# All Questions

**2**

votes

**4**answers

136 views

### Simple bound for generalized geometric series

Let $b \in (0,1)$, $m\in \mathbb{N}$ and $a>0$. I want to bound
$$\sum_{k=m+1}^\infty b^{k^a} \leq c \; b^{m^a}, $$
where $c>0$ is independent from $m$.
Is there a simple way of proving this ...

**-1**

votes

**1**answer

82 views

### What is the definition of maximal ε-separated set

Nowadays, I am just studying the book wrote by Joram Lindenstrauss and Yoav Benyamini,i.e. Geometric Nonlinear Functional Analysis. The putfroward "maximal ε-separated set".I really can not understand ...

**1**

vote

**0**answers

117 views

### Hamiltonian potentials of holomorphic vector fields on modifications of Kahler manifolds

let $(M,\omega)$ be a compact Kähler manifold. Let $\mathfrak{g}=H^{0}(M,T_{M})$ be the Lie algebra of holomorphic vector fields on $M$.We can decompose $\mathfrak{g}$ as
...

**0**

votes

**1**answer

46 views

### perfect Lie algebra with a nonabelian solvable radical

Suppose you want to construct a perfect Lie algebra with a nonabelian solvable radical $\mathfrak{r}$, say with a commutator series of length 2. What are the conditions that guarantee the Lie algebra ...

**-3**

votes

**0**answers

27 views

### Poisson Distribution [on hold]

Connections arrive at a switch at a rate of 12 per ms. The number of arrivals is Poisson distributed:
What is the probability that the number of calls arriving in 2ms is greater that 7 and less ...

**6**

votes

**0**answers

200 views

### Global sections for a locally free sheaf over curves

Let $B$ be a complete algbraic curve of genus $g$, and $\mathcal{E}$ be a semi-stable locally free sheaf of rank $r$ over $B$. Assume that the slope of $\mathcal{E}$ is $\mu(\mathcal E):=\frac{\deg ...

**0**

votes

**0**answers

28 views

### Explaining of lost probalbity over random loss channel [on hold]

I am reading a paper about packet loss probability over random loss channel. In this paper, the author give a equation about loss probability as $(1)$. However, I cannot understand the meaning of it. ...

**0**

votes

**0**answers

54 views

### Show that $H=\oplus_{\alpha \in \sigma(T)}\text{ker}(\alpha I -T)$ [on hold]

Suppose $T$ is an operator on a Hilbert space $H$ such that $\sigma(T)=\sigma_{p}(T)$ (point spectrum of $T$), and for each $\alpha \in \sigma(T)$, the corresponding eigenspace ker$(\alpha I-T)$ is a ...

**5**

votes

**1**answer

487 views

### Is the set of certain polynomials finite or infinite?

Let us consider the set of all polynomials with the following properties:
i) all coefficients are integer;
ii) the leading coefficient equals one;
iii) all zeros are real and simple and belonging ...

**-1**

votes

**0**answers

33 views

### about the boundary of convex sets with not $C^1$ regularity [on hold]

I am reading a paper, and the author uses the following property:
Let $\Omega \subset R^n$ a open, bounded and convex domain. Let $x_0 \in \partial \Omega$ and suppose that $\partial \Omega$ is not ...

**0**

votes

**1**answer

34 views

### Determinant of block covariance matrix [on hold]

I wonder how to express the determinant of a block covariance matrix. For example, I have a covariance matrix
$\Sigma=\left[
\begin{array}{cc}
\Sigma_1 & \Sigma_{12} \\
\Sigma_{21} ...

**3**

votes

**2**answers

98 views

### Number of monomials of deg D where each variables has low degree

Let $D,n,d$ be three positive integers.
I am looking for the number of monomials of degree $D$ in $n$ variables where each variable appears with exponent at most $d$.
As a result of an application ...

**3**

votes

**2**answers

171 views

### $ \text{Lan}_KN(-/\mathcal C)\cong N(-/K) $

Let $N(-/\mathcal C)\colon \mathcal C\to \mathbf{sSet}$ be the functor sending $c\in\mathcal C$ to the nerve of the coslice category $c/\mathcal C$.
Given a functor $K\colon\mathcal{C}\to ...

**3**

votes

**1**answer

69 views

### Geodesic comparison in Hadamard space

Let $X$ be a hadamard space and $\gamma_1, \gamma_2 \colon \mathbb{R}\rightarrow X$ be two geodesics. Part 2 of Coroallary 2.5 in
...

**3**

votes

**1**answer

120 views

### Polygamous stable marriage/ assignment problem

I'm not sure under which 'algorithm' it falls under, but here is the problem:
I need to match each person to 5 people from the opposite gender (each guy gets 5 girls, each girl gets 5 guys). Not all ...

**6**

votes

**1**answer

140 views

### Which ordinals can be proof-theoretic ordinals of a reasonable theory?

When talking to a friend recently he asked a question - are there any reasonable first-order theories which have proof theoretic ordinal equal to small or large Veblen ordinal? I have then extended ...

**0**

votes

**0**answers

19 views

### Adding an edge to a MST generated from a distance matrix [on hold]

Given an N×N distance matrix, but not an adjacency matrix for a connected, weighted, undirected graph G, I've managed to find a minimum spanning tree (with N−1 edges) using Prim's algorithm. Now I ...

**2**

votes

**0**answers

81 views

### Orders of Clifford algebra

Let $C_n$ be the Clifford algebra over $\mathbb{Q}$ associated to negative definite quadratic form $-I_n$ (i.e. $-x_1^2-\dots-x_n^2$). Let $\mathcal{O}$ be a $\mathbb{Z}$-order of $C_n$.
Q1) Is it ...

**13**

votes

**1**answer

596 views

### Proving the Irrationality of this Number

I found this problem on Math.SE:
Prove that $\log_35+\log_25$ is irrational.
http://math.stackexchange.com/q/986227/173397.
I labored on it for a few days, and couldn't find an algebraic ...

**6**

votes

**2**answers

566 views

### Decidability of decidability

The questions I'm going to ask are non formal because they concern decidability of decidability, and I couldn't find any references on that after some quick searches. I hope that this thread is still ...

**3**

votes

**0**answers

42 views

### Boundedness Spectral Triple Axioms for de Rham Complex

In Connes' axioms for a spectral triple $(A,H,D)$, they have a representation of an algebra $A$ in bounded operators on a Hilbert space $H$, and (unbounded) operator $D$, such that $[D,a]$ is bounded. ...

**3**

votes

**0**answers

75 views

### Is exponential function in a C*-algebra injective on self-adjoint elements?

I asked this question in stackexchange, but it flashed and disappeared:
Let $A$ be a C*-algebra and $\exp(x)=\sum_{n=0}\frac{x^n}{n!}$, the usual exponential function from $A$ into $A$. Is it true ...

**2**

votes

**0**answers

94 views

### generalized Atiyah-Hirzebruch spectral sequence from Postnikov truncation

The Atiyah-Hirzebruch spectral sequence
\begin{equation*}E^2_{p,q}=H_p(B,h_q(F))\Rightarrow h_{p+q}(E),\end{equation*}
computes the generalized homology $h$ of a total space $E$ of a Serre fibration ...

**5**

votes

**1**answer

157 views

### Anti-bidiagonal matrix with main anti-diagonal {1,2,3,…} and first sub-anti-diagonal {-1,-2,-3,…} has eigenvalues lambda={1,-2,3,-4,…}

Consider the anti-bidiagonal matrix $B_6\in\mathbb{R}^{6\times 6}$, defined along its anti-diagonals as follows
$$
B_6=\begin{bmatrix} & & & & & 6\\
& & & ...

**9**

votes

**1**answer

209 views

### Riemann's formula for the metric in a normal neighborhood

I would love to understand the famous formula $g_{ij}(x) = \delta_{ij} + \frac{1}{3}R_{kijl}x^kx^l +O(||x||^3)$, which is valid in Riemannian normal coordinates and possibly more general situations.
...

**6**

votes

**0**answers

219 views

+50

### Proving that the kernel of this matrix is of dimension 2

Using a computational software program, I found that the kernel of the following matrix is of dimension 2 but I haven't managed to prove it:
\begin{equation}
\text{for almost all } t_1>0,\quad ...

**9**

votes

**3**answers

227 views

### Locus of complete curves on $\mathcal M_g$

Is the union of the complete curves on $\mathcal M_g$ Zariski dense? ($g \gg 0$)
I know it is hard to find higher-dimensional complete subvarieties of $\mathcal M_g$, but a quasiprojective variety ...

**-4**

votes

**0**answers

32 views

### Probability of coin tosses [on hold]

I have a probability problem.
Given 14 coins what is the likelyhood that on one given toss of all 14 at once 7 land heads and 7 land tails?

**-4**

votes

**0**answers

28 views

### Limits sum explanation required [on hold]

$\lim _{x\to 0}\left(\left(\left(x+bx^2\right)^{0.5}\:-\:x^{0.5}\right)/\left(bx^{1.5}\right)\:\right)$
How do I solve this, i tried online solvers but the ended up giving me the answer 1/2 but not ...

**4**

votes

**0**answers

130 views

### How find this binomial-coefficients sum $\sum_{k_{1}+k_{2}+\cdots+k_{d}=n}\binom{n}{k_{1},k_{2},\cdots,k_{d}}^2$ [duplicate]

Assmue that $d$ is give postive integer numbers,and
$$(x_{1}+x_{2}+\cdots+x_{d})^n=\sum_{k_{1}+\cdots+k_{d}=n} \binom{n}{k_{1},k_{2},\cdots,k_{d}}x^{k_{1}}_{1}x^{k_{2}}_{2}\cdots ...

**-2**

votes

**1**answer

130 views

### The number of Sylow subgroups of a group [on hold]

Let $ G $ be a finite group of order $ 2^4\times 3\times 7\times 13$. If $13 $-Sylow subgroup of $ G $ is not normal then $ G $ has 14 Sylow $13$-subgroups. Then $ G$ is $2 $-transitive on the set ...

**2**

votes

**0**answers

71 views

### Regularity of measures in the theorem of Riesz

There are two concurrent theories of measure/integration on a locally compact topological spaces: either as positive linear forms on the space of continuous functions with compact support, or as Borel ...

**5**

votes

**2**answers

168 views

### Normal Covering of a Finite Group

Suppose $G$ is a finite group and $N_1, N_2, \cdots, N_k$ are proper normal subgroups of $G$. The set $\{ N_1, \cdots, N_k\}$ is called a normal cover for $G$, if $G = \cup_{i=1}^kN_i$. I need to the ...

**1**

vote

**1**answer

49 views

### Expected value of the inverse of a random, truncated Haar matrix

Let $Q$ be a (say 4x4) unitary matrix, distributed according to the Haar distribution. Denote the upper left 2x2 submatrix of $Q$ as $Q_{1:2,1:2}$. I am interested in the following expectation:
$E(I ...

**2**

votes

**0**answers

114 views

### Uniqueness of scalar curvature

I'm reading Gromov's notes
http://www.ihes.fr/~gromov/topics/SpacesandQuestions.pdf
and at page 7 they say that there is a unique second order differential operator $S$ from the space of Riemannian ...

**-1**

votes

**0**answers

17 views

### Probability of rolling the same number n or more times in m rolls of a k-sided dice [migrated]

So the only approach I can find to solve this problem is making computer simulations, anyone can explain a mathematical way to solve it? or recommend a book that can explain this topic.
thanks.

**-1**

votes

**1**answer

40 views

### How to construct a semi-positive definite matrix in this form: (L=D-A')

As known, the graph Laplacian $L = D - A$ is semi-positive definite.
What if there is a matrix $A'$ where
$$ A'_{ij} = \begin{cases} A_{ij}, \quad if A_{ij} >0 \\ -\varepsilon, \quad if A_{ij} = ...

**2**

votes

**2**answers

214 views

### System of boolean equations, Satisfiability

Are there any methods to "solve" large systems of boolean equations?
$$x_{i1}\vee x_{i2}\vee x_{i3} = b_i, \quad\text{for}\quad i=1,\dots,N,$$
where $x_i, b_i \in\{0, 1\}$
For example
$$x_{1}\vee ...

**8**

votes

**1**answer

113 views

### Reconstructing a string from random samples

What is known about the following problem?
Reconstruct a string $\sigma$ of known length $n$ over a known
alphabet $\Sigma$ from a collection of uniformly and independently
chosen $k$-long ...

**0**

votes

**0**answers

36 views

### connected Polish groups

We know that a connected locally compact Hausdorff topological group is a pro-Lie group, by the Gleason-Yamabe theorem. Is there a known characterisation of the connected Polish groups?

**0**

votes

**1**answer

101 views

### Complementation in tensor products

This question, however looks innocent, looks non-trivial to me. Suppose that $X$ and $Y$ are Banach spaces and let $\alpha$ be any reasonable cross-norm on $X\otimes Y$. Reasonable means that ...

**0**

votes

**1**answer

204 views

### Is there a formula that can predict the primes in the sequence of ratios of consecutive superior highly composite numbers? : $2, 3, 2, 5, 2, 3, 7,…$

This is the sequence of prime numbers which are the elementary building blocks for the superior highly composite numbers:
$2, 3, 2, 5, 2, 3, 7, 2, 11, 13, 2, 3, 5, 17, 19, 2, 23, ...$
The $n^{th}$ ...

**1**

vote

**1**answer

115 views

### Divisibility of divisors in some tori and lattices

Let $E$ and $E'$ be two general elliptic curves. We consider the $2$-dimensional torus $A:=\frac{E\times E'}{(u\times u')\left((\mathbb{Z}/2\mathbb{Z})^2\right)}$, where ...

**6**

votes

**1**answer

127 views

### Lie group actions with only one orbit type, but not defining a principal bundle

Searched-for situation: A compact connected Lie group acts effectively on a closed Riemannian manifold by isometries, such that there is only one orbit type of dimension strictly less than that of the ...

**11**

votes

**1**answer

174 views

### Can infinitely many alternating knots have the same Alexander polynomial?

There exist many constructions of infinite families of knots with the same Alexander polynomial. However, alternating knots seem very special. While there are also many result on restricting the form ...

**0**

votes

**0**answers

44 views

### Independent Quasi Monte Carlo Sequences

I am generating some copulas with MonteCarlo and QuasiMonteCarlo sequences. In particular, I would like to generate a Student's t copula with QMC numbers.
Here is my problem: for Student's t copula I ...

**0**

votes

**0**answers

47 views

### Odd length repetends in recurring decimals [on hold]

For any number n the reciprocal can be expressed as a decimal, which will be composed of a recurring pattern as long as n is co-prime with 2 and 5. In general terms 1/n will produce a recurring ...

**1**

vote

**0**answers

87 views

### Applications of composition operators on Sobolev spaces

I wold like to know some examples where composition operators on Sobolev spaces are useful. I'm in the following situation.
$L^1_p(D)$ - homogeneous Sobolev space, in other words space of locally ...

**8**

votes

**1**answer

296 views

### Is more alternating always better?

While thinking about this interesting question asked by Dylan Thurston, it occured to me that in every case that I know, the closer a knot diagram is to being alternating, the better its properties. ...

**3**

votes

**1**answer

84 views

### Existence of subgraphs when given its degree sequence

For a given simple graph $G$ with $n$ vertices $v_1,v_2,\dots v_n$, the corresponding degree sequence is $d_1,d_2,\cdots,d_n$. My qusetion is:
How to determine whether there exist subgraphs in $G$ ...