# All Questions

**0**

votes

**0**answers

21 views

### Weyl group representation

Let G be a reductive p-adic group.
Let W be a weyl group. if x,y in W
I want to know in which case we have x y x^-1 = y ?
in case if y(θ)=θ where θ is a subset of simple roots, and x is the longest ...

**0**

votes

**0**answers

8 views

### Statistics of strongly connected components in random directed graphs

I'm interested in the statistics of strongly connected components in random directed graphs. However, I'm unable to find any results on this, partly because I don't know the terminology to search for.
...

**-2**

votes

**0**answers

41 views

### The most general splitting of a field extension

This question has been posted here on math.stackexchange, but I felt it was maybe better to post it here.
Take $L/K$ an extension of the field $K$. I have questions on how we can "split" the ...

**0**

votes

**0**answers

15 views

### format of grading Witt Lie Algebra

Let $W(n,m)$ be generalized Jacobson-Witt algebra over a field of characteristic p>3, according to the grading of $W(n,m)$ , we know that it inherit the grading from $A(n,m)$ as follows: ...

**1**

vote

**0**answers

34 views

### Question regarding a theorem of Erdos and Renyi on $B_2(g)$ sequence

Let $S \subset \mathbb{N}$. We say $S$ is of type $B_2(g)$ if the number of representation
of the form $n = s_1 + s_2 \ (s_1 \leq s_2)$ is bounded by $g$ for every $n \in \mathbb{N}$.
Let $S(n)$ be ...

**0**

votes

**0**answers

58 views

### endomorphisms algebra of a real representation

Let $G$ be a finite group. Given a real irredcible representation of $G$, we know that its endomorphisms algebra is a division algbra and hence is the real, complex or quaternion algebra. Is there a ...

**-5**

votes

**0**answers

74 views

### What is the calculus based proof for 0.(9)=1? [on hold]

0.(9)=0.9 repeating infinitely. I have heard of simple proofs but I was curious of the calculus based proof.
Thanks in advance

**-7**

votes

**0**answers

52 views

### Polinominal equations [on hold]

Explain why it is possible that polynomial has no real solutions. Use reasoning
to expand your explanation to find the general characteristics of polynomials that have no
real solutions

**1**

vote

**0**answers

31 views

### solution to a parabolic PDE

I'm reading a paper where the following parabolic PDE is considered:
$u_t(x,t)=u_{xx}(x,t)+b(x)u_x(x,t)+\lambda(x)u(x,t)$, with boundary conditions
$u_x(0,t)=qu(0,t) \text{ and } u(1,t)=\int_0^1 ...

**4**

votes

**0**answers

23 views

### Find subset of collection of sets whose intersection has minimum average value

Let $a_1,\ldots,a_n>0$, and let $S_1,\ldots,S_d\subset\{1,\ldots,n\}$ (all non-empty).
For any $I\subseteq\{1,\ldots,d\}$, define $S(I)=\bigcap_{i\in I} S_i$.
Given some $1\leq s < d$, consider ...

**1**

vote

**0**answers

31 views

### A cohomology associated with a codimension one foliation(2)

What is an example of a codimension one foliation of a manifold for which this cohomology is finite dimension for all dimension $*$?
Moreover what is the description of this cohomology for ...

**0**

votes

**1**answer

128 views

### Sum of two squares - Number of steps in Fermat descent

If a prime $p$ can be written as the sum of two squares, then one can construct this representation via Fermat descent if we know an $x$ such that $x^2 \equiv −1 \mod p$. Is there a possibility to say ...

**-1**

votes

**1**answer

48 views

### How to compute the Expectation of the random variable using Taylor Series expansion

I don't know how to solve the following expression:
$ = nm^2 E \bigg[\frac{ \exp(\theta) {(\log(R))}^2}{N(R,x)}\bigg] \hskip 5 pt Eq(4) $ which I have explained below. $R$ follows Poisson ...

**3**

votes

**1**answer

52 views

### Are there 2-connected regular graphs whose maximum matching leaves 3 vertices uncovered?

I'd like to use Corollary 5 of a paper by Hell & Kirkpatrick on graph packings to obtain an NP-hardness result. They want a 2-vertex-connected graph $F$ such that every matching in $F$ leaves at ...

**3**

votes

**1**answer

64 views

### A multinomial-type sum over compositions of an integer

I find myself needing to compute (or asymptotically estimate) the following sum over the $2^{S-1}$ compositions of $S$. I am hoping an expert in combinatorics (I am a computer scientist) will ...

**-2**

votes

**0**answers

99 views

### Ext of Skyscraper sheaf [on hold]

Let $X$ be projective curve over the complex number field; and let $\mathbb C_p$ be the skyscraper sheaf whose fiber aver $p\in X$ is $\mathbb C$ and $0$ otherwise.
How could we prove that ...

**0**

votes

**0**answers

29 views

### Supremum of positve kernel

Let $A(x,y)\geq 0$ $\forall x,y$ be a positive kernel of a bounded, positive operator $A$.
How does one prove that
$$\sup_{x,y}A(x,y)=\sup_x A(x,x)?$$

**1**

vote

**0**answers

16 views

### Unitary transformation of a Hermitian indefinite pencil to a real non-symmetric pencil

Given a Hermitian indefinite pencil $(A-\lambda B)$ where both $A=A^H$ and $B=B^H \in \mathbb{C}^{n\times n}$ are possibly indefinite, it is straightforward to show that the eigenvalues are either ...

**0**

votes

**1**answer

20 views

### Reorder rows and columns to find as close to block diagonal structure in a non-symmetric sparse matrix

I have a sparse matrix with no apparent structure and am wanting to reorder the rows and columns in such a way that the matrix becomes as close to block diagonal as possible. I am using R and have ...

**0**

votes

**0**answers

118 views

### Twisting sheaf of Serre

I'm sorry if my question is rather trivial, but I can't figure it out.. Given $A$ a ring and $P=Proj(A[X_0,\cdots,X_n])$, I know that $\oplus_n H^0(P,\mathcal{O}(n))=A[X_0,\cdots,X_n]$. This equality ...

**10**

votes

**3**answers

159 views

### Sets of points containing permutations - a Ramsey-type question

The following question arised as a side-question in a geometric problem. It has a "feel" similar to problems in Ramsey-theory, but I have not found any mention of it (also I'm not very familiar with ...

**1**

vote

**0**answers

14 views

### Finite elements $W^{1,\infty}$ error estimates

Are there finite element method setups that provide error estimates in the $W^{1,\infty}$ norm (i.e., bounds on $\|u'_h - u'\|_\infty$)? Which families of elements can be used for implementing them?

**1**

vote

**0**answers

32 views

### connectedness of coincidence set

Consider the following obstacle problem in the whole domain $\mathbb{R}^n$
min{$\Delta u$, $u$-$\phi$}=0
with prescribed boundary value $\lim_{|x|\rightarrow\infty}u(x)=0$ and $\phi$ (can be assumed ...

**0**

votes

**0**answers

65 views

### Under which conditions the inclusion of a sub-simplicial set of the nerve of a category is a Joyal equivalence?

Let $i: X \to N\mathcal C$ be a monomorphism in the category of simplicial sets, with $C$ a category and $NC$ its nerve. I am looking for sufficient conditions (and not too difficult to check) under ...

**0**

votes

**1**answer

53 views

### Discrete Taylor's Formula in n dimensions [on hold]

I am searching for discrete form of Taylor's formula in n dimensions. Please share the appropriate resources.

**1**

vote

**0**answers

130 views

### Polynomial existence over finite field

Denote $\mathcal{F_n}$ as collection of multiaffine polynomials $f\in\Bbb F_2[x_1,\dots,x_n]$.
Denote total degree of $f\in\mathcal{F_n}$ as $deg(f)$ (note $deg(f)\leq n$).
Denote ...

**1**

vote

**1**answer

82 views

### Combinatorics problem involving counting the number of certain substrings

I'm not sure if this question is suited for MO, but it does seem quite challenging to me, and is required for a research problem in chemistry I'm working on. I did try getting help from elsewhere ...

**1**

vote

**0**answers

20 views

### A curious example envolving moment's convergence

Let $\{X_n\}$ be a random variable sequence and $X\sim N(0,\sigma)$. In general, the convergence $E(X_n^k) \stackrel{n}{\longrightarrow}E(X^k)$ doesn't implie that $E(X_n^{k+1}) ...

**0**

votes

**0**answers

33 views

### An embedding of modules by tensor product over a Noetherian domain

I have a problem on Ring theory. I would like to prove or disprove the following statement:
Let $R$ be a Noetherian domain. Then by the Goldie theorem $R$ have $Q$ as a full ring of quotients and $Q$ ...

**5**

votes

**0**answers

105 views

### Conjugation of the quotient of $SL(n,\mathbb{C})$ by a finite subgroup

EDITED Let $G={SL}_{n,{\mathbb{C}}}$, the special linear group over ${\mathbb{C}}$.
Let $H\subset G$ be a finite subgroup.
Set $X=G/H$ be the corresponding homogeneous space, it is a complex variety.
...

**0**

votes

**0**answers

73 views

### Can anyone solve a stochastic differential equation - related to neuroscience research?

I'm a neuroscience grad student, and I'm hoping one of ya'll could help me solve this problem regarding particle diffusion. It relates to my research on molecular-level neural plasticity, but I've ...

**0**

votes

**0**answers

28 views

### Helmholtz boundary value problem in 2D

I want to solve the Helmholtz equation in 2D with constant nonhomogeneities: $$\nabla^2w-\lambda w=C$$ and with Dirichlet boundary conditions such that $$w(0,0)=0$$ ...

**5**

votes

**0**answers

76 views

### Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic

Let $X$ be a complex space.
We say that $X$ is Brody hyperbolic if there is no non-constant holomorphic map $f\colon\mathbb C\to X$.
We say that $X$ is Kobayashi hyperbolic if the Kobayashi ...

**-4**

votes

**0**answers

35 views

### Prove that a Graph is connected using eigen values $\lambda$ [on hold]

Prove that for a graph is connected if and only if $\lambda_{max}$ > $\lambda_{1}$
Prove that for a $d$-regular graph $\lambda_{\max} = \lambda_1 =
\cdots = \lambda_{k-1}$ if and only if the graph ...

**0**

votes

**0**answers

36 views

### Asymmetry of functions defined on the $n$-th roots of the unity

Let $\mathcal{A} = \{V : \mathbb{U}_n \rightarrow \mathbb{C}\}$ where $\mathbb{U}_n$ is the group of the complex $n$-th roots of the unity. This group naturally acts on $\mathcal{A}$: for any $a \in ...

**0**

votes

**0**answers

65 views

### A Lie algebra assiciated with a one dimensional foliation

A non vanishing vector field $X$ on a manifold is called "well behaved" if for every non vanishing smooth function $f$ we have $$C(X)\simeq C(fX)$$ This means that the centralizer Lie algebras ...

**1**

vote

**1**answer

59 views

### A cohomology associated with a codimension one foliation

Let $\alpha$ be a non vanishing one form on a manifold which which defines a codimension one foliation. With this $\alpha$ we define the following complex:
$$\phi:\Omega^{i}(M)\to ...

**7**

votes

**0**answers

189 views

### Primes and Parity

This problem is motivated by the polymath4 project. There, the aim was to find an efficient deterministic algorithm for finding a prime larger than $N$. The hope was to find a polynomial algorithm in ...

**3**

votes

**1**answer

64 views

### Homogeneous polynomial vector fields tangent to the unit sphere

This question has something to do with that one.
Let $n\ge1$ and $d\ge1$ be two given integers. Consider the polynomial vector fields $v=(v_1,\ldots,v_n)$ whose components $v_j$ are homogeneous of ...

**3**

votes

**2**answers

382 views

### Co-Hausdorffification

Given a topological space $(X,\tau)$ we can define the "$T_2$-ification" of $X$ by setting $T_2(X,\tau) = X/\simeq$ where $x\simeq y$ in $X$ if and only if for every open neighborhood of $x$ has ...

**3**

votes

**0**answers

40 views

### Connected sum of chiral manifolds

Let $M,N$ be two closed, smooth, orientable manifolds of the same dimension and assume that these manifolds are chiral, i.e. they do not admit an orientation reversing automorphism. Then there are two ...

**0**

votes

**2**answers

124 views

### Parabolic subgroup

I have a question about root set corresponding to $P_θ ∩ M_Ω$
where $θ$ is a subset of simple roots, $Ω=θ∪{α}$ where $α$ is a simple root and not in $θ$, $P_θ$ is a parabolic subgroup corresponding ...

**1**

vote

**1**answer

97 views

### Does a line bundle on a normal Noetherian algebraic space come from a Weil divisor?

Let $X$ be a normal Noetherian algebraic space and $\mathscr{L}$ a line bundle on $X$. If $X$ is a scheme, then there is locally principal Weil divisor on $X$ that gives rise to $\mathscr{L}$. Is the ...

**5**

votes

**0**answers

147 views

### Twisted equivariant modular forms?

I'd like to know where I can find information about a class of objects which I think deserve to be called twisted equivariant modular forms. Let me guess a definition, indicate how it can be made more ...

**2**

votes

**1**answer

154 views

### When is a homogeneous space connected?

Let $G$ be a Lie group (not necessarily connected) and let $H$ be a closed subgroup of $G$. I am after an algebraic (group theoretic) characterization of when the homogeneous space $G/H$ is connected.
...

**2**

votes

**0**answers

60 views

### Chern character of Schubert structure sheaf

Let $X_\lambda \subset Gr = Gr(k,n)$ be a Schubert variety in the Grassmannian and $\mathrm{ch} : K_0(Gr) \otimes \mathbb{Q} \to A^\bullet(Gr) \otimes \mathbb{Q}$ the Chern character isomorphism.
Is ...

**4**

votes

**3**answers

248 views

### What is the difference between p-adic Lie groups and linear algebraic groups over p-adic fields?

I thought they were the same, just different names. Let me make question more precise:
Let $G$ be any linear algebraic group over a p-adic field $\mathbb{Q}_p$, is $G$ a p-adic Lie group w.r.t. the ...

**0**

votes

**0**answers

36 views

### Shuffle multiplication and generalized Leibniz rule in tensor calculus

The headline already says it: Is anybody (except me) aware of this formula for higher total covariant derivatives of tensor products?
It is the simplest application of the commutative shuffle product ...

**5**

votes

**1**answer

278 views

### How many geometric structures on manifolds are there?

Let $M$ be a smooth manifold, of dimension $n$. I know that there are many types of geometric structures on $M$. A large number of them are captured by the notion of a $G$-structure, which is a ...

**0**

votes

**0**answers

24 views

### Projected Alternating Minimization

Assume that $f(x,y)$ is a non-convex function for $x,y\in \mathbb{R}$. Assume that we want to minimize this function (even locally) with respect to $x$ and $y$ such that $x \in \mathcal{X}$ and $y \in ...