All Questions
5,074 questions with no upvoted or accepted answers
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345
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maximum principle on compact manifolds with boundary
Let us consider the equation $Lu + f(u) = 0$ on a compact manifold $\overline{M} = M \cup \partial M$ with boundary, with Dirichlet boundary conditions. $L$ is a linear elliptic operator, and $f$ ...
- 11
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70
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$\Gamma$ cohomology of principal series
Let $G$ be a noncompact connected real semisimple Lie group with finited center. Let $\Gamma$ be a cocompact discrete subgroup of $G$, and let $P$ be a parabolique subgroup
with Langlands ...
- 1,111
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284
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Convergence proof for fictitious play!
In "Fictitious play property for games with identical interests" by D. Monderer and L.S. Shapley, the convergence of fictitious play to a Nash equilibrium is proved for a potential game with players ...
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142
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Laumon's "Sur les modules de Krichever"
I'm looking for a copy of the preprint mentioned in the title.
Thank you very much in advance for any help!
- 2,029
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237
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Integral Cohomology of Symmetric Groups
Does anybody know a reference for the explicit description of the integral cohomology ring of $S_5$ and $S_6$. I can not find them anywhere in the internet. For $S_4$, I found C. B. Thomas's nice ...
- 131
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234
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Sum-epimorphisms and prod-monomorphisms
Sum-epimorphisms
A longer time ago I have introduced the bi-onto maps for the topological category. Let me formulate here its general categorical definition:
DEFINITION 1 ...
- 7,500
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561
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The fundamental group of the complement of codimension 2 submanifold
Suppose that $M^n$, $V^{n+2}$ are connected, compact smooth manifolds.
Let $f\colon M^n\to V^{n+2}$ is a smooth embedding.
Let $K_f$ be the kernel of the inclusion induced homomorphism $\pi_1(V-f(...
- 11
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120
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Fractional Poincare inequality on closed manifold
Let $u \in H^{\frac 12}(M)$ on a compact closed Riemannian manifold. Can someone refer me to a source where the inequality
$$\lVert u - \bar u \rVert_{L^{2^*}} \leq C|u|_{H^{\frac 12}}$$
is proved, or ...
- 11
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100
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Summing a function at integer points
For a real function $f$ defined on the reals, and real $y$, define the 2-way infinite sum
$$ F_f(y) = \sum_{i\in\mathbb Z} f(y+i). $$
If $F_f(y)$ is defined for all $y$, it is periodic of period 1.
...
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134
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Reference Request: Category of explicit maps between primitive recursive sets?
[Edited]
Let $\mathsf{PR}$ be the category defined as follows:
Choose a specific presentation of Primitive Recursive Arithmetic, that is, with a specific set of terms for primitive recursive ...
- 437
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173
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Property theories
Property theory is, as I have understood it, first of all characterized by an attempt to approach naive comprehension type-freely and without committing to extensionality.
There is e.g. the work of ...
- 3,574
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66
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Quotient groups of "Abelian-times-compact", what are they called?
In what I am doing now this class of groups appears all the way: (Hausdorff) quotient groups of $A\times K$, where $A$ are locally compact abelian groups, and $K$ compact groups.
I wonder, if this ...
- 7,426
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74
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Equivalent of Lauricella $F_D$ on an elliptic curve?
Lauricella's hypergeometric function $F_D$ is related to (weighted) configurations of points on $\mathbb{P}^1$. I am looking for generalizations to weighted point configurations on an elliptic curve. ...
- 111
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115
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Are the Standard Quantum Groups Coordinate Rings Noetherian?
Are the standard quantum groups $C_q[G]$ Noetherian and if so what is a standard reference?
- 163
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76
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Estimation of the number of local extrema
I have a question about a simple proposition, I suppose that this is something
well-known or a special case of something well-known:
Let $D\subset\mathbb{R}^{2}$ be the closed unit disk in the plane ...
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163
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Help in understanding "Local well-posedness for the Maxwell-Schrodinger system"
Is there someone who knows the following paper
"Local well-posedness for the Maxwell-Schrodinger system" by M.Nakamura and T.Wada.
I'm trying to study it but I've some doubts. In particular I'm not ...
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226
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What is the state of the art of visualizing bifurcations for "difficult" dynamical systems?
This question is related to my other recent question on MO (although I am not confident that the dynamical system described in that other question is actually "difficult," in the sense that I will ...
- 709
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70
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Covering number of the range of a function
I have come across the need to know a bound on a certain curious quantity: the covering number of the range of a continuous function $f: D \rightarrow \mathbb{R}^n$, where $D \subseteq \mathbb{R}^m$. ...
- 183
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163
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Reference : Special case of Banach-valued function integration by parts
Let $u \in L^p (0,T; L^1(\Omega))$ with $\partial_t u \in L^p(0,T; L^1(\Omega))$ and $v \in L^q (0,T; L^\infty(\Omega))$ with $\partial_t u \in L^q(0,T; L^\infty(\Omega))$ (with $1/p+1/q=1$ and $p \in ...
- 171
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110
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Reason for the Choice of Line Parameters in the Radon Transform
Why are the lines, over which the integrals in a Radon Transform are calculated, apparently always parameterized as $L(t,\phi,\alpha) := (t*\sin(\alpha)+s*\cos(\alpha),-t*\cos(\alpha)+s*\sin(\alpha))$,...
- 13.2k
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88
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Regularity of solutions to $u' + Au = f$ for nonlinear monotone operator $A$
Consider the equation
$$u' + Au = f$$
$$u|_{\partial \Omega} = 0$$
$$u(0) = u_0$$
where $A:L^p(0,T;W^{1,p}_0) \to L^q(0,T;W^{-1,q})$ is some monotone nonlinear operator (with additional assumptions). ...
- 93
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418
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Defining density of a random function using Radon-Nikodym Theorem
Let $(\Omega,\mathbb{F},P)$ be a probability space and $E$ be an infinite dimensional Banach space and $\mathbb{B}$ be the $\sigma$-algebra of Borel subset of $E$.
Let $X$ be random function defined ...
- 213
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237
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Proper monomorphisms in complex analytic spaces
In the algebraic geometry of schemes, we know that monomorphisms which are universally closed (= every pullback is a closed map) and of finite type are closed immersions. See Gortz, Wedhorn "Algebraic ...
- 163
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222
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Reference for a special case of the Hanson-Wright inequality
I would like find tail bounds for the expression
$$
\begin{align*}
\left|\left\langle a,\phi\right\rangle \left\langle \phi,b\right\rangle -\left\langle a,b\right\rangle\right|,
\end{align*}
$$
where $...
- 215
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85
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Kontsevich integral for 2-bridge knots
Are there any articles that explain a formula for Kontsevich integral of 2-bridge knots?
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71
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Name for generalization of bivariate weighted-homogeneous polynomials
A polynomial $f = \sum_j c_j X^{\alpha_j}Y^{\beta_j}\in\mathbb K[X,Y]$ is said weighted-homogeneous if there exist $p$, $q$ and $d$ (where $p$ and $q$ are not both $0$) such that $p\alpha_j+q\beta_j=d$...
- 456
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138
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Noncommutativization of fixed point theory
What papers or references have been devoted for a noncommutativization of "Fixed point theory". Here the terminology Noncommutativiztion, as usual, indicates to that famous table with 2 columns: ...
- 366
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196
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Reference for a proof of a projective representation of $A_6$
This question is copied from math.stackexchange, in hope that it might get some attension.
I want to understand the proof of
There is a projective representation of $A_6 \hookrightarrow PSU(3).$ ...
- 111
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243
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A (different) foliation arising from Hopf fibration
In this question, first we fix an isomorphism between $TS^{3}$ and $S^{3}\times \mathbb{R}^{3}$.(To be more precise we consider the global trivialization of $TS^{3}$ with help of $3$ global ...
- 366
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193
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Gauss's Cirlce Problem #lattice points in circle
Can someone link me the proof that $E(r)/r^{1/2}$ -> infinity when $r$->infinity?
Where #lattice points in circle = $Pi*r^2+E(r)$
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442
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Pull-back of the tautological vector bundle and the number of trivializations
I've heard about the following result: for each two natural numbers $d,n\in\mathbb{N}$ one can find a number $k\in\mathbb{N}$ with the following property: for each CW-complex $X$ with $\dim X\leq d$ ...
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66
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Non-Convex Polygons with "Antipodal Visibility"
by "antipodal visibility" of planar, simple polygons I mean the following property:
if two points $p$ and $q$ on the polygon's boundary divide the polygon's boundary into two polylines of equal length,...
- 13.2k
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176
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Lyapunov stability, nonlinear system
Please, is there any reference for proposition below or does it perhaps follow from a standard fact? I've got it for some other problem but I actually do not know how to comment it in my article.
...
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359
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Thickness of the category of perfect complexes with finite length homology
Let $R$ be a commutative Noetherian local ring and let $D(R)$ be the derived category of $R$-modules. Recall that a chain complex $C_\bullet$ of modules over $R$ is called perfect if it is isomorphic ...
- 3,101
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179
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Which "concrete" morphisms of varieties and motives induce bijections of their lower Chow groups?
This question is a continuation of Varieties with Chow groups supported in positive codimension: examples and properties?
What examples are known of morphisms of varieties and Chow motives (say, over ...
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96
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Reference needed for Hilbert-Schmidt result regarding basis of $V \subset H$
I am seeking a reference that says:
If $V \subset H \subset V^*$ is a Gelfand triple with all spaces Hilbert spaces and if $V \subset H$ is a compact embedding, then there is a basis of $V$ which ...
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191
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Why $D^b(S)\cong D^b_{\text{Car}}(\text{cosq}(X\rightarrow S))$?
Let $p: X\rightarrow S$ be a map between topological spaces and we can construct the simplicial space $\text{cosq}(X\rightarrow S)$ where $X_0=X$, $X_1=X\times_S X$ and
$$
X_n=\underbrace{ X\times_S \...
- 9,019
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234
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Strong Dependence
I don't know if this definition has been already given.
Suppose $X$ and $Y$ are two random variables over finite alphabets $\mathcal{X}$ and $\mathcal{Y}$. We say $Y$ is strongly dependent on $X$ if ...
- 1,109
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163
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Asymptotic decay for the inhomogeneous Schrödinger equation
Let $H$ be an Schrödinger operator $(-\Delta+V(x))$ with a radially symmetric and smooth potential and $H$ is e.s.a. on $C^\infty_0(\mathbb{R}^n)$, furthermore let $\lambda$ be an element of the ...
- 428
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285
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Davenport's proof that almost all integers are the sum of 4 cubes
Where can I find a pdf that describes Davenport's proof that almost all integers are the sum of $4$ cubes?
- 1,890
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Exactness of the relative de Rham complex restricted to subschemes
I think that the statement below about relative de Rham complex is true (am I wrong?) If it is the case, a reference would be very helpful. (I admit that the statement sounds somewhat technical and ...
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223
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Reference on calculation of 2nd cohomology group
Let $G$ be a finitely generated, infinite, countable discrete nonamenable group with zero first Betti number, I.e., $H^1(G, \ell^2(G))=0$, e.g., $G=F_2\times F_2$, the product of free groups of two ...
- 1,528
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139
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First Description of how to Remove Radicals from Equations
Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ? ...
- 13.2k
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222
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adjoint representation of 2-Lie groups
Baez and Crans in their paper on Lie 2-algebras refer to adjoint representations of Lie 2-groups but don't say much, as far as I can tell, except to say that such a representation acts on a 2-Lie ...
- 1,710
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Non-Abelian Fourier Analysis
I'm currently thinking to generalize a known result on abelian groups to non-abelian groups. This is the problem. Fix an abelian group $G$. We know that:
$\mathbb{E}_{\chi\in \hat{G}}\chi(g)=\left\{\...
- 901
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90
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Jumps of jump diffusions
Let $W$ be a Brownian motion and $N$ a Poisson random measure defined on $\mathbb R_+ \times \mathbb R_0^n$ ($\mathbb R_0^n:=\mathbb R^n-\{0\}$) with compensator $\tilde N(dt,dz):= N(dt,dz) - dt \,\nu(...
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269
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$L^{p}(\mathbb R)\subset L^{1}(\mathbb R) \ast L^{p}(\mathbb R), (1< p< \infty)$?
Let $\mathbb T$ be a circle group.
In 1939, Salem, has shown that, every member of $L^{1}(\mathbb T)$ can written as a product(convolution) some other two members of $L^{1}(\mathbb T),$ that is, $L^...
- 1,051
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437
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A question related to the Grauert semi-continuity theorem
Let $f\colon X\to Y$ be a proper holomorphic map of complex analytic manifolds. Assume $f$ to be submersive for simplicity, but probably it is not important. Let $\mathcal{F}$ be a coherent sheaf on $...
- 21.8k
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61
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Generalizing Concepts of Planar Euclidean Geometry to Symmetric TSP-Instances
To me it seems possible, to successfully look at symmetric TSP instances from a geometry-point of view.
Examples are:
the diagonals of the convex hull of a set of points in the euclidean plane; ...
- 13.2k
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226
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Is this function space a "classical" Sobolev space?
I apologise if this is indeed classical but my functional analysis is quite rusty...
My work recently led me to the norm: $(\|u\|_p)^p=\int_D (|u|^p+|\Delta u|^p)d\lambda$ where $D$ is the unit disk ...
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