0
votes
0answers
22 views

Is triple point intersection 'generic' in Teichmuller space?

Let $S$ be a hyperbolic surface of finite type and $\alpha,\beta$ be two closed curves. Consider $X$ to be the set of all those points $\chi$ in the Teichmuller space $\mathcal{T}(S)$ of $S$ such that ...
1
vote
0answers
53 views

Kontsevich integral for 2-bridge knots

Are there any articles that explain a formula for Kontsevich integral of 2-bridge knots?
1
vote
0answers
29 views

Cell(J) vs Cof(J) in $\text{sSet}_{\text{Quillen}}$

consider sSet equipped with its Quillen model structure $\text{sSet}_{\text{Quillen}}$, we know that a trivial cofibration is a retract of a transfinite composition of pushouts of horn inclusions. I ...
-1
votes
0answers
66 views

Help me to proof Mobius-Euler equation [on hold]

Can you help me to proof that $$ \sum_{d | n}^{\, } \left ( \mu \left ( d \right ) \times \varphi \left ( d \right ) \right ) = 0\: for\: \mathbf{n}\geq 2, \mathbf{n}\: is\: even $$ where ...
0
votes
0answers
29 views

Poisson bivector on the product of two manifolds [migrated]

Let $X, Y$ be two manifolds. Let $(U, x_1, \ldots, x_n)$ and $(V, y_1, \ldots, y_m)$ local coordinates of $X, Y$ respectively. A Poisson bivector on $X$ is defined by \begin{align} \pi_X = \sum_{i,j} ...
0
votes
0answers
30 views

A question related to Bernoulli trial [on hold]

I'm thinking a Bernoulli process $X_1, X_2, X_3, ...$ that stops when $n\left( X=0 \right)+2n\left( X=1 \right)\ge A$, where $n(X=0)$ and $n(X=1)$ are the number of 0 and 1 in the sequence ...
17
votes
4answers
2k views

Massive cancellations

Let $A=\{a_1,\ldots,a_k\}$ be a fixed, finite set of reals. Let $S_A(n)$ be the set of all reals that are expressible as the sum of at most $2^n$ terms, where each term is a product of at most $n$ ...
0
votes
0answers
34 views

Bound on change of function given bound on Hessian

Suppose I have very some smooth function $F(x)$, and let $x_0 = \text{argmin}_x F(x)$. I would like to bound $F(x) - F(x_0)$ from above, in terms of the gradient $\nabla f(x)$ and the Hessian matrix ...
0
votes
1answer
89 views

Normals along a Sphere [on hold]

Let $M \subset \mathbb{R}^d$ be a smooth 2-manifold that is homeomorphic to a sphere or a connected sum or tori. Does there always exists two points $x,y \in M$ such that the normals $\angle(n_x, n_y) ...
-2
votes
0answers
26 views

Ezcontour in Matlab [on hold]

I am using ezcontour to plot an ellipse in matlab, but I would like to get only level 1 contour. How can I specify that I only want level 1 contour? I can't find anything about this in the ...
0
votes
0answers
60 views

Is there an improvement for the Schur-Horn inequalities for positive semi-definite matrices?

By the Schur-Horn inequality I am thinking of the statement that for any Hermitian matrix $H$ its diagonal n-tuple $(H_{11},H_{22},..,H_{nn})$ for any choice of basis lies in the convex hull of the ...
0
votes
0answers
96 views
+50

Eigenvalue of a linear map over finite field

Let $ F_q $ be a finite field with $ q $ elements. Let $ g $ be a multiplicative generator of $ F_{q^2}^* $. It implies that $ <g^{q+1}> = F_q^* $. Let $ l $ be a prime greater than $ q^2-1 ...
2
votes
0answers
51 views

“Semiclassical approximation” in random matrix theory

I am reading Planar Diagrams by Brezin, Parisi, Itzykson and Zuber. If you specialize the discussion in section 5 there we seem to derive the eigenvalue distribution of $N \times N$ random Hermitian ...
-4
votes
0answers
50 views

Let Z be the set of integers, and consider the function f : Z → Z defined f(x) = 2x. Which of the following is correct? [on hold]

a) f is invertible b) f is injective c) f is bijective d) f is surjective I put b, though apparently that's wrong. Thanks :)
1
vote
0answers
50 views

translation invariance of the Laughlin wave function

This is a translation into math of the following question, posted on PhysicsOverflow. Let $H:=L^2(\mathbb C)$. For every $N$, let $\psi_N\in\Lambda^N H\cong (L^2(\mathbb C^N))^{S_N}$ be the function ...
0
votes
0answers
31 views

Calculating Swaps and Swaptions [on hold]

Hi all I have a problem when I have to calculate swaps/swaptions. n=10-period binomial model for the short-rate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1−q=1/2. 1.Compute the ...
8
votes
3answers
265 views

Reference for a strong intermediate value theorem for measures

Let $\mu$ be a finite nonatomic measure on a measurable space $(X,\Sigma)$, and for simplicity assume that $\mu(X) = 1$. There is a well-known "intermediate value theorem" of Sierpiński that states ...
-1
votes
0answers
55 views

On multilinear linear combinations

If $K$ is algebraically closed field, then consider $m$ multilinear polynomials $f_i$ for $i=\{1,\dots,m\}$ in $K[x_1,\dots,x_n]$ of degree $d_i$ each with no common root. We know there exists $g_i$ ...
4
votes
1answer
262 views

Free action of $\mathbb{Z}(2^{\infty})$ on a compact space

Assume that $X$ is a Hausdorff compact space such that $\forall n\in \mathbb{N}$, we have a free action of $\mathbb{Z/{2^{n}}\mathbb{Z}}$ on $X$. Must $\mathbb{Z}(2^{\infty})$ act freely on ...
0
votes
0answers
55 views

Number of graphs with M edges that does not contain K-clique [on hold]

If we consider the space of graphs $G(n,M)$ where $M$ denotes the number of edges. Is there any known way of calculating the number of graphs within this space that does not contain any k-cliques? Can ...
3
votes
1answer
131 views

Nuclearity noncommutative torus

I read that the Noncommutative torus (rotation algebra) is nuclear when $\theta\in\mathbb{R}\setminus\mathbb{Q}$. Unfortunately, I haven't found a proof. Could someone give me a reference and/or an ...
-2
votes
2answers
39 views

Systems of ODEs that fulfill a matrix relationship at steady state [on hold]

It is well known that for a system of linear ODE $$x'(t) = A(t) \cdot x(t) + b(t)$$ with initial condition $x(t_0) = x_0$, that for a solution at any other time point $t_1$, $x(t_1) = (z_1, \ldots, ...
6
votes
2answers
133 views

Exactness of an additive left Kan extension

Let $\phi:R\to S$ be a flat ring homomorphism and consider the induced adjoint pair $$\phi_!:R-Mod\rightleftarrows S-Mod:\phi^*,$$ where $\phi_!=(S\otimes_R -)$. The right adjoint $\phi^*$ is easily ...
1
vote
1answer
143 views

Can we say that $A$ is a complement for a group $G$?

Let $A$ be a frobenius complement for a group $G$ i.e. $A$ act on $G$ by automorphism s.t. $C_A(g)=e$ for all nonidentity $g$. Now, Action of $A$ can be linearly extended so that $A$ act on $F[G]$. ...
0
votes
0answers
25 views

Best s-term approximation and unit balls in weak $\ell^p$ norm

In the book "A Mathematical Introduction to Compressive Sensing" by Foucart and Rauhut there is the following asymptotic estimate at page 332, equation (11.1): $$\sup_{\mathbf{x}\in B^N_{r,\infty}} ...
-4
votes
0answers
28 views

Find solution of signle element $y_i$ in vector $y$ subject to $Ay=c$ [on hold]

I have a interesting question about linear algebra problem. Assume that I have a matrix $A^{m \times n}$ and vector $c^{n \times 1}$ are known and I want to find the solution of vector y subject to ...
-4
votes
0answers
36 views

An exercise related to Arzela- Ascoli theorem [on hold]

I am looking for some hint to prove the set A={x belonging to C[a,b]| sup|x| +sup|x'|<=1} is compact. Can you help me? I will appreciate any help!
-7
votes
0answers
89 views

How to understand mathematics [on hold]

How do I achieve a good understanding of university level mathematics in order to do research in ? How do I know that the piece of math is understood and that I can go ahead?
1
vote
2answers
56 views

A question on deficient values of entire functions

Recently I come cross a question about deficient values of entire functions. I find that many examples in the book about functions $f$ whose deficient values are singularities of the inverse ...
0
votes
1answer
52 views

Question on affine buildings

Let $X$ be an affine building. Assume that $X$ is periodic, by which I mean that there exists a covering $X\to F$ of a finite simplicial complex. Let $\Gamma$ denote the group of deck transformations, ...
10
votes
2answers
363 views

Are there known cases of the Mumford–Tate conjecture that do not use Abelian varieties?

(For a formulation of the Mumford–Tate conjecture, see below.) The question As far as I know, all non-trivial known cases of the Mumford–Tate conjecture more or less depend on the Mumford–Tate ...
4
votes
1answer
42 views

Additivity of simplicial volume

I have read for example in the introduction of http://arxiv.org/pdf/math/0506338v2.pdf about the property that if we glue hyperbolic manifolds with geodesic boundary consisting of tori along some ...
19
votes
0answers
240 views

Can one properly embed a differential manifold into numerical space of double dimension? [duplicate]

If $X$ is a $ C^\infty$ differential manifold of dimension $n$, then there exists an embedding $f:X\to \mathbb R^{2n+1}$. This is a not too difficult theorem due to Whitney, proved in many textbooks. ...
5
votes
1answer
238 views

lower-bound for $Pr[X\geq EX]$

Given n random variables, $X_1, ..., X_n$, each takes value 0 or $a_i \in[0, 1]$. $X = \sum_{i=1}^n X_i$ and $EX \geq 1$ is the expected value of $X$. Can we get a lower-bound for $Pr[X \geq EX]$? It ...
0
votes
0answers
8 views

LYX: how to mark power set? [migrated]

This is my first time here and I did my best to figure out if such a question is in place here. If I missed something I apologize. My questions is how can I mark a power set in the lyx document ...
0
votes
1answer
90 views

Stability conditions of coherent sheaves on abelian 3-folds

My work for now consists on understanding stability conditions of coherent sheaves on abelian 3-folds. I have the book by D. Huybrechts (the geometry of moduli spaces of sheaves), But I would like to ...
0
votes
0answers
106 views

A question about a subset in R^n homeomorphic to an open subset [on hold]

Let A be a subset of n-dimensional Eucliean space R^n, A is homeomorphic to an open subset of R^n. Then whether A is also an open subset of R^n? Is it a theorem in somewhere? Thank you very much.
1
vote
0answers
58 views

Periodic Growth behaviours of Cayley graphs

This question is related to On the size of balls in Cayley graphs and Folner sequences of amenable groups of exponential growth Given a Cayley graph of a group $G$ with finite generating set ...
5
votes
1answer
78 views

Isomorphic Hadwiger graphs

Let $G$ be a graph, then we define its Hadwiger graph $\textrm{Hadw}(G)$ in the following way: $V(\textrm{Hadw}(G)) = \{S\subseteq (V(G): S\neq \emptyset\textrm{ and } S \textrm{ is connected}\}$; ...
2
votes
1answer
44 views

Density for Translated Process

Let $M$ be a (compact) Riemannian manifold. Let $v$ be a smooth vector field on $M$ with flow $\Theta_t$. Let $L$ be an elliptic second order differential operator on $M$ that generates the Ito ...
0
votes
1answer
127 views

When a proper morphism of schemes is a closed imbedding?

Let $X$ and $Y$ be finitely presented schemes over $\mathbb{C}$. Let $f\colon X\to Y$ be a proper morphism. Let us assume that for any finitely presented scheme $S$ the induced map $$Mor_{Sch}(S,X)\to ...
-1
votes
0answers
54 views

Is it true that standard R-algebra remains standard after going modulo a homogeneous ideal [on hold]

Is it true that any standard R-algebra remains standard after going modulo a homogeneous ideal?
2
votes
1answer
178 views

Counting Ribbon graphs

Let $G$ be a ribbon graph (sometimes called fat graph) with $v$ vertices and $e$ edges. Furthermore each vertex is of degree $d$. Q) What is the number of $G$ with the above properties? I mean does ...
13
votes
1answer
476 views

Is it possible to define higher cardinal arithmetics

In number theory there are several operators like ‎addition, ‎multiplication and ‎exponentiation defined from ‎$‎‎‎\omega‎‎\times‎‎\omega‎$ ‎to ‎‎$‎‎‎\omega‎$. Each ‎of ‎them ‎is defined as an ...
0
votes
0answers
26 views

asking for some basic computation of pseudodifferential operator

i am reading Kashiwara's paper"Analyse microlocale du noyau de Bergman". In the page 9 he computed the following: suppose $h=\sum_{j=1}^{n}|z_j|^4$ and $\delta(f)$ is the dirac function $Y(f)$ is ...
2
votes
0answers
93 views

Siegel Walfisz Theorem for algebraic number fields

Is there a generalization of the Siegel Walfisz to algebraic number fields? This has been done for the prime number theorem in the prime ideal theorem.
2
votes
0answers
41 views

relationship of max-sat and min-cut in theory and practice

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
0
votes
0answers
58 views

Approximation of quadratic variation

Here $M$ and $N$ are two bounded continuous martingales with respect to some filtration $(\mathcal F_t)_t$. I found this claim in a paper I was reading: $t$ being fixed, then a.s. $$\lim_{h\rightarrow ...
0
votes
0answers
48 views

Maximum Entropy for Dirichlet with Constrained Expectation [on hold]

How would I find the maximum entropy distribution of a Dirichlet with a known expectation (i.e if I know the expected value, a multinomial, how would I find the concentration parameter that maximizes ...
0
votes
0answers
163 views

On degrees of polynomials with matching zeros in a subset

Let $S\subsetneq \Bbb R^n$ such that $|S|<\infty$ and for all partitions $S_1$ and $S_2=S\backslash S_1$ of $S$, there exits a multilinear polynomial $h$ such that $h(s)=1-h(s'),\mbox{ }\forall ...

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