All Questions
5,076 questions with no upvoted or accepted answers
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Heat asymptotics
Consider a compact manifold $M$ with smooth boundary, with either the Dirichlet or the Neumann boundary conditions. Consider a (time-dependent) open ball $B_t \subset M$. Given a fixed $u \in L^1(M)$, ...
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75
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A source for integral operators in the context of Arthur-Selberg trace formula
Could you suggest a textbook for integral operators
(in the context of Arthur-Selberg trace formula)?
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358
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Boundedness of heat semigroup on $L^1(\Omega)$
On a bounded domain $\Omega \subset \mathbb{R}^n$ with smooth boundary, consider the Laplacian $-\Delta$ with either the Dirichlet or Neumann boundary conditions. More generally, one can also consider ...
- 1
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83
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Good covering of a (singular) curve in a complex surface
Let $W$ be a $2$-dimensional complex manifold and $C\subset W$ a compact complex curve (possibly singular). I would like to know a reference for the following fact: there exists a collection $\{V_j\}...
- 1,205
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115
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Riemannian simplicial complex and quasi-conformal complex
In this paper by Robert Young, the author defines
We define a riemannian simplicial complex to be a simplicial
complex with a metric which gives each simplex the structure of a riemannian
...
- 447
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584
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When an integral with respect to a Poisson point process is finite?
Let $N(ds,dv)$ be a Poisson measure on $\mathbb{R} _+ \times \mathbb{R} _+$ with intensity $dsdv$. Let $N = \sum\limits \delta_{(s_i,v_i)}$. Assume that $N$ is compatible with a filtration $\{ \...
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57
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References for symmetric α-stable process (SSP) for $a>2$
Many properties of Brownian motion have been extended to SSP's for $0\leq \alpha\leq 2$ and so it is quite easy to find literature on them. However, I am currently studying the SSP for $\alpha>2$ ...
- 5,474
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representing quasicrystal as tilings and appearing frequencies of each tile
Quasicrystal can be fully represented either using projection method or tilings with constraints. For the latter, is there some sort of study on the "appearing frequency" of each tile or even ...
- 867
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54
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majorizing measures for small ball probabilities
This is a reference request. Can Majorizing measures be used to estimate small ball probabilities? Any help would be appreciated.
Thank you.
- 157
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105
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Counting path generating sentences in a specific formal language
Given a formal grammar of a language or an Turing machine of the language, can we count the path that generating sentences of the language?
For example, we know that if the grammar is context-free ...
- 3,104
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210
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Exact diagonalization of tridiagonal centrosymmetric matrices
It is said that one can diagonalize a tridiagonal matrix using the analytical Lanczos method http://arxiv.org/abs/cond-mat/9712283v1. In some references in it, they always say that the starting point ...
- 101
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110
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Proof that Markov shift is pointwise dual ergodic
I am looking for a reference of the proof that a Markov shift is pointwise dual ergodic, I tried google it but with no success.
- 1,594
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137
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SVD of Frechet derivative
This is mainly a reference request. Is there a particular characterization of operators A from a Hilbert space H to itself such that the Frechet derivative A'(u) exists for each $u \in H$ and for any ...
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192
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Thin profinite groups - nonabelian analogues of p-adic integers
Let $p$ be a prime number, $S = C_p$ a cyclic group of order $p$, $G = \mathbb{Z}_p$ the profinite additive group of $p$-adic integers. It is well known that all the closed nontrivial subgroups of $G$ ...
- 11.3k
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153
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extension of function in an abstract metric space
my question is the following.(Maybe my title is not quite proper for this question):
Let $(E,d)$ be a Polish space (or a separable metric space), let $\xi: E\to R_+$ be a Lipschitz function. Now set $...
- 1,835
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268
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Holomorphic vector bundles over $\mathbb{CP}^1$ and elliptic curves
Can anyone suggest a good exposition of the classification of holomorphic vector bundles over $\mathbb{CP}^1$? Also does there exist any analytic or more elementary proof of Atiyah's classification of ...
- 2,106
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66
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construction of four dimensional regular convex polytopes
Could anybody give me a reference book about the explicit construction of the 6 regular four dimensional convex polytopes. I cannot easily find Schläfli's original paper so I am looking for a modern ...
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186
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Repeatedly changing queue behavior
I'm not sure if this question is suited to MO. I will happily delete if not.
Situation
Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose ...
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189
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Action of the (special) orthogonal group on differential forms
I was told that the following facts are true. I am looking for a reference to them.
1) The action of $O(n,\mathbb{C})$ on $\wedge^l\mathbb{C}^n$ is irreducible for any $l$.
2) The action of $SO(n,\...
- 21.8k
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85
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Linkage between homotopy equivalence and identification of algorithms
I vaguely recall that someone says there is linkage between homotopy equivalence and identification of algorithms which may be isomorphic or morphism or something like that,the algorithm may be ...
- 3,104
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369
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K-theory of $\mathbb{RP}^\infty$
can anyone give some reference of K-theory and K-homology of $\mathbb{RP}^\infty$, both $K_0$ and $K_1$.
PS: also posted in stackexchange
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332
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Examples of functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition
there are examples of lacunary functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition.I want to know more examples of those functions,the more the better,...
- 3,104
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75
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The set of (property) elements of a locally compact group is closed
For which properties $(P)$ is the following statement known to be true?
In any locally compact group $G$, the elements of $G$ that satisfy $(P)$ form a closed subset of $G$. In other words, the ...
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351
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Reference: A nowhere vanishing section of a vector bundle is locally split
Well-known fact:
If $(A, \mathfrak{m})$ is a local Noetherian ring, $E$ is a finitely generated free $A$-module, and $e\in E$ is an element not contained in $\mathfrak{m}E$, then $E/eA$ is also a ...
- 7,338
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88
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References for LWP of a NLS Equation
I am studying the LWP of $$i \partial_t \psi + \Delta \psi = \left| \psi \right|^{p-1} \psi + \frac{1}{\left| x \right|^2} \psi$$ in $\mathbb{R}^{1+2}$ given appropriate Cauchy data. It will probably ...
- 516
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100
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Unions of orbits of dimension $\leq n$
Let $G$ be a complex linear algebraic group acting on a smooth complex projective variety $X$ with finitely many orbits. Note that each $G$-orbit is a smooth locally closed subvariety of $X$.
For a ...
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166
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Where are there defined objects between gerbes and bundle gerbes?
Consider a special kind of/something like a gerbe where there is first given local trivialization data with equivalence over 2-fold overlaps but not isomorphism.
Does this exist in the literature?
- 3,880
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112
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Ref request: If an affine subspace $V$ of $\mathbb R^n$ meets an $n$-dimensional polytope $P$, then it meets $P$ in a face of dimension $\le n-\dim V$
Let $P$ and $V$ be, respectively, a bounded full-dimensional polytope and an $m$-dimensional affine subspace of $\mathbb R^n$, and assume $P \cap V$ is non-empty.
Q1. Could you provide me with a ...
- 10.5k
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152
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Chain-complex and Co-chain-complex valued Topological Quantum field theories
My research has led to me considering chain-complex and co-chain-complex valued topological quantum field theories. However, I am unable to find any literature that extensively studies this. Is there ...
user62675
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289
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Third variation of area of a minimal surface
There is a formula for the third variation of area on page 96 of Nitsche's book,
Lectures on Minimal Surfaces, vol. 1 (English version). He says at the bottom of the
page it is good for normal ...
- 1,233
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81
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Sources in unimodular rows
I'm beginning to study more advanced material of module theory and I need to study more about unimodular rows. I would like a good introductory book or pdf speaking about unimodular rows with theorems,...
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549
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Fitting ideal sheaves and determinant bundles
I am working on a problem in algebraic geometry which comes down to a fact in commutative algebra that I am hoping is well-known.
Suppose $F$ is a coherent sheaf on a smooth variety $S$, and that the ...
- 5,857
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240
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On $n$-th prime $\pmod {n}$
Has it been proved or disproved that for any fixed $a\geq 1$ there are infinitelly many primes $p_n\equiv a\pmod{n}$?
I believe i have proved that for every $a\geq1$ there are infinitelly many ...
- 3,876
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107
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Maximum Independent set of sparse graphs with few triangles
Notations used
$\alpha(G) = $ Max sized independent set of graph $G$.
$n(G) = $ Number of vertex in graph $G$.
Theorem (by Ajtai et al.): For a triangle-free graph $G$ and max degree being $\Delta$,...
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234
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On the irrationality measure of generalized Stoneham numbers
Pick non-zero integers $a,b,c$ with $a,b \ge 2$ and let $\xi_{a,b,c}$ be the sum of the series $\sum_{n=1}^\infty a^{-b^n} c^{-n}$ (no restriction is made on the sign of $c$); when $b = c$ and $\gcd(a,...
- 10.5k
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694
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"Descending cohomology, geometrically" by Mazur:
(Exist texts of that talk or related texts: http://ttv.mit.edu/collections/harris60/videos/13881-problem-session-barry-mazur ?) Article: http://www.math.harvard.edu/~mazur/papers/page37.pdf
- 10.8k
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215
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Invariance of the (Liouville-Roth) irrationality measure under rational Möbius transformations
For a real number $x$, we define the (Liouville-Roth) irrationality measure of $x$, here denoted by $\mu(x)$, as the infimum, with respect to the poset $(\mathbb{R}_0^+ \cup \{\infty\}, \le)$, of the (...
- 10.5k
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230
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Is there a translation invariant measure on an infinite dimensional space 'without points'?
This is just a reference request. I thought I'd come across a paper demonstrating that there is a translation invariant measure on an infinite-dimensional space without 'points' whilst browsing the ...
- 2,369
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177
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Existence of special pants decompositions for non-elementary representations into PSL(2,R)
A Theorem by Gallo, Goldman and Porter states the following:
Let $S_g$ be a closed orientable surface of genus $g$ with fundamental group $\Gamma_g$, and fix a non-elementary representation $\rho\...
- 3,749
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158
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symbol map in algebraic K theory
I have a smooth projective morphism $X \to S$ or relative dimension 1 (i.e.
a family of smooth curves over base $S$). There should be a map $H^2(X, K_2) \to H^1(S, K_1) = Pic(S)$ given by integration ...
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327
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Endomorphism ring of a direct sum of tilting modules
I have found that a category of modules over a Lie algebra has an infinite number of (partial) tilting modules and that direct sum of these tilting modules is also an object in this category.
What ...
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473
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Cohomology of bundles and local systems
I'm wondering if there are general techniques to calculate the singular cohomology groups of a fiber space (specifically, a non-smooth elliptic fibration) using methods of algebraic topology. More ...
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575
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Known and unknown about Ramanujan's tau function
What is a good reference for open problems relating to the Ramanujan tau function?
I know about Lehmer's conjecture. I know the following reductions of the problem: the smallest counterexample must ...
- 3,655
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160
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Two Different Representations of Multivariate Bernstein Polynomials
In the literature the multivariate Bernstein polynomial of a function $f:[0,1]^m\rightarrow\mathbb{R}$ is often defined as the following:
$$B_{f,n}(x_1,\dots,x_m)=\sum_{\mathbf{k}\in \{0,\dots,n\}^m}...
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141
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Reference Request: a paper by Yoseloff about a proof of Sperner's Lemma
Dear Overflow,
Apologies in advance if I'm posting this in the bad place, but I was hoping some of you could point out to me a place where I could read online the following paper by Yoseloff, where ...
- 625
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80
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relationship between different function classes
I was wondering if there is a survey of relationship between several different well-studied function classes ?
ps - The question may be vague but I am looking for something along the lines of - http:/...
- 1
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218
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Series of linear maps: on a paper by Evans and Hanche-Olsen
I was reading this paper by Evans and Hanche-Olsen. In theorem 2, there are six equivalent statements given. I write just two of them, which I want to use.
Let $L$ be a bounded self-adjoint
...
- 421
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440
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Foliations in positive characteristic
Ekedahl wrote about foliations in positive characteristic, over the field $\mathbb{Z}/p\mathbb{Z}$ as a subsheaf of the tangent sheaf, that are closed with respect to involution and $p$-power.
My ...
- 1
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71
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products/factoring of two hypergraphs with same vertex set?
all the basic products for graphs have been extended to hypergraphs[1].
is there a concept of a product of hypergraphs with the same vertex set? has this been studied?
normally the hypergraph ...
- 529
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188
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Conjugate subgraphs and (maybe) a generalized Burnside's lemma?
It's rather straightforward, I guess, to define conjugate subgraphs of a graph via its conjugate nodes. (Two nodes $x,y$ are conjugate when there is an automorphism $g$ such that $x = g(y)$.)
...
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