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

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4
votes
1answer
190 views

exact definition of Fiedler vector

For a given N-vertex similarity graph $ G=(V,A) $ the eigenvalues of the unrenormalized (graph) Laplacian may be denoted as $$ 0= \mu_0 \leq \mu_1 \leq ... \leq \mu_N $$ where the corresponding ...
2
votes
2answers
300 views

Irreducible algebraic sets via irreducible polynomials

There are many results about irreducible polynomials over finite fields: we know a cardinality of all irreducible polynomials with given degree, we know explicit examples of irreducible polynomials, ...
2
votes
1answer
143 views

Small object argument for multiple factorization systems

Is there something similar to the small object argument, but related to a chain of factorization systems on a category $\cal C$? It is easy to see that one can give a chain of "generating morphisms" ...
0
votes
0answers
57 views

“Downward closed” relation on a poset

I say that a relation $R$ on a poset $P$ is downward closed if for each $(x,y)\in R$, and $x'\le x$, then $(x',y)\in R$. Is there a reference where this thing is studied, maybe under a different name? ...
12
votes
5answers
513 views

Applications of space filling curves

I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.
3
votes
0answers
38 views

covariant derivative of manifold-valued function and logarithm map

Let $M$ be a Riemannian manifold and $f\colon \Omega\subset \mathbb{R}^d\rightarrow M$ a smooth, i.e. $C^\infty$, function. For any $p\in M$ let $T_pM$ be the tangent space at $p$ and $\log_p\colon U\...
3
votes
0answers
55 views

Characteristically simple locally compact abelian groups

Say a topological group $G$ is topologically characteristically simple if there does not exist a closed subgroup $1 < K < G$ such that $K$ is invariant under all automorphisms of $G$ (here `...
3
votes
1answer
163 views

discrete Grothendieck construction

In "BASIC CONCEPTS OF ENRICHED CATEGORY THEORY", (version Reprints in Theory and Applications of Categories, No. 10, 2005), chapter 4.7 p.75-76, Kelly introduces the "discrete Grothendieck ...
0
votes
2answers
280 views

The Zeta Function Before Riemann [duplicate]

Leonhard Euler studied the function that is now known as the Riemann zeta function. I have not found the notation $\zeta$ in any of the works of any mathematicians prior to Bernhard Riemann's paper On ...
0
votes
1answer
82 views

The pointwise Lipschitz-ness of a function on a dense set, implies its pointwise Lipschitz-ness everywhere?

Some definitions: Let $(M,d)$, $(M',d')$ be metric spaces. For $f:M\to M'$, $x\in M$ and $r>0$, define $$D_r(f)(x):= \sup\{r^{-1}d'(f(x),f(y)): y\in M,\,d(x,y)\leq r\}.$$ Define the pointwise ...
3
votes
1answer
140 views

Are braid groups conjugacy separable?

I would like to re-ask a question that was raised in the comments here: Normal subgroups of braid groups Namely, a group $G$ is called conjugacy separable, if it holds that for every two elements $x,...
4
votes
2answers
219 views

Error estimate in the spectral theorem of compact operators on a Hilbert space

Given a compact self-adjoint operator $K$ mapping $L^2(\mathbb{R}^d) \rightarrow L^2(\mathbb{R}^d)$ as $f \rightarrow \int K(x,y) f(y) d\mu(y)$, let us define its eigenvalues $\lambda_i$ and eigen-...
2
votes
1answer
86 views

About eigen-functions of the Gaussian kernel

If I look at the Guassian kernel function $e^{- \frac {\vert x - y\vert_2^2 }{2 w^2 } }$ for $x, y \in \mathbb{R}$. Then w.r.t the Gaussian measure $N(\mu,\sigma)$ I believe it is true that this has a ...
3
votes
1answer
136 views

Decreasing the binding number of an open book while increasing the genus of the pages

Let $(B,\pi)$ be an open book decomposition of a closed, connected, oriented 3-manifold $M$ with odd (even) binding number and with pages of Euler characteristic $\chi$. Is it possible to define ...
1
vote
1answer
144 views

What are the best known bounds on the Hermite polynomials?

The best I could find on the net is this paper, http://arxiv.org/pdf/math/0401310.pdf Has this been improved?
6
votes
2answers
219 views

The Thom space of a Whitney sum of vector bundles

Let $\xi$ and $\eta$ be vector bundles over the same base space $X$. Their Whitney sum is a bundle $\xi\oplus\eta$ over $X$. I read somewhere (without proof) that its Thom space is given by $$ T(\xi\...
2
votes
0answers
261 views

An explicit formula for $\zeta(2m+1)$ with good convergence

The question: Is the following formula known? $$\zeta(2m+1)=\frac{(-1)^m 2^{4m+2}\pi^{2m}}{2^{2m}-1} \sum\limits_{k=1}^m \frac{(2^{2k}-1)b_{2k}}{2^{2k}(2k)!}\cdot \sum\limits_{v=k}^m \frac{(2^{2v-2k+...
4
votes
0answers
102 views

Good reference for noncommutative $L^p$ spaces

I'm looking for good references to learn about $L^p$ spaces associated with von Neumann algebras. I already know about Uffe Haagerup's paper "$L^p$-spaces associated with an arbitrary von Neumann ...
15
votes
4answers
2k views

Languages beyond enumerable

A language is a set of finite-length strings from some finite alphabet $\Sigma$. It is no loss of generality (for my purposes) to take $\Sigma=\{0,1\}$; so a language is a set of bit-strings. ...
2
votes
1answer
501 views

A paper by Y. Morita

The corresponding bibliographical details are: Yoshihito Morita, Elementary proofs of the commutativity of rings satisfying $x^{n}=x$. Mem. Defense Acad. 18 (1978), no. 1, 1–24. Does anybody here ...
2
votes
0answers
69 views

reference for KK theory

I wanted to ask you, if you have any good references (book or pdf) to learn about the KK theroy of Kasparov. I think the presentation of Blackadar is too close from the commutative theory. I was ...
16
votes
0answers
325 views

Is this a model for $K$-theory of a triangulated category?

The recent question Complete the following sequence: point, triangle, octahedron, . . . in a dg-category reminded me of something I wanted to clarify long time ago; most likely this is now well known ...
2
votes
1answer
115 views

Graph Isomorphism for Triangle Free graph

Is there any specific computational complexity result of Graph Isomorphism for Triangle Free graphs? Anything close to the subject will help and of course, I have searched Google.
2
votes
0answers
53 views

Estimates for hyperbolic metrics on nested surfaces

Suppose that $X$ and $Y$ are connected hyperbolic Riemann surfaces, with $X\subsetneq Y$. Let $\rho_{X,Y}$ be the density of the hyperbolic metric of $X$ with respect to that of $Y$; then $\rho_{X,Y} &...
3
votes
0answers
111 views

“Parameterising” extensions $0\to E\to W\to F\to 0$ by $\mathbb P(H^1(E\otimes F^*))$?

Let $X$ be a complex projective manifold and $E$ and $F$ be holomorphic vector bundles on $X$. The extensions of $F$ by $E$ are classified by elements $e\in H^1(E\otimes F^*)$. On the other hand, for ...
3
votes
0answers
71 views

Can one push a path out of an algebraic set with control on length?

Consider a real algebraic set $A\subseteq\mathbb{R}^n$. The case I am interested in is a homogeneous cone (i.e., if $x\in A$ then also $\lambda x\in A$ for each scalar $\lambda>0$) where each ...
3
votes
1answer
79 views

Functional equations associated with addition theorems for elliptic functions

I'm trying to read the article "Functional equations associated with addition theorems for elliptic functions and two-valued algebraic groups" by Bukhshtaber,V. M. Russian Mathematical Surveys(1990),...
4
votes
1answer
77 views

Operator space structures on CB(H,K) where H and K are Hilbertian operator spaces?

(I'd be grateful if anyone thinking of putting MathJax in the question title refrains from doing so.) By consulting various standard sources (Effros-Ruan's book, Pisier's book, the lexicon of ...
1
vote
0answers
70 views

A family of rank two bundles on $\mathbb CP^1$ parameterized by $H^1(O(-2n))$

Let $n$ be a positive integer. Consider the family of extensions $$0\to O(-n)\to E\to O(n)\to 0,$$ parameterized by $H^1(O(-2n))$. For each element $e\in H^1(O(-2n))$ we get a rank two bundle $E$ ...
1
vote
0answers
35 views

What are the central points of a semi-nice region in the plane?

For a convex set in Euclidean space, there is an obvious notion of its center: namely, its center of mass, which by convexity lies in the set. For a nonconvex set there is just as obviously no nice ...
3
votes
2answers
129 views

Hausdorff dimension of sequence space

Let $\Omega =\{0,1\}^{\mathbb{N}}$ denote the set of infinite sequences with elements $0$ or $1$. Let $d$ be the metric on $\Omega$ given by $d((x_n),(y_n))=1/2^m$, where $m=\min\{i\in\mathbb{N}\,:\,...
8
votes
2answers
312 views

$l^1$ versus $l^2$

Is there an elementary proof of this Banach space fact? If the Banach space $V$ is linearly isomorphic to $l^1$, then it does not isometrically contain euclidean spaces of arbitrarily large finite ...
1
vote
0answers
44 views

Influence of independent variables on boolean functions?

Suppose a simple connected graph $G$ where its vertices are assumed to be independent. An event with uncertainty corresponds to each vertex. My instructor guides me that even though the vertices (...
4
votes
1answer
222 views

Finite group action on quasi-projective varieties

Let $X$ be a smooth, quasi-projective variety, $G$ be a finite group which acts freely and properly on $X$. Denote by $\alpha:X \to X/G$ the quotient. Is $\alpha$ generically etale? Also, as I am ...
9
votes
0answers
275 views

A conjecture of Blakley and Dixon about odd powers of positive matrices

In a 1966 paper Blakley and Dixon conjecture the following. Let $S$ be a symmetric matrix with nonnegative entries and let $u$ be a unit vector with nonnegative entries. For integers $k\ge j$ both odd,...
4
votes
1answer
154 views

Formula relating the cup product in dimensions n and n+1

Let's will write $K_n$ for the Eilenberg-MacLane space $K(\mathbb{Z},n)$. I remind that $K_n$ is equivalent to the loop space of $K_{n+1}$. Let’s consider the map $\smallsmile:K_n\times K_m \to K_{n+...
5
votes
0answers
128 views

$p$-adic uniformisation of abelian varieties

In the paper $p$-adic L-functions and $p$-adic periods of modular forms of Greenberg and Stevens $\S3$ page $420$ they make the following statement: Let $A$ over $\mathbf{Q}_p$ be an abelian variety ...
3
votes
0answers
85 views

Reference for Superelliptic Curves

A curve is called superelliptic if $y^n = (x-\alpha_1)^{d_1}...(x-\alpha_s)^{d_s}$ where $n \ge 2$ and $d_i > 0$. From googling around, I found several papers which talk about these curves and ...
0
votes
0answers
79 views

applications of ergodic theory to periodicity of regular continued-fractions

The usual application one sees of ergodic theory to the regular continued-fractions is the Gauss-Kuzmin Theorem on the frequency of positive integers in the continued fraction expansion for almost all ...
8
votes
3answers
344 views

Connection between solution for Schrödinger equation and solution for heat equation

It's known, that if you write imaginary unit into a heat equation you'll get time-dependent Schrödinger equation. Recently one guy discovered a connection between solutions for these two equations (...
23
votes
2answers
896 views

What is the relation between sphere spectrum and supersymmetry?

In this this google+ post of Urs Schreiber, he says: "Grading over the sphere spectrum is supersymmetry" and then he redirect us to the abstract idea of superalgebra (in nLab). Are there some ...
2
votes
1answer
139 views

Differential equations → predicate logic mapping

I was watching Tom LaGatta's talk on category theory recently, and one of the audience brought up a statement that caught my attention (around the 56:15 mark): I was gonna say, there was a book I ...
1
vote
1answer
48 views

Unbounded convex domains in 2D

Let $\gamma$ be a smooth planar curve. Assume that $\gamma$ divides the plane into two domains and, it addition, that one of these domains is unbounded and convex. What can be said about the behavior ...
4
votes
0answers
50 views

Reference request: local cohomology in disjoint union

I have a topological space $X$ and two disjoint, closed subspaces $Y$ and $Z$ of $X$. I believe that in this situation, for any abelian sheaf $\mathcal{F}$ on $X$ and any $p \in \mathbb{N}$, there is ...
4
votes
1answer
175 views

Is the number of intervals you get by slicing the closed region under a nice graph continuous from below?

Let $I$ be a closed interval in $\mathbb{R}$, and let $f:I \to \mathbb{R}$ be a bounded function, smooth except at finitely many points (piece-wise smooth). There are also only finitely many critical ...
3
votes
1answer
121 views

How to embed $S^2\mathbb{C}^2$ into $S^2S^3\mathbb{C}^2$ and get the ideal of the twisted cubic?

Let $X:=x^3$, $Y:=x^2y$, $Z:=xy^2$ and $W:=y^3$ be the 4 independent generators of $S^3\mathbb{C}^2$, and observe that the kernel of the natural epimorphism (total symmetrisation) $$ p:S^2S^3\mathbb{C}...
4
votes
1answer
136 views

how to define the injectivity radius of manifolds with boundary?

For manifolds without boundary one defines the injectivity radius as the maximal radius where the exponential map is a diffeomorphism. One can then show that the injectivity radius is the maximum ...
1
vote
1answer
67 views

Asymptotic for zeroes of $L(s,\chi)$ in a disk $|s|<R$

In 'Remarks on Weil's quadratic functional..' p.191 Bombieri claims any given $L$-function $L(s,\chi)$ has at least $$\big(\frac{1}{\pi}+o(1)\big)R\log R$$ zeroes in a disk $|s|<R$. Is there a ...
3
votes
1answer
140 views

Schubert varieties and Young diagrams

In his book Young Tableaux, Fulton asserts, in Exercise 9.4.18 on p. 152, that the Schubert variety $\Omega_{\lambda}$ is defined by the conditions $\text{dim}(V \cap F_{n+i- \lambda_{i}}) \geq i$ for ...
6
votes
1answer
200 views

Theorem of Bukovsky characterizing ground models

It was mentioned in a talk that Bukovsky proved the following are equivalent for inner models $M \subseteq V$: (1) There is a partial order $\mathbb P \in M$ and a $\mathbb P$-generic filter $G \in V$...