**0**

votes

**0**answers

1 view

### Existence of internal Homs and equivalence of monoidal categories

Let $(\mathcal{C}, \otimes)$ and $(\mathcal{D}, \otimes')$ be two monoidal categories which are monoidaly equivalent. Assume $\mathcal{C}$ has internal Homs, that is, Hom$(X,1_{\mathcal{C}})$ can be ...

**0**

votes

**0**answers

2 views

### what operators annihilate all lattice periodic functions

Let $F$ be the space of functions $R^n \to C$ that are periodic on
a lattice $\Lambda$ : $f(x+\lambda)=f(x)$ for all $f \in F$,
$\lambda \in \Lambda$; what operators $T$ annihilate all of $F$?
($T f = ...

**0**

votes

**0**answers

2 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

18 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

**1**answer

41 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 ...

**-1**

votes

**0**answers

20 views

### free quotient in Limit groups

Let G a limit group.
Exist N normal subgroup of G such that G/N é a free group finitely generated and d(G)=d(G/N)?, where d() is the minimum number of generators of G.

**-2**

votes

**0**answers

22 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 ...

**0**

votes

**0**answers

16 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 ...

**-5**

votes

**0**answers

20 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. ...

**-1**

votes

**0**answers

68 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 ...

**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

30 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?

**-6**

votes

**0**answers

26 views

### Fourier transformation [on hold]

I need an example s.t. The function f belongs to L^2 but not in L^1, and the fourier transformation is in L^1?
If you have any hint that will be perfect.

**2**

votes

**0**answers

54 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 ...

**0**

votes

**0**answers

23 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"? ...

**-5**

votes

**0**answers

17 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

86 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**

vote

**1**answer

50 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}, ...

**0**

votes

**0**answers

15 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

45 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) ...

**0**

votes

**0**answers

16 views

### Variant of (WEAK) PARTITION with 2 distinct solutions

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

**1**answer

42 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 ...

**8**

votes

**1**answer

73 views

### Forcings that are not equivalent to Levy collapse

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

**0**

votes

**0**answers

132 views

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

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

**0**

votes

**0**answers

22 views

### Steklov averages in PDE: what to do when we have time-dependent elliptic operator

One may have an equation (with boundary conditions omitted below)
$$u_t - Au = f$$
$$u(0)=u_0$$
which has a weak solution $u \in L^2(0,T;V) \cap C([0,T];H)$ in the sense that
$$-\int_0^T \int_\Omega ...

**3**

votes

**2**answers

120 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

24 views

### Composition algebra of Gevrey function

Let $g,f$ be real-valued functions defined on the real line. Let $s$ be a real number.
Assuming that $g,f$ are both in the Gevrey class $G^{(s)}$, is it true that $g\circ f$ belongs to $G^{(s)}$? ...

**3**

votes

**1**answer

84 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:
...

**1**

vote

**1**answer

50 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

85 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
...

**3**

votes

**1**answer

61 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
...

**4**

votes

**1**answer

126 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 ...

**1**

vote

**1**answer

76 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 ...

**1**

vote

**1**answer

69 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 ...

**7**

votes

**1**answer

160 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 ...

**0**

votes

**0**answers

39 views

### Anisotropic limit of a Dirac delta function [on hold]

I hope this is the right place for this question, sorry if it is not. As part of a fairly long equation which I will not bore you with I have a Dirac delta function $\delta({k}-{k}_1-{k}_2)$ where the ...

**4**

votes

**0**answers

175 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 ...

**2**

votes

**0**answers

54 views

### good choice of extension of equivariant map

Let $K$ be a compact Lie group. Let $C_K$ denote the category whose objects are the compact lie groups containing $K$ and whose morphisms are inclusion of the groups. Let $Y$ be a $K-$space such that ...

**0**

votes

**0**answers

36 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 ...

**0**

votes

**0**answers

40 views

### Non-normality of limit of random variables

I have encounter the following difficulty in the study of limits of random variables. Assume that $\{X_n\}_{n\geq 1}$ is a sequence of real-valued random variables such that
...

**-2**

votes

**0**answers

50 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 ...

**1**

vote

**0**answers

32 views

### Power-spectrum of quasi-periodic functions

From Scholarpedia:
Quasiperiodic oscillation is an oscillation that can be described by a quasiperiodic function, i.e., a function $F$ of real variable $t$ such that ...

**5**

votes

**1**answer

75 views

### references for faithful orthogonal (or unitary) representation of symmetric groups

Let $S_n$ be the symmetric group of $n$ points. I want to find references (or proofs) for the following statement (1).
(1). There does not exist any faithful orthogonal representation
$$
...

**2**

votes

**0**answers

59 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 $s_k(x_1,x_2,x_1,x_2)$ ...

**0**

votes

**1**answer

62 views

### Convex cones: strict separation

Consider two closed convex cones $A$ and $B$ in $\mathbb{R}^3$. Assume that they are convex even without zero vector, i.e. $A \setminus \{0\}$ and $B \setminus \{0\}$ are also convex (it helps to ...

**5**

votes

**1**answer

87 views

### Conformal changes of metric and geodesics

Suppose $(M,g)$ is a Riemannian manifold. Let us assume that $X$ denotes a vector field in this manifold and consider the integral curves of this vector field.
Does there exist a conformal factor $c$ ...

**-2**

votes

**0**answers

46 views

### Rearrangement of difficult algebraic equations [on hold]

I have always had difficulty when rearranging large equations of functions to find the roots and also the turning points(using derivatives) and was hoping some people could give me some tips when it ...

**0**

votes

**0**answers

31 views

### Embedding Riemmanian Manifold Linearly

Given a Hilbert Manifold $M$ does there exist a smooth map into some very large Hilbert space taking geodesics to straight lines?

**6**

votes

**1**answer

88 views

### Is an elliptic curve that is isomorphic to its Frobenius conjugate defined over $\mathbb{F}_p$?

Let $p$ be prime and $q = p^n$. Let $E$ be an elliptic curve over $\mathbb{F}_q$, and let $E^{(p)}$ be the pullback of $E$ by the $p$-power Frobenius of $\mathbb{F}_q$. If $E$ is isomorphic (over ...

**2**

votes

**0**answers

29 views

### Construct a sequence of i.i.d random variables with a given distribution function, diagonalization? [on hold]

Assume we have a sequence of i.i.d. random variables $X_1, X_2, \dots,$ on a probability space $(\Omega, \mathcal{F}, P)$ with$$P(X_n = 1) = P(X_n = -1) = {1\over2}.$$Given a distribution function ...