This tag is used if a reference is needed in a paper or textbook on a specific result.

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25 views

Reference request: has this semilinear version of Navier Stokes been studied?

I have noticed that the Navier Stokes equations can be written as a semilinear symmetric first order system $$ u_t+A_1u_{x_1}+A_2u_{x_2}+A_3u_{x_3} = f(u) $$ for a 9 by 1 vector $u$ containing the ...
6
votes
1answer
107 views

What is the Essential Reason that allows a PTAS for the EUCLIDEAN TSP?

Questions: Is there some understanding of the reason, why the euclidean TSP allows a PTAS, whereas the metric TSP in general does not and, is the PTAS stable under sufficiently small perturbation ...
3
votes
0answers
96 views

Generalization of notion of convexity

I am searching for the correct term for the following, if it exists. A set $X\subset \mathbb{R}^2$ is called $r$-convex if for any two points $x_1, x_2\in X$ such that there exists an arc of radius ...
6
votes
1answer
109 views

Properties of the time integral of Wiener process

Let $W_t$ be a Wiener process and consider the time integral $$ X_T:= \int_0^T W_t dt $$ It is often mentionend in literature that $X_T$ is a Gaussian with mean 0 and variance $T^3/6$. I am ...
0
votes
0answers
77 views

Jacobian change of basis matrix for different dimensions

I am considering a real Lie group $G$ acting transitively on an open set $U$ in a real Euclidean space of lower dimension. Given a smooth, compactly supported function $f: U \rightarrow \mathbb{R}$ ...
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0answers
78 views

Could one recover the relative K-theory from the quotient derived category?

Let $A\to B$ be a full embedding of exact categories that induces an embedding $D^b(A)\to D^b(B)$. My question is: what can one say about the relation of the homotopy cofibre $K(A)\to K(B)$ (the ...
0
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0answers
77 views

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?
1
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0answers
61 views

K-theory of ringed spaces (including henselian and formal schemes); excision and Mayer-Vietoris

Given a ringed topological space $S$ one can easily define its K and K'-theory as the K-theories of the categories of locally free sheaves and of the category of coherent sheaves on it, respectively. ...
4
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0answers
77 views

$SL(n) \times SL(n)$-invariants of $m$-tuples of matrices

I work over field of complex numbers. Let $G=SL(n) \times SL(n)$, and $(A,B) \in G$ acts on $m$-tuples of matrices $M_{n \times n}(\mathbb{C})^{\oplus m}$ as follows $$ (A,B) \cdot (M_1, \ldots, M_m) ...
6
votes
0answers
62 views

When were bordered Heegaard Floer homology's DA bimodules invented?

This is less of a strictly mathematical question and more of a reference request. In their paper "Bordered Heegaard Floer Homology (http://arxiv.org/pdf/0810.0687.pdf)," Lipshitz-Ozsvath-Thurston ...
3
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1answer
224 views

What year was Hechler forcing created?

Hechler forcing is described on page 278, Jech. Does anyone know when Hechler forcing was first used in a publication?
4
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0answers
136 views

Universal property of module categories over monads

Let $T$ be a monad on a cocomplete category $\mathcal{C}$. Let's assume that $T$ preserves reflexive coequalizers (or something weaker?). Then the category of $T$-modules $\mathsf{Mod}(T)$ is ...
3
votes
1answer
73 views

Extremal graph theory for directed graphs

In extremal graph theory, there are results such as $$t(C_4,G)\geq t(K_2,G)^4,$$ where $G$ is an undirected graph, $C_4$ is a cycle graph on 4 nodes, $K_2$ is a complete graph of $2$ nodes, and ...
1
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0answers
73 views

Is there inverse FFT algorithm for Fourier transform of a integer-valued random variable?

In many applications, it is possible to derive an explicit expression for the Fourier transform of a random variable $X$ $$\varphi (\theta ) = \sum\limits_{n = 0}^\infty {{p_n}} {e^{in\theta }}$$ ...
3
votes
1answer
81 views

Reference for Frobenius’s proof of Schur’s finite version of the Rogers - Ramanujan identities

In his paper “Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche” I. Schur has stated that Frobenius has communicated to him a simple direct proof of his finite version of the ...
0
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0answers
39 views

First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric

This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions. We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ ...
5
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0answers
70 views

Comparison of K-groups of (affine) singular schemes with K'=G-groups

It is well known that Quillen K-theory coincides with $K'=G$-theory for regular schemes, and can be distinct from it for singular ones. Are there any methods for studying this distinctions? In ...
3
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0answers
61 views

Cancellations in products of two elements of a hyperbolic group

Let $G$ be a non-abelian free group with the standard generating set and the corresponding word metric. If we take two elements $g,h\in G$ and compute their product $gh$, some letters might cancel, ...
1
vote
1answer
92 views

On the geometry of roots of a sum of complex linear fractions

I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form $$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$ where the $a_j$'s are nonzero complex ...
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0answers
61 views

Reference Request: Algebraic Serre's Duality Theorem for Curves

Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne ...
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4answers
174 views

Bruhat order and Schubert cycles

I am looking for a good (textbook) reference for the basic fact (due to Chevalley) that for every semisimple Lie group $G$ (without compact factors) with Weyl group $W$, the Bruhat order on $W$ ...
0
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0answers
57 views

Reference request: Heat kernel regularity near the boundary

Let $D$ be a domain in $\mathbb{R^d}$ and $p(t,x,y)$ be the heat kernel of $D$ (for the Dirichlet problem). I was told that if the boundary of $D$ is real-analytic, then the function $y\mapsto ...
3
votes
1answer
161 views

References for von Neumann Algebras

I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in ...
0
votes
1answer
63 views

reference request: trace/lifting operator for $L^{\infty}$ data in bounded $\Omega\subset R^d$

I know the answer to my question must be somewhere in the literature. Probably in [Adams-Fournier], [Dautray-Lions] or something alike, but I don't have access to a library right now so I'll ask ...
2
votes
2answers
145 views

If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?

Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post). Basically following some ideas of W. Lawvere (but not his ...
5
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0answers
360 views

Different approaches to the multiverse of sets

There are some different approaches to the multiverse of sets, in particular: 1) The approach by Woodin, 2) The approach by Sy Friedman, ..., 3) The approach by Hamkins. I wonder to know if ...
0
votes
1answer
60 views

Laplacian matrix of a graph with negative weights

I am trying to calculate the Laplacian and Adjacency matrix of a graphs for positive and negative weights. If a graph be simple with only non-negative weight it is easier. But in my graph I have some ...
2
votes
0answers
57 views

Genericity of maps which are transverse when restricted to a submanifold

Let $M$ and $N$ be smooth manifolds, and $A\subset M$, $B\subset N$ be smooth embedded submanifolds. I am looking for a reference for a theorem on the following lines: The set of smooth maps $h\in ...
4
votes
2answers
223 views

Reference for $p$-adic Hodge theory with coefficients

Let $K$ be a $p$-adic field and $L$ be a finite or infinite extension (maybe algebraic ?) of $\mathbb{Q}_p$. Is there a reference for $p$-Hodge theory for representations $\rho : Gal_K \rightarrow ...
5
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0answers
388 views
+50

Continued fraction representation of Zeta

A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any. I found this at arxiv, but it doesn't apply to Zeta.
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0answers
51 views

Bases of a matroid such that their complement is an independent set

Let $M$ be some matroid on $[n]$ with set of bases $\mathcal{B}$. I am interested in the subset $\mathcal{B}' \subseteq \mathcal{B}$ of bases $b \in \mathcal{B}$ with the property that $[n] \setminus ...
1
vote
2answers
252 views

How to prove $\mathop {\lim }\limits_{x \to \infty } \sum\limits_{{f_x}(p) = 1} {\frac{1}{p}} = \ln 2$ for $p \le x$?

Let ${f_x}(m) = \sum\limits_{\left. p \right|m} {{f_x}(p)}$ be a strongly additive function on positive integer number $m$, where $p$ is a prime number. Set $${f_x}(p) = \left\{ ...
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0answers
55 views

Reference request for the irreducibility of the adjoint representation of $SU(n)$ [closed]

I would like to quote the following fact: "The adjoint representation of $SU_n$ on its Lie algebra $\mathfrak{su}_n$ is irreducible." Do you know any standard reference?
6
votes
2answers
178 views

Literature on “real” $C^*$-algebras

I am trying to get a better understanding of "real" $C^*$-algebras. I encountered them in the paper D. Voiculescu, Dual algebraic structures, J. Operator Theory 17(1987), 85-98, which cites G.G. ...
9
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1answer
294 views

Applications of SCH outside of set theory

Recall that the Singular Cardinals Hypothesis (SCH) says that if $\kappa$ is a singular cardinal and $2^{cf(\kappa)}<\kappa,$ then $\kappa^{cf(\kappa)}=\kappa^+.$ Clearly it has many applications ...
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0answers
68 views

Exposition of the Calabi complex

I am interested in a complex derived by Eugenio Calabi in his article "On compact Riemannian manifolds with constant curvature". The complex is referenced as "Calabi complex" in various citing ...
4
votes
1answer
96 views

Generalized permutahedron and random polytopes

The Birkhoff polytope $B_n$ is defined as the convex hull of the set of permutation matrices, which gives us the set of doubly stochastic matrices. A concept which is intimately related is that of the ...
4
votes
2answers
125 views

Embedding a linearly ordered free monoid into a linearly ordered group

A linearly ordered (shortly, l.o.) monoid is a triple $\mathbb M = (M, \cdot, \le)$ for which $(M, \cdot)$ is a (multiplicatively written) monoid and $\le$ is a total order on $M$ such that $xy < ...
5
votes
2answers
326 views

Looking for paper: The Cauchy integral by M. Privalov

I am looking for a paper titled The Cauchy integral by M. Privalov (Saratov, 1919). The paper is written in Russian. It is being cited (for instance) by A. Kolmogorov in the paper Sur les fonctions ...
3
votes
4answers
342 views

Reference for Kronecker-Weyl theorem in full generality

The Kronecker-Weyl theorem asserts the following: fix real numbers $\theta_1,\dots,\theta_d$, and consider the infinite ray $t(\theta_1,\dots,\theta_d)$ $(t\in\Bbb R)$ inside the $d$-dimensional torus ...
2
votes
1answer
240 views

Looking for paper: Weil's original 1952 “Sur les formules explicites de la théorie des nombres premiers”

I am looking for a source (preferably online) for Weil's original 1952 paper on the explicit formula. I am aware of an english translation available here, but would like to have access to the original ...
7
votes
4answers
457 views

Conjugation Quandles and… “Quandle-Groups”? From quandles to Groups

This question is already asked MathSE A quandle $(Q,*,/ )$ is a idempotent right-distributive and right invertible structure. 1) $a*a=a$ 2) $(a*b)*c=(a*c)*(b*c)$ 3) $(a*b) ...
3
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0answers
81 views

Bicategorical limits with parameters

(This question was asked in http://math.stackexchange.com/questions/741334/bicategorical-limits-with-parameters with no answer.) Let $F(-,-)\colon \mathcal{A}\times \mathcal{B}\to \mathcal{C}$ be a ...
2
votes
1answer
157 views

Classical theory for the incompressible Euler equation (reference request)

I have recently been interested in the incompressible Euler equation, but since I am new to the topic, I would like to inquire what are the standard sources/references (for self-study) regarding the ...
7
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0answers
99 views

Algebraic construction of the modular representation of $\mathrm{SL}_2(\hat{\mathbf Z})$

The answer to this question is probably to be found in the theory of automorphic forms, but (I don't know much about it and consequently) after some tries, I did not catch it. Thus I'd be grateful if ...
4
votes
1answer
110 views

Graph presentation of Lexicographic shifts

Consider a finite alphabet $\{0,1, \ldots, n-1\}$. Let $\Sigma_n = \mathop{\prod}\limits_{j=1}^{\infty}\{0, \ldots n-1\}$ be the set of infinite one sided sequences and $\prec$ the lexicographic ...
3
votes
1answer
142 views

Understanding a particular approximation for Stirling's number of the second kind

I noticed and employed (without a problem) an approximation for Stirling's number of the second kind found on Wikipedia (http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind), in ...
3
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1answer
52 views

Reference request: results on the asymptotic distribution of singular values related to a random orthogonal matrix

Let $Q$ be a random variable taking as its values the set of $n \times k$ real matrices with orthogonal columns, and whose distribution is the Haar measure on the Stiefel manifold $O(n)/O(n-k)$. This ...
4
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0answers
112 views

Is there a version of Serre's modularity conjecture for projective representations?

Serre's modularity conjecture asserts that a continuous odd irreducible representation $$\overline{\rho} : G_\mathbb{Q} \rightarrow \mathrm{GL}_2(\mathbb{F}_q)$$ must be modular, in the sense that ...
0
votes
0answers
46 views

Discrete Fourier tranform on $L^2(\mathbb{R})$

I'm studying on the following construction: For $\lambda\in\mathbb{R}$, denote $$Y_{\lambda}=\left\{g\in L^{2,loc}(\mathbb{R})\,:\,g(t+2\pi)=e^{2\pi i\lambda}g(t)\right\}$$ We give to $Y_{\lambda}$ ...