# All Questions

**1**

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**0**answers

97 views

### Is there a non-integer in the dimension spectrum for the Heisenberg group?

Let $\Gamma = \langle a,b,c \ | \ c=aba^{-1}b^{-1}, \ ac=ca, \ bc = cb \rangle$ be the discrete Heisenberg group.
Let $\ell: \Gamma \to \mathbb{N} $ be the word length on $\Gamma$. This group has a ...

**3**

votes

**0**answers

97 views

### Kunneth decomposition of the relative diagonal of a projective bundle

Let $\mathcal{E}$ be a projective bundle of rank $r$ over a smooth complex quasi projective variety $B$, and form its associated projective bundle $\chi :=\mathbb{P}(\mathcal{E})$. Let $\pi : \chi ...

**-3**

votes

**0**answers

47 views

### Find function $h$ so that $h(U,V)$ equals density of $f(a)da$ for $f(a)=\frac{1}{2}e^{-\small|a|} ,a \in \mathbb R$ [on hold]

Let $f(a)=\frac{1}{2}e^{-\small|a|}$, $a \in \mathbb R$
and let $U,V$ be two independently uniformly distributed random variables on $[0,1]$.
Now I want to find a function $h$ so that $h(U,V)$ is ...

**2**

votes

**0**answers

103 views

### Semistability of a sheaf on nodal curve

Suppose $X$ is a projective, connected, nodal curve (can be reducible) over an algebraically closed field $k$ of arbitrary characteristic. Let $F$ be a pure sheaf on $X$ and denote by $\pi^{*}(F)$ its ...

**-5**

votes

**0**answers

40 views

### Difficult derivative of the log of a function [on hold]

Can someone help me figure out how the derivative of log p(x) wrt. theta becomes to solution below ?
$ -\frac{\delta logp(x)}{\delta \theta} = \frac{\delta F(x)}{\delta \theta } - \sum p(x) ...

**3**

votes

**0**answers

58 views

### How many unimodular lattices does it take to fill a cube with high probability?

Consider $C_a$ in $\Bbb Z^n$ a cube of height $a$ at origin in positive coordinates with one corner at origin.
Consider the set $M_c$ of all unimodular matrices in $\Bbb Z^{n\times n}$ with each ...

**4**

votes

**0**answers

77 views

### Singular symplectic reduction in infinite dimension

In 1991, Sjamaar and Lerman [1] introduced the notion of stratified symplectic spaces. Namely, if $M$ is a symplectic manifold and $G$ a Lie group acting properly (but not necessarily freely) on $M$ ...

**3**

votes

**0**answers

44 views

### Are Bipartite Matching and General Matching Really Different Problems?

Questions:
Have there been attempts to either prove or disprove, that every general matching problem can be transformed into a bipartite matching problem, from whose solution the solution ...

**0**

votes

**0**answers

56 views

### Reference request: Uniformly totally bounded classes of compact metric spaces are Gromov-Hausdorff precompact

The following Theorem can be found for instance here (Theorem 7.4.15):
Theorem. (author ?) Any uniformly totally bounded class $\mathfrak X$ of compact metric spaces is pre-compact in the ...

**7**

votes

**0**answers

97 views

### Determinants of octonionic hermitian matrices

For quaternionic hermitian matrices (i.e. quaternionic square matrices $(a_{ij})$ satisfying
$a_{ji}=\bar a_{ij}$) there is a nice notion of (Moore) determinant which can be defined as follows.
...

**5**

votes

**0**answers

51 views

### Lower bound for smallest eigenvalue of symmetric doubly-stochastic Metropolis-Hasting transition matrix

For my master's thesis research, I stumbled upon a question concerning the Metropolis-Hasting transition matrix $W$.
Context $\quad$
Let me start with some context. I consider connected undirected ...

**0**

votes

**0**answers

80 views

### Mathematical consulting or bioinformatics related careers for mathematicians with good statistics and coding experience in West Europe [on hold]

Before I start, apologies if the question is very specific, but these are exactly what I want to be. I should mention that I already studied:
"Industry"/Government jobs for mathematicians
...

**2**

votes

**1**answer

66 views

### IFS maps on circle

A systems $<f_0,f_1>$ is minimal if the set $\{h(x): h=f_{i_n}\circ f_{i_{n-1}}\circ...\circ f_{i_1}, i_k \in \{0,1\},n>0\}$ is dense in $S^1$, for every $x\in S^1$.
Consider $f:S^1 \to S^1, ...

**1**

vote

**1**answer

35 views

### Maximizing joint entropy?

I'm stuck trying to find the maximum entropy probability distribution taking into account a joint distribution.
Basically, I want to find the maximum entropy expression for $p(x,y)$ when the marginal ...

**0**

votes

**0**answers

61 views

### Derandomizing AP existence in $A\subseteq \{1,\ldots,N\}$ for $\delta(A) \geq 1/k$

In the answer to the mathoverflow question here, it was established that if we let $p$ be the probability of including point $v$ in $A\subseteq \{1,\ldots,N\}$ and this is done independently for all ...

**12**

votes

**1**answer

261 views

### Measuring the failure of pushforward to commute with Steenrod squares

Let $f \colon X \rightarrow Y$ be a map of topological spaces. Let's say that they are (closed) manifolds (not necessarily orientable), though to be honest I'm really interested in the more general ...

**3**

votes

**0**answers

48 views

### Real interpolation of weighted Sobolev spaces with different weights

Let $\Omega \subseteq \mathbb{R}^n$ be open and let $w_0$ and $w_1$ be measurable and almost everywhere positive and finite functions defined on $\Omega$. Let $L^2_{w_0}(\Omega)$ be the weighted ...

**1**

vote

**0**answers

77 views

### Decompositon of the Euler class in the ideal generated by Weyl-invariant polynomials

Let $G$ be a complex reductive Lie group, $B$ be a Borel subgroup, $T\subset B$ be a maximal torus, $W$ be the Weyl group. Then the space $X:=G/B$ is a complex manifold of dimension $n$, denote by ...

**0**

votes

**0**answers

55 views

### Splitting of totally geodesic Riemannian foliations

Let $\mathcal F$ be a non-singular Riemannian foliation on $(M,g)$ whose leaves are totally geodesic. Suppose further that the leaves are Riemannian products of irreducible manifolds $L=L_0\times ...

**5**

votes

**1**answer

166 views

### Bounding the degree of an algebraic extension containing solutions to polynomials

Also posted on math.stackexchange...
Let $F$ be a field, and let $f_{1},\ldots, f_{s}$ be polynomials in $F[x_{1},\ldots, x_{t}]$. Assume that the degree of the polynomials is bounded by $d$, by ...

**5**

votes

**1**answer

114 views

### Density of non-algebraic leaves in the characteristic foliation

Let $X$ be a compact complex manifold equipped with a holomorphic symplectic form $\omega$. Let $D$ be a smooth divisor on $X$. At each point of $D$, the restriction of $\omega$ to $D$ has ...

**6**

votes

**0**answers

175 views

### Universal Property of Fontaine's Period Ring $B_{dR}^+$

In the introduction to his Asterisque Expose "Le Corps des Periodes p-Adiques",
Fontaine announces a characterization of $B_{dR}^+$ by some universal property. Unfortunatly,
at least for $B_{dR}^+$ ...

**0**

votes

**0**answers

39 views

### On a count of certain number of primes in an interval

Fix a prime $p$, $\alpha\in(0,1)$ and $\beta\in(1,2)$ and let $\mathcal U$ be primes in $[p^\alpha,\beta p^\alpha]$ such that if $b\in\mathcal U$ and if $d$ is multiplicative inverse of $b$ in $\Bbb ...

**1**

vote

**3**answers

115 views

### Hadwiger number and minimal degree

Suppose $G$ is a finite simple graph and $\eta(G)$ is the maximal $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$. If $\delta(G)$ is the minimal degree, do we have $\delta(G)\leq\eta(G)$?

**11**

votes

**0**answers

154 views

### Concept associated to the Eudoxus reals

I am aware of three different constructions of the field of real numbers :
The Cauchy sequence construction : in this case, we see the field $\mathbb{Q}$ as a metric space and $\mathbb{R}$ is the ...

**0**

votes

**0**answers

283 views

### Becoming a Mature Mathematician [on hold]

I am currently a sophomore in my undergraduate mathematics program. It has taken me a while to take school seriously; I was one of "those" students who just skated by without studying until Linear ...

**2**

votes

**0**answers

122 views

### Are these moduli problems of curves “well-behaved”?

Let X be a smooth projective surface over $\mathbb C$, and let $d\geq 3$ be an integer. Suppose that all smooth hypersurfaces of degree $d$ are of genus $g\geq 2$.
Let $H_{X,d}$ be the Hilbert scheme ...

**-6**

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**0**answers

27 views

### applications that involves the Legendre Polynomials [on hold]

i am requested to make a basic research about the applications that involve the Legendre Polynomials.. thanks in advance

**1**

vote

**1**answer

165 views

### harmonic analysis on $p$-adic $x^2 + y^2 + z^2 = 1$?

Are there p-adic analogues to spherical harmonics? In the case of $K = \mathbb{R}$, the spherical harmonics form a basis to $L^2 [SO(3)]$ where
What happens in the $p$-adic case? Is there sphere ...

**1**

vote

**0**answers

17 views

### History of the Vertex Disjoint Cycle Cover with Minimal Edgeweight Sum

Questions:
who first posed the problem of determining a collection of (directed) cycles, whose edgeweight sum is minimal and, for which each vertex belongs to exactly one of the cycles?
who came up ...

**2**

votes

**0**answers

43 views

### If $f$ is dynamically coherent, is there a unique invariant foliation tangent to $E^{c}$?

Let $f$ be a diffeomorphism of a closed manifold $M$ such that $f$ is partially hyperbolic if the tanget bundle of $M$, $TM$ splits into three invariant sub-bunbles
$$
TM = E^{s} \oplus E^{c} \oplus ...

**-4**

votes

**0**answers

38 views

### finding eigenvector [on hold]

I have
where λ1 = λ2 = 6 and λ2 = λ3 = 0.
I wish to find the eigenvectors for these eigenvalues above.
I've tried to turn it into equations and trying to solve them (this is for λ1 & λ2):
...

**0**

votes

**0**answers

11 views

### Stucture of inverse (MP) of totally positive rectangular matrix

The special structure of inverse of non-singular totally positive square matrix (whose all entries are positive) discussed in MO(see here). The inverse has a special structure (M-matrix).
With some ...

**0**

votes

**0**answers

41 views

### SVD alternatives for symmetric matrices

Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices
$$
A = E'E
$$
Practically this can be done easily using SVD ...

**0**

votes

**0**answers

60 views

### How to find a basis of weight vectors? [on hold]

I have to following Lie Algebra $L=\{x\in End(\mathbb{C}^6)\colon x^tS+Sx=0\}$, where $S=[\begin{smallmatrix} 0&I_3 \\ I_3&0 \end{smallmatrix}]$, and the subalgebra $H$ given by the diagonal ...

**0**

votes

**0**answers

27 views

### Mixed PDE/finite difference equation

I have the following mixed pde/finite-difference equation for $f(t,x,y)$:
$a x^2 f_{xx} + bxf_x + f_t - bxy + c\sinh(d\delta) = 0$
subject to $f(T,x,y)=0$, $x>0,\ t\geq 0,\ y\in\mathbb Z$,
...

**15**

votes

**0**answers

203 views

### What are the indecomposable $U_q\mathfrak{sl}(2)$-modules?

Let $\mathfrak g=\mathfrak{sl}(2)$.
Let $\zeta$ be a primitive root of unity of even order. Say $\zeta=e^{2\pi i/6}$, for concreteness.
Let $U_q\mathfrak g$ be Lusztig's integral form of the ...

**2**

votes

**1**answer

140 views

### projectivity with assumption of big and semi-amplness

Let $X$ be a compact Kaehler manifold with $D$ be an effective divisor on $X$ such that $K_X+D$ is semi-ample and big then $X$ is projective?

**3**

votes

**0**answers

58 views

### Correspondence between dual center and linear characters of finite reductive group

Let $(G,F)$ be a connected reductive group defined over $\mathbb{F}_q$ via the Frobenius $F$ and let $(G^*,F^*)$ be a group in duality with $(G,F)$ with respect to rational maximal tori $T \subseteq ...

**2**

votes

**1**answer

124 views

### (quasi)metric on Riemannian manifolds via Brownian Motion?

Given points $a$ and $b$ on a Riemannian manifold $M$, I would like a (quasi)metric that corresponds to some property of Brownian Motion from $a$ to $b$ (or rather, to $\epsilon$-ball $B = \{ x : |x - ...

**-2**

votes

**0**answers

24 views

### Cumulative distribution function and sum of random variables [on hold]

For two continuous (iid) random variables $X$ and $Y$, we have (ref): $$ \mathbb{P}(X+Y \le a) =\int_{-\infty}^\infty \int_{-\infty}^{c-x} \big ( f(x,y) dy \big ) dx$$ with $f$ being the joint density ...

**1**

vote

**0**answers

89 views

### Presentation of hyperbolic groups [on hold]

Is it true that all hyperbolic groups are finitely presented? If yes, what is the right reference for that?

**3**

votes

**1**answer

78 views

### geodesics on $G/K$ which are not the orbits of a 1-parameter subgroup of $G$

Let $G$ be Lie group and $K \subset G$ a closed subgroup, such that there exists a $v \in T(G/K)$ whose isotropy-group $G_v$ is discrete (so iff $\dim G_v =0$). Lets assume $g$ acts properly on ...

**-1**

votes

**1**answer

51 views

### Hadwiger number of total graph

Let $G=(V,E)$ be a finite, simple, undirected graph, and let $T(G)$ be its total graph. The Hadwiger number $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$.
Is there an ...

**9**

votes

**0**answers

269 views

### What's wrong with Advanced Studies in Contemporary Mathematics (Kyungshang)?

By some reason the Journal mentioned in the title is no longer covered by the AMS Math. Reviews. On the MathSciNet web page it says:
Last Issue: 24, no. 1 2014
Indexed cover-to-cover
Status: No ...

**1**

vote

**1**answer

149 views

### s(n) = kn or s(n) = n/k? [on hold]

This is not an important question, just for fun.
Definition:
$\sigma (n)$ = sum of the positive divisors of $n$.
$s(n)$ = sum of the proper positive divisors of $n$.
For $s(n) = kn$ , where $k$ ...

**-5**

votes

**0**answers

41 views

### Homomorphism, Group Theory [on hold]

Let G=Z4, the group of integers modulo 4, and let H be the Klein four group, let f: G->H be a homomorphism. Why does the kernel of f must contain the element of 2 of G?

**3**

votes

**0**answers

111 views

### Critical case of Sobolev Embedding

I got stuck in the following lemma:
Lemma 1: Let $B$ be the unit ball in the 4 dimensional Euclidean space. Suppose that $u\in W^{2,2}(B)$, then $e^{u}\in L^{q}$ for any $q\geq1$.
Actually, I ...

**4**

votes

**1**answer

51 views

### $G$-orbits in Springer resolution (or, stabilizer actions on Springer fibers)

This may be an elementary question, but I'm having trouble coming up with an answer: Let $\tilde{N} = T^*(G/B)$ be the Springer resolution of the nilpotent cone. Does it have finitely many ...

**30**

votes

**2**answers

3k views

### Why is this new result such a big deal?

This popular article reports a recent result in reverse mathematics, showing that a certain theorem in Ramsey theory is provable from RCA$_0$, the base theory in SOSOA. Then there are a bunch of ...