# All Questions

**1**

vote

**0**answers

4 views

### Can approximately periodic functions be perturbed to periodic functions on a locally compact group?

Let $G$ be a locally compact group and $H\subset G$ a closed and cocompact subgroup. I wish to consider bounded continuous functions from $G$ to $\mathbb{C}$ that are periodic in the following strong ...

**3**

votes

**0**answers

14 views

### Chern-Simons forms, characteristic numbers, and boundary terms?

For any principal $G$-bundle $P \to M$ with principal connection $\omega$, given a $G$-invariant polynomial $p: \mathfrak{g} \to \mathbb{R}$ we can construct a form $p(F_\omega)$ on $P$ which descends ...

**0**

votes

**0**answers

4 views

### Construction of point process having same pair correlations as GUE

The distribution of the pair correlations of the eigenvalues of the GUE satisfies (in the limit, when being normalized appropriately)
$$
g(u) = 1 - \left(\frac{\sin(\pi u)}{\pi u}\right)^2 + ...

**2**

votes

**0**answers

24 views

### Sufficient conditions for $\sum_{n \ge 1} a_n e^{-(a_1+\cdots+a_n) s} \sim \frac{1}{s}$ as $s \to 0^+$

Let $(a_n)_{n \ge 1}$ be a sequence of non-negative real numbers such that $\sum_{n \ge 1} a_n = \infty$, and set $\lambda_n := a_1 + \cdots + a_n$ for each $n$. Then the (generalized Dirichlet) ...

**0**

votes

**0**answers

19 views

### What would be simple way of calculating the area of a 3D PieChart's slices? [on hold]

I have created a 3D Pie Chart able to be rotated. -> http://plnkr.co/edit/QIYu8sJUWPmxcby1ky9l?p=preview
I did it to demonstrate how the visual perception of data in a Pie Chart can be distorted ...

**1**

vote

**0**answers

9 views

### $V(A)$ semi group of equivalent projections in $M_∞(A)$ cancelative?

I found in the book of Murphy, C*- Algebras and Operator Theory, the Theorem 7.1.2 :
the semi group $V(A)$ of equivalent projections (under Murray Von
Neumann equivalence) in $M_∞(A)$ is ...

**4**

votes

**0**answers

25 views

### When is a crossed-product algebra a division algebra?

Let $L/K$ be a finite Galois extension with Galois group $G$. For every 2-cocycle $\gamma$ of $G$ with values in $L^\times$ there is the crossed-product $K$-algebra
$$S(L,G,\gamma) = \bigoplus_{g\in ...

**-3**

votes

**0**answers

15 views

### Get angle of Trajectory of a projectile [on hold]

Formula1
Since a view hours I'm desperately trying to solve this equation after alpha.
I can't use Formula2 because my launch starts at the height h.
Thanks for your guys guidance and help.

**2**

votes

**0**answers

67 views

### When is $(1^2+1)(2^2+1)\dots (n^2+1)$ a perfect square? [duplicate]

Find all such $n$. Natural guess is that $n=3$ is the only solution.
It is natural to try something like Bertrand's postulate for Gaussian integers with imaginary part 1, but what is known?

**3**

votes

**1**answer

88 views

### Can we always attain another prime via inserting digits between the digits of a fixed prime?

The sequence OEIS A080437 is
For n > 10, let m = n-th prime. If m is a k-digit prime then a(n) = smallest prime obtained by inserting digits between every pair of digits of m.
I don't see why ...

**2**

votes

**0**answers

13 views

### Carving a rectilinear polygon

In this question, carving a polygon $P$ means removing an axis-parallel rectangle adjacent to the boundary of $P$. Carving $P$ might break it into two or more polygons.
You are given a square $P$. ...

**1**

vote

**0**answers

12 views

### Difference between Schmidt decomposition and singular value decomposition

Schmidt decomposition of an operator is a useful tool of quantum information theory nowadays. Let $O$ be an operator acting on the Hilbart space $\mathcal{H}_{d_1} \otimes \mathcal{H}_{d_1}$. ...

**0**

votes

**0**answers

8 views

### Points in Convex Configuration with Trivial Optimal Tour

Which property guarantees, that for set of $n$ points of the Euclidean plane, that are convex configuration, the optimal tour visiting all points consists of the $n$ shortest edges of the induced ...

**2**

votes

**0**answers

49 views

### Exponential analogue of formal connections

Let $F=\mathbb{C}((t))$. Let $G=GL_n$. Then $G(F)$ acts on $\mathfrak{g}(F)$ by gauge transformation:
$$
g.x:=gxg^{-1} + \dot{g}g^{-1},\quad \quad g\in G(F), \quad x\in \mathfrak{g}(F).
$$
Here, ...

**1**

vote

**0**answers

17 views

### A quantitative version of Pelczynski's property ($V^{*}$)

Let me first fix some notations. Let $A$ be a bounded subset of a Banach space $X$. Set $$wk_{X}(A)=\widehat{d}(\overline{A}^{w^{*}},X)=\sup\{d(x^{**},X):x^{**}\in \overline{A}^{w^{*}}\},$$ where ...

**-1**

votes

**0**answers

22 views

### finite Projective plane [on hold]

Let Z=PG(q,2) be a finite Projective plane over a finite field Fq, q a prime power. Show that there exists a commutative binary operation * in Z such
that
(i) x*y is neither x nor y for any x and y, ...

**1**

vote

**0**answers

18 views

### Stochastic calculus in $L^1$

Does there exist a more general (than Malliavin or Itô) "Stochastic calculus" defined on $L^1$ space, or some Orlicz space between $L^2$ and $L^1$?

**1**

vote

**1**answer

56 views

### Opposite of an E2-algebra

Suppose $C$ is the monoidal $\infty$-category of modules over an $\mathcal{E}_2$-ring spectrum $A$. Let $C' = C$ as a category, but with opposite monoidal structure to $C$. Is $C'$ the category of ...

**2**

votes

**1**answer

41 views

### Area of an irregular, n-sided, non-intersecting (edges) polygon algorithm

I need to generate an irregular, n-sided polygon of non-intersecting edges (n= 200, for example) with the smallest area possible. The position of the vertex is random and I've tried designing a couple ...

**-4**

votes

**0**answers

42 views

### Advice question? [on hold]

How to get to do paid mathematics reserach in graph theory pure mathematics in private by myself by getting some fund to help me support my family any advise?
At present I am doing my post doctoral ...

**-1**

votes

**1**answer

36 views

### Computing the inverse of a Cholesky decomposition [on hold]

I have chol(A) and I would like chol(A^-1). One way to do this is to construct the inverse positive definite symmetric matrix and then take its Cholesky decomposition (with Dpotri and Dpotrf for ...

**-10**

votes

**0**answers

77 views

### Please help me for answers to question. best regards [on hold]

Find the definition of a locale and its dual (i.e. a frame) and consider the
definition of a Grothendieck topology. Discuss the differences between this
concept and an ordinary topology on a set ...

**-4**

votes

**0**answers

60 views

### look for a right technique to solve logarithmic functional equations [on hold]

I would like to solve this equation but can not find a standard technique
f(f(x)) = log(x)

**1**

vote

**1**answer

58 views

### Discrete spectrum and almost periodicity

According to Vershik, an ergodic invertible measure-preserving transformation $T$ on a Lebesgue space $X$ has discrete spectrum if and only if for every bounded measurable function $f\colon X \to ...

**1**

vote

**2**answers

91 views

### Probability of at most $K$ consecutive zeroes in a sequence of 0s and 1s [on hold]

I want to prove that in a sequence W of length n, consisting of 1s and 0s, $P$( in $W$ there is at most $\frac{\log_2n}2$ consecutive zeroes ) $\leq \frac{K}{n} $ for some constant K. Can anyone ...

**-4**

votes

**0**answers

146 views

### What area of maths have I reinvented? [on hold]

I was trying to solve the issue of calculating (total) utilities with infinite numbers of people. This is problematic, because many infinite series are divergent, so there does not appear to be a way ...

**3**

votes

**1**answer

40 views

### Converging to moments obeying Carleman's condition

I believe that the following is true, and I'd like to make sure that it is and to have a reference. Suppose that $\mu_N$ are a sequence of measures on $\mathbb{R}$. Let $m_{N,k}$ be the $k$-th ...

**9**

votes

**2**answers

217 views

### Stable homotopy groups of $RP^{\infty}$

Are the stable homotopy groups $\pi^s_i(\mathbb R P^{\infty})$ known for small $i$? In particular, I would be interested in the values for $i = 5,6$. A quick Internet search did not lead to anything.

**1**

vote

**0**answers

49 views

### Counting growing tree trajectories

I am looking for help:
Beginning with a single node ($\circ$), at each discrete time step I can add a node/link pair to any node currently in the tree. Nodes are unlabelled and the tree is ...

**-2**

votes

**0**answers

40 views

### concentric spheres with common radius [on hold]

I am trying to think of a way to solve this problem but I am not sure if it is doable or not. Here goes:
Assume we have n spheres that share a common radius (x0,y0,z0).
For each sphere we have one ...

**7**

votes

**2**answers

210 views

### Circle Action on Quaternionic Projective Space

Quoting from Wikipedia article on quaternionic projective space:
Therefore the quotient manifold
$$
\mathbb{HP}^{2}/\mathrm{U}(1)
$$
may be taken, writing $U(1)$ for the circle group. It has ...

**-1**

votes

**0**answers

16 views

### Probability of an event based on percentage in fixed lapse of time [on hold]

I am a software engineer. I am also a former triathlete that rides with a large group of friends every time we have a chance.
i am trying to come up with a little software to distribute among us ...

**-2**

votes

**0**answers

21 views

### Find the number of connected components in pseudospectra [on hold]

Suppose:
$B_i \in \mathbb{C}^{n \times n}$, $0<w_i\in \mathbb{R}$ $(i = 0,1,2,\ldots,m)$
${\rm P}(x) ={\rm{B}_m} x ^m + \cdots + B_1 x + B_0$ is a matrix polynomial, and $x $ is a complex ...

**-1**

votes

**0**answers

110 views

### The eigenvalue of operator $-\Delta$

Let $\Omega\subset \mathbb R^N$ be open bounded, smooth boundary. We know the eigenfunction of Laplacian operator $-\Delta$ is an orthonormal basis of $L^2$. Let $\{\omega_n\}$ denote the ...

**5**

votes

**2**answers

115 views

### Splitting subspaces and finite fields

Hellow. I'm sure that the following is truth, but I can't prove it.
Let $R<S<K, R=\mathrm{GF}(q),\ S= \mathrm{GF}(q^n), \ K= \mathrm{GF}(q^{mn})$ be a chain of finite fields and
$A = ...

**2**

votes

**0**answers

62 views

### 3-dimensional vectors satisfying certain equalities

Question: Are there 5 distinct vectors $u,v,w,x,y \in \mathbb{R}^3$, all on the unit sphere (i.e. $||u||=||v||=||w||=||x||=||y||=1$), such that:
$||u+v+x||=||u+v+y||=||u+w+x||=||u+w+y||=1$
?
Also, ...

**-2**

votes

**0**answers

10 views

### Best algorithm to compute the first eigenvector of symmetric matrix [migrated]

Assume that we have a real symmetric matrix $\mathbf{A}\in\mathbb{R}^{n\times n}$ obtained as following :
$$\mathbf{A}=\mathbf{N}-\mathbf{P},$$
with $\mathbf{N}\in\mathbb{R}^{n\times n}$ and ...

**3**

votes

**0**answers

58 views

### When is a map from a logarithmic tangent bundle to a normal bundle surjective?

Suppose that $X$ is a smooth algebraic variety with free divisor $D$ so that the logarithmic tangent bundle $\mathcal{T}_X(-\log D)$ is locally free. Suppose moreover that $\iota\colon Y\to X$ is a ...

**1**

vote

**2**answers

100 views

### Four Sphere Fibrations

Does there exist a manifold $M$ and a compact Lie group $H$ such that we have a fibration $H \to S^4 \to M$, where $S^4$ is the four sphere?

**-3**

votes

**0**answers

49 views

### Does this numerical series have any special name? [on hold]

I don't have enough background to find the answer for this on my own, so I am posting it here with the hope to get some pointers.
Assume a descending sequence of K numbers $\{n_1, ..., n_K\}$ where ...

**2**

votes

**1**answer

89 views

### First proof of the integral representation of the hypergeometric function $F(a,b,c;\cdot)$

Assuming $\lvert x\lvert<1$ and $0<a<c$, the following formula holds true
$$F(a,b,c;x)=\sum_{n=0}^{+\infty} \frac{(a)_n(b)_n}{(c)_n(1)_n} x^n=\frac{\Gamma ( c ...

**2**

votes

**0**answers

61 views

### 2nd order partial differential equation with non-constant coefficients

During my research I came across the following differential equation:
$$f(x,y) = \left(y^2 \partial_{x}^{2} + x^2 \partial_{y}^{2} \right)f(x,y)$$
Any ideas how to solve it without using series ...

**5**

votes

**0**answers

72 views

### Sets of matrices which are irreducible but not strongly irreducible

A set of $d \times d$ real or complex matrices is commonly called irreducible if those matrices do not jointly preserve a linear subspace with dimension strictly between zero and $d$. A stronger ...

**0**

votes

**0**answers

133 views

### One-dimension Algebraic groups

I am searching for a possible analogue of a result in algebraic groups in a non-commutative setting, so I am looking for different proofs of the following :
Let $K$ be an algebraically closed field. ...

**-1**

votes

**0**answers

21 views

### 2D convolution property [on hold]

If I have three square matrices a,b, and c of equal size. say each of them are 3x3 matrices. then practically it is possible that
d = (a.b) * c .....(1)
= a * (b.c) .....(2)
that is 2D convolution ...

**0**

votes

**0**answers

53 views

### Extension of a valuation on a function field

Let $K$ be a field, and $K(x)$ the field of rational functions over $K$. Consider the degree valuation $v$ on $K(x)$, That is
$v\left(\frac{f(x)}{g(x)}\right)=\deg(g)-\deg(f)$. So for every $f(x)\in ...

**6**

votes

**1**answer

185 views

### Up to $2000$, $A145722(n-1) \equiv \sigma(4n-3) \pmod{5}$

A145722 is
Expansion of f(q) * f(q^5) / phi(-q^2)^2 in powers of q where f(), phi() are Ramanujan theta functions.
Using the pari program and offset 0, up to ...

**1**

vote

**1**answer

130 views

### Does every ultrafilter contain sets of sup-measure $0$?

Let $\mathbb{N}$ be the set of positive integers and for $A\subseteq {\mathbb{N}}$ set $$m(A) = \text{lim sup}_{n\to\infty}\frac{|A\cap\{1,\ldots,n\}|}{n}.$$
Does every ultrafilter ${\cal U}$ on ...

**0**

votes

**0**answers

23 views

### Isomorphisms of well ordered sets [migrated]

Let $A$, $B$ be well ordered sets. If there exist order-preserving functions $f : A \to B$ and $g : B \to A$ (do not need to preserve initial segments), are $A$ and $B$ isomorphic? I know this is not ...

**2**

votes

**0**answers

111 views

### Questions about configuration spaces on the sphere and higher loop spaces

In the paper Configuration spaces on the sphere and higher loop spaces, Paolo Salvatore, Mathematische Zeitschrift
November 2004, Volume 248, Issue 3, pp 527-540, I have some questions about ...