
This question stems from a ZBmath search I did yesterday evening, and it is somewhat related to the following MathOverflow question: "On which regions can Green's theorem not be applied? ".
...
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2
votes
1
answer
314
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Identity for A000123
Let
$a(n)$ be A000123 (i.e., number of binary partitions: number of partitions of $2n$ into powers of $2$), whose ordinary generating function is $$ \frac{1}{1-x} \prod\limits_{j=0}^{\infty} \frac{1}{...
- 5,890
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0
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78
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Existence of normal element whose spectrum coincides with a realizable spectrum
Let $A$ be a $C^*$ algebra. Assume that $x\in A$ is a given element.
Does there exist a normal element $n\in A$ whose spectrum coincides with the spectrum of $x$ namely $\sigma(n)=\sigma(x)$? If the ...
- 616
4
votes
1
answer
332
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An elementary problem on univariate polynomials
Suppose that $p(x) = \sum_{i=0}^d a_i x^i$ is a univariate polynomial of degree $d$ over the field of real numbers. Suppose that $d > 2$, and that $a_d, a_{d-1} \not = 0$.
Assume that for some $\...
- 379
1
vote
0
answers
45
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Subharmonic functions of general bilinear forms
It is well known that $|\nabla u|^2$ is subharmonic whenever $\Delta u = 0$. This is the usual Bochner identity.
I am looking for generalizations of this in the following sense: Let $u$ be a smooth ...
- 537
13
votes
1
answer
594
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Where can I find a reference table for ordinal arithmetic?
I am working on a calculator for ordinal arithmetic.
Ordinal arithmetic is extremely tricky. So much so that there have been academic papers on the very subject that got some results wrong. Not to ...
- 231
5
votes
0
answers
67
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When is the Kobayashi metric Riemannian?
Let $X$ be a complex manifold. On the tangent space $T_X$ we have the Kobayashi infinitesimal pseudonorm $F_X$, which is in general upper semi continuous as a function on the total space of $T_X$, and ...
- 8,032
1
vote
0
answers
109
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Blockwise measure-positive subsets of $\mathbb{N}$
$\def\N{\mathbb{N}}$There are different notions of when a set $A\subseteq \N$ has "positive measure", to which I want to compare a third notion. We say that $A\subseteq \N$ is
blockwise ...
- 51.1k
2
votes
0
answers
63
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Are there Chern number inequalities for symplectic manifolds?
There are some inequalities of Chern numbers of complex manifolds or algebraic varieties. For example, for surfaces of general type we have the Bogomolov-Miyaoka-Yau inequality and the Noether ...
- 243
3
votes
1
answer
107
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Locally compact topology on subsets of Cantor set
Cross-posting this question from MSE.
Let $C\subseteq \mathbb R$ denote the Cantor set and let $A\subseteq C$ be dense with $|A| = |\mathbb R|$, and assume $A$ doesn't contain its infimum. Is there a ...
- 193
2
votes
0
answers
81
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Image of the evaluation map of family rational curves
Let $X$ be a smooth projective Fano variety of dimension $N$. Let $Y$ be a component of $\text{Mor}^d(\mathbb{P}^1, X)$. Let $V$ be a irreducible component of the closed subset of $Y$ consisting non-...
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3
votes
1
answer
86
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Hermite-type convex interpolation
Let $f : [0, 1] \to \mathbb{R}$ be a smooth strictly convex function.
Let $0 \leq x_1 < \dots < x_n \leq 1.$
I am interested in whether there exists a polynomial $p$ such that it is convex on $[...
- 105
2
votes
0
answers
61
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Name of a certain type of "generalisation"
This question is sort of metamathematical, so I hope it's appropriate for the site.
Let's say that Proposition A says that all objects satisfying property X have property Y. Now say that Proposition B ...
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