# All Questions

29 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 ...
37 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!
93 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?
61 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 ...
53 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, ...
365 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 ...
44 views

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 ...
241 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. ...
263 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 ...
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 ...
91 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 ...
110 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.
59 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 ...
80 views

Let $G$ be a graph, then we define its Hadwiger graph $\textrm{Hadw}(G)$ in the following way: $V(\textrm{Hadw}(G)) = \{S\subseteq (V(G): S\neq \emptyset\textrm{ and } S \textrm{ is connected}\}$; ...
48 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 ...
129 views

50 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 ...
166 views

24 views

### matrix summation and uniform convergence of matrix sequence [closed]

I start studying summation theory and as we know a matrix is called a Schur matrix if i)lim (a)nk= x when n goes to infinity and ii)the sum of (a)nk that means the convergence is uniform in n. can ...
76 views

### Finding nodes with a particular weight in a graph

Say that an edge $e$ is incident to a node $v$ if one of its two extremes is $v$. Then we can also say that $v$ is hit by $e$. We might define the notion of "weight of a node $v$" as the sum of all ...
99 views

55 views

### Criterion for global dimension of subring

All rings are assumed to be associative and unital. If $B$ is a commutative sub-ring of $A$ (which itself needs not be commutative) then what properties of $B$ are both necessary and sufficient for ...
145 views

86 views

### Calculating the quotient group $\mathbb{Z}\times\mathbb{Z}/<(1,1),(1,-1)>$ [closed]

Let $G$ be the group $\mathbb{Z}\times\mathbb{Z}$ and $H$ be the subgroup of $G$ generated by $(1,1)$ and $(-1,1)$. I am trying to calculate the quotient group $G/H.$
For quite some time I have been trying to solve the following system of differential equations for the two functions $G$ and $H$ defined on the interval $[0,1]$:  \begin{align}x ...