# All Questions

0answers
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### 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 ...
0answers
53 views

### Kontsevich integral for 2-bridge knots

Are there any articles that explain a formula for Kontsevich integral of 2-bridge knots?
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 ...
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 ...
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} ...
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 ...
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 $n$ ...
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 ...
1answer
89 views

0answers
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### “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 ...
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 :)
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 ...
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 ...
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 ...
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 $g_i$ ...
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 ...
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 ...
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 ...
2answers
39 views

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 $t_1$, $x(t_1) = (z_1, \ldots, ... 2answers 133 views ### Exactness of an additive left Kan extension Let$\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 ... 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$F[G]$. ... 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}} ... 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 ... 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! 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? 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 ... 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, ... 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 ... 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 ... 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. ... 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 ... 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 ... 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 ... 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. 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 ... 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}\}; ... 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 ... 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 ... 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? 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 ... 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 ... 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 ... 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. 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 ... 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 ... 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 ... 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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