**2**

votes

**1**answer

65 views

### Is $2^n -1$ finitely many times the product of consecutive primes?

This question was asked at MSE but recieved no attention at all.
Here it is:
Are there finitely many $(n,k) \in \mathbb{N}^2$ with $2^n-1=p_1p_2\cdots p_k$ ?
$p_1=3,p_2=5 , ...,p_k$ are ...

**4**

votes

**0**answers

33 views

### positions of polyhedrons with vertices on the unit sphere

Let $S^2$ be the unit $2$-sphere canonically embedded in $\mathbb{R}^3$. Let $P$ be a polyhedron whose all vertices are in $S^2$. Let $\text{Iso}(S^2)$ be the isometry group of $S^2$ and ...

**3**

votes

**0**answers

23 views

### Conditions on the hierarchy for Thurston's hyperbolization theorem

From my understanding the proof of Thurston's hyperbolization theorem for Haken $3$--manifolds consists of cutting the manifold along a hierarchy (collection of incompressible, ...

**2**

votes

**1**answer

130 views

### Polynomial differential forms on $BG$

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets, where the codomain is the category of commutative differential graded algebras ...

**4**

votes

**0**answers

24 views

### Idea behind the proof of consistency of club filter of $\omega_1$ is ultrafilter + ZF + DC

I've been trying to understand Radin Forcing and some of its applications, one of which is the use of it to prove the consistency of ''Club filter of $\omega_1$ is an ultrafilter + ZF + DC''. However, ...

**5**

votes

**1**answer

82 views

### History of spectral methods to the study of real analytic $GL_2$-Eisenstein series

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the ...

**1**

vote

**0**answers

14 views

### Geodesically convex neighborhood in Finsler manifolds

It is well known that every point of a Riemannian manifold $(M,g)$ possesses a fundamental system $\{U_n\}_{n\in\mathbb N}$ of geodesically convex neighborhoods. This means that every pair of points ...

**15**

votes

**2**answers

229 views

### Non-negative polynomials on $[0,1]$ with small integral

Let $P_n$ be the set of degree $n$ polynomials that pass through $(0,1)$ and $(1,1)$ and are non-negative on the interval $[0,1]$ (but may be negative elsewhere).
Let $a_n = \min_{p\in P_n} \int_0^1 ...

**8**

votes

**1**answer

191 views

### Which weighted projective spaces (and their finite quotients) are local complete intersections?

Let $G$ be a finite subgroup of $\textrm{Gl}_{n+1}(k)$ (where $k$ is an algebraically closed field). My question is: do there exist examples of $G$ such that the corresponding quotient $P$ of ...

**2**

votes

**1**answer

27 views

### Proving compatibility of two Partial differential equations

Given two PDE(s): $F(x,y,z,p,q)=0$
and $G(x,y,z,p,q)=0$
In I.A.N Sneddon's "Elements of Partial Differential Equations",If every solution of $F=0$ is a solution of ...

**17**

votes

**1**answer

1k views

### Are the following identities well known?

$$
x \cdot y = \frac{1}{2 \cdot 2 !} \left( (x + y)^2 - (x - y)^2 \right)
$$
$$
\begin{eqnarray}
x \cdot y \cdot z &=& \frac{1}{2^2 \cdot 3 !} ((x + y + z)^3 - (x + y - z)^3 \nonumber \\
...

**10**

votes

**1**answer

118 views

### Forcings that are not equivalent to Levy collapse

Assume GCH and that $\kappa$ is a regular uncountable cardinal. Let $\mathbb{P}$ be a separative, $<\kappa$-directed closed, nowhere trivial, $\kappa^+$-cc poset of size $\kappa^+$. Must ...

**2**

votes

**1**answer

157 views

### Doob Martingale: Where is the catch?

I am working on a research problem in uncertainty propagation that involves sums of possibly dependent random variables with bounded sets of support.
I am attempting to use the method of bounded ...

**-1**

votes

**0**answers

49 views

### free quotient in Limit groups [on hold]

Let G a limit group.
Exist N normal subgroup not trivial of G such that G/N is a free group finitely generated and d(G)=d(G/N)?, where d() is the minimum number of generators of G.

**3**

votes

**0**answers

48 views

### Enriching categories and equivalences

Let $\mathcal{C}$ and $\mathcal{D}$ be two equivalent categories. Furthermore, assume $\mathcal{C}$ is enriched over a monoidal category $(\mathcal{M}, \otimes)$. Can one use the equivalence to ...

**-2**

votes

**0**answers

109 views

### Smoothness and Cohen Macaulay

One always get the idea (almost a slogan in Alg. Geom.) that Cohen-Macaulay varieties will have some (mild) singularities and Gorenstein can be smooth.
I found a smooth scheme that by construction ...

**2**

votes

**0**answers

22 views

### Conditions on the fusion data of symmetric fusion category

We know that every symmetric fusion category (SFC) gives rise to data
$N^{ij}_k$ that describe the fusion of simple objects:
$i\times j = N^{ij}_k k$, and the data $\theta_i =\pm 1$ that describe the ...

**3**

votes

**1**answer

56 views

### Spin Structures for Quaternionic-Kaehler and Hyper-Kaehler Manifolds

As is well-known (see Friedrich's book for example) every Kähler manifold is spin (or at least spin$^c$) and the Dirac is given (up to a twist) by $\partial + \partial^*$. What happens in the ...

**3**

votes

**1**answer

78 views

### Another question on Heath-Brown's “Prime twins and Siegel zeros”

With a graduate student, I'm going through the paper (Proc. London Math. Soc. (3) 47 (1983), no. 2, 193–224.)
Here's the background and notation.
We have a quadratic character $\chi$ modulo $q$, ...

**-5**

votes

**0**answers

51 views

### Infinite sum of n from 1 to infinity tend to -1/12 in String Theory? [on hold]

Why is this wrong result:
$$
\sum\limits_{n=1}^{\infty}n\rightarrow-\frac{1}{12}
$$
Used here: Volume I - String Theory - Joseph Polchinsky
Can someone explain its meaning in this book?
EDIT
I ...

**0**

votes

**0**answers

10 views

### Hilbert transform on boundary value of analytic bounded functions

I am considering the boundary values of a bounded holomorphic functions. Suppose $w$ is a bounded holomorphic function in upper half plane, with continuous and bounded boundary value $f$ on real axis. ...

**-6**

votes

**0**answers

37 views

**5**

votes

**1**answer

101 views

### Schur polynomial, change of variable

Let $k=(k_1,k_2,k_3,k_4)\in \mathbb{N}^4$ and let $s_k(x_1,x_2,x_3,x_4)$ be the Schur polynomial on $GL_4$.
Question 1: If I replace $x_3$ with $x_1$ and $x_4$ with $x_2$, can $s_k(x_1,x_2,x_1,x_2)$ ...

**3**

votes

**1**answer

116 views

### triviality of whitney sums of a vector bundle

Let a $3$-dimensional subspace $V$ of $\mathbb{R}^4$ be $$V=\{(x_1,x_2,x_3,x_4)\in\mathbb{R}^4\mid\sum_{i=1}^4x_i=0\}.$$ The alternating group $A_4$ acts on $V$ by
...

**0**

votes

**0**answers

25 views

### Stability of moment representation of a scalar real-valued function

Let $f \in C([0,1],\mathbb R)$ be a continuous function. Define the moments of $f$ by
\begin{align*}
m_i(f) := \int_0^1 x^i f(x) dx,
\end{align*}
which yields a sequence of real numbers.
Now given ...

**-4**

votes

**0**answers

34 views

### Perfect matching in a graph [on hold]

Is it true, that in every 2-regular graph with 14 vertices there is a perfect matching ? If you think it's true - prove it, otherwise show counter-example
this is my excercise. I think that it's true ...

**1**

vote

**1**answer

71 views

### Questions on topologies on space of Radon measures

Consider the space $C_c(\mathbb{R})$ of continuous real-valued functions on $\mathbb{R}$ equipped with the inductive limit topology by $C_c(\mathbb{R}) = \bigcup_{n \in \mathbb{N}} C_c(\mathbb{R}, ...

**3**

votes

**2**answers

130 views

### Lefschetz Principle for semisimplicity

I think I can prove the following using the compactness of first order logic and I am wondering what a purely algebraic proof would look like.
Let $R$ be a unital ring (not necessarily ...

**0**

votes

**0**answers

52 views

### A question regarding forcing in $NGBC^{-f}$+$BAFA$

Suppose one has a model $M$$\vDash$$NGBC^{-f}$+BAFA. Does there exist a (class) forcing extension $M[G]$$\vDash$$NGBC^{-f}$+$BAFA$ that has a submodel $N$$\vDash$$NGB^{-f}$+$BAFA$+$\lnot$$AC$? Can ...

**3**

votes

**1**answer

97 views

### unwinding the definition of $H_i(KU)$ as a map of spectra $\mathbb{S}^i \to HZ \wedge KU$

I asked this on mathstackexchange but didn't get any response (or many views) so I'm asking it here, although clearly it belongs over there.
In the answer to this question on mathoverflow, it says:
...

**2**

votes

**0**answers

67 views

### When does a “universal” quot scheme exist?

Suppose $M$ is a moduli space of semistable sheaves on a projective variety $X$. Let $v$ be some the discrete invariants. I would like to form a space $\mathcal Q(v) \rightarrow M$, where the fiber ...

**1**

vote

**0**answers

143 views

### Examples of beautiful theories without applications [on hold]

What are examples of beautiful theories, which have no known applications?

**0**

votes

**0**answers

48 views

### Is there any $ABCDS$ pyramid (where $ABCD$ is a rectangle) in which each 2 edges have different lengths and $|AS|+|CS|=|BS|+|DS|$? [on hold]

I had geometry quite a while ago and I wonder if anyone has any idea how to tackle this problem:
Is there any $ABCDS$ pyramid (where $ABCD$ is a rectangle) in which each 2 edges (except for the base) ...

**4**

votes

**1**answer

136 views

### Vector bundles on open (affine) curves

It is well-known by Grothendieck (or earlier by Dedekind-Weber) that every vector bundle on $\mathbb{P}^1_k$ for $k$ a field decomposes into a sum of the line bundles $\mathcal{O}(k)$.
As ...

**-5**

votes

**0**answers

23 views

### Finding equivalent matrix combination [on hold]

I have a program I've written that is solving some problems with some matrix-vector math, but I have a feature I want to add and while I've found a work around an analytic solution would be superior. ...

**-5**

votes

**0**answers

38 views

### mutual information problem [on hold]

In mutual information we have: if $x$ and $y$ are independent then
$p(x,y)=p(x)p(y)$ and then $I(X;Y)=0$.
Do If $I (X;Y) = 0$ when $x$ and $y$ are independent?

**0**

votes

**0**answers

24 views

### Existence and summability of cumulant [on hold]

I posted this question on math stackexchange, but no one answered. So I am seeking help here.
1) Is the statement "the $r$-th order moment exists" equivalent to "the $r$-th order cumulant exists"? ...

**1**

vote

**1**answer

83 views

### Perfect centerless normal subgroups

Let $S$ be a non-trivial simple group and suppose $S \trianglelefteq G$ if $C_G(S)=1$ then $S$ is characteristic in $G$. To prove this let $\phi$ be an automorphism of $G$ and note that the ...

**3**

votes

**1**answer

93 views

### Generalized Theorem of Laguerre

There is known theorem of Laguerre, that every linear ordinary differential equation of second order
$$y''+A(t)y'+B(t)y=0$$
by point transformation could be mapped into
$$y'' = 0,$$ that in few words ...

**0**

votes

**0**answers

14 views

### Interpolation with double second differences [on hold]

My question is about an interpolation method used in an astronomy book that I would like to understand, and that can be found here: ...

**-5**

votes

**0**answers

21 views

### mutual information entropy problem [on hold]

In mutual information we have: if $x$ and $y$ are independent then
$p(x,y)=p(x)p(y)$ and then $I(X;Y)=0$.
Do If $Y (X;Y) = 0$ when $x$ and $y$ are not necessarily independent?

**1**

vote

**1**answer

54 views

### Showing that a particular area is small

Note: I posted this on math.stackexchange.com earlier (original post here: http://math.stackexchange.com/questions/1471331/showing-that-a-particular-area-is-small), but it received no responses and ...

**3**

votes

**1**answer

65 views

### Is the sum of spectral projections a projection?

Let $T$ be a closed operator on a Hilbert space with discrete spectrum. Then for $\{\lambda_1,...\lambda_n\}\in\sigma(T)$ one can define the spectral projections
...

**15**

votes

**2**answers

197 views

### Which partitions of $[0,1]$ are collection of level sets of a real continuous function?

Let $f:[0,1]\to[0,1]$ be given. The level sets of $f$ (ie the collection of all sets of the form $\{x\in[0,1]:f(x)=y\}$, for each fixed $y\in[0,1]$) partition the domain of $f$. I am curious for set ...

**1**

vote

**1**answer

70 views

### Sum of Stirling numbers with exponents

I have a trouble with the following sum
$\sum_{i=0}^n\binom{n}{i}S(i,m)3^i$, where $S(i,m)$ is the Stirling number of the second kind (the number of all partitions of $i$ elements into $m$ nonempty ...

**56**

votes

**12**answers

4k views

### Proposals for polymath projects

Background
Polymath projects are a form of open Internet collaboration aimed towards a major mathematical goal, usually to settle a major mathematical problem. This is a concept introduced in 2009 by ...

**4**

votes

**0**answers

189 views

### What is the algebraic fundamental groups of $SO(n)$ and $Sp(2n)$?

Let $k$ be an algebraically closed field of characteristic zero. and let $$\sigma: SL_n(k)\rightarrow SL_n(k)$$
be an involution.
My questions are:
How could one calculate the fundamental group of ...

**0**

votes

**0**answers

23 views

### Discrete random walk with uniformly distributed transition p, set initially

I've been working on a discrete version of the "unreliable friend" distribution. It would seem that what I've come up with is equivalent to the following random walk:
Choose $p$ from $U(0,1)$
Start ...

**0**

votes

**0**answers

20 views

### Variant of (WEAK) PARTITION with 2 distinct solutions [on hold]

I am interested in the complexity of the following problem:
Input: A list $a1\leq ⋯ \leq a_n$ of positive integers.
Question: Are there two vectors $x, x'\in\{−1,0,1\}^n$ such that
...

**-2**

votes

**0**answers

56 views

### A general theory for boundary value problems

One can study the characterization of a linear differential operator $T$ from scalar product $(f,g)=\int_{a}^{b}f(t)g(t)dt$ and the theory of adjoint operators solving $Tf=g$ by finding a right ...