0
votes
0answers
5 views

Lyndon–Hochschild–Serre spectral sequence for not normal subgroup

Is there Lyndon–Hochschild–Serre spectral sequence for not normal subgroup? What can you say about it? Can you describe $E^{p, q}_1$ ? What is about $E^{p, q}_2$? What is the best technique to get ...
1
vote
0answers
18 views

Dualization of a theorem of Øystein Ore

This post is a dualization of Generalization of a theorem of Øystein Ore in which we have proved: Theorem: Let $(H \subset G)$ be an inclusion of finite groups such that the lattice ...
0
votes
1answer
18 views

Series estimate

Let $\theta\in(0,1)$ be given. I define for $a>0$ and $\lambda \ge 1$, $ S(\lambda,a )=\sum_{k\ge 1} k^{\frac12-\theta}e^{-a\vert k-\lambda\vert}. $ I want to prove that $$ ...
0
votes
0answers
29 views

Consequences failure of $\tau$ conjecture

A question Bounds for constructing $n!$ with additions, subtractions, and multiplications starting from $1$ was asked on constructing $ak!$ with ring operations. $\tau$ conjecture states if $\exists$ ...
0
votes
0answers
21 views

Ring of integers in Artin-Schreier extension

Question put in mathstackexchange but received no answer. It is well-know( see Goldschmidt book: Algebraic Functions and Projective Curves) that a for $q$ a power of $2$ a quadratic separable ...
0
votes
0answers
7 views

Some questions about “inspecting” the boundary of a closed ball in Hilbert space

Let H be a separable Hilbert space and suppose that H is infinite dimensional. Let B be a closed ball of H-which has a positive radius-and let S be the boundary of B. A non-empty subset C of H is an ...
-1
votes
0answers
14 views

Find steady-state solution

Governing equation: ∂Ω/∂t = (∂^2)Ω/(∂x^2)-DH(∂Ω/∂x) Find the steady-state solution Ω(x) from the governing equation with boundary conditions Ω(0) = 1 and Ω(1) = 0
-2
votes
0answers
56 views

Mathematical Expositions on Motivation [on hold]

I wanted to ask this question, However I hope that it is not too soft for this site. What I want to ask is if writing an exposition on motivation for a topic of mathematics would be relevant? I.e., I ...
0
votes
0answers
56 views

Solution to a PDE with constant data - what is the fault in my proof?

Let $C=\Omega \times (0,\infty)$. We want to find a solution $v \in H^1(C)$ such that given $u \in H^{\frac 12}(\Omega)$, $$\int_0^\infty\int_\Omega \nabla v \nabla \varphi + v_y\varphi_y = ...
0
votes
0answers
24 views

Number of solutions of the congruence, $x-y \equiv z \pmod{n}$,$x,y\in U_{n}$?

I known number of solution of the congruence, $x+y \equiv z \pmod{n}$,$x,y\in U_{n}$ is $N(z)=n\prod_{ p\backslash n}\left(1-\frac{\varepsilon(p)}{p}\right)$,where $\varepsilon(p)$=$\left\{ ...
17
votes
0answers
150 views

What is a Frobenioid?

Since there will be a long digression in a moment, let me start by reassuring you that my intention really is to ask the question in the title. Recently, there has been a flurry of new discussion ...
0
votes
0answers
33 views

projective map from $\overline{\mathcal{M}}_{0,n}$

Suppose I have a morphism $f:\overline{\mathcal{M}}_{0,n} \to \mathbb{P}^N$ birational onto its image, and I know exactly what $F$-curves are contracted (or "dually", what divisors are contracted). Is ...
-6
votes
0answers
50 views

Please reply fast. [on hold]

Is there any formula for product of sines like sin a sin b sin c sin d. Please tell me the formula for this , if any for both product upto a specific number of terms and that to infinite number of ...
3
votes
1answer
82 views

Reference request: Topology on the space of smooth compact submanifolds

In Allen Hatchers short exposition of the Madsen-Weiss Theorem he defines the topology on the space $\mathcal{C}^n$ of smooth oriented properly embedded $d$-dimensional submanifolds of $\mathbb{R}^n$ ...
0
votes
0answers
29 views

How many expressions can be formed with $k$ commutative and associative functions?

This is a generalization of a question I posted to Math.SE here. Suppose we have $k$ binary functions $f_1, f_2, \ldots, f_k$, all of which are commutative and associative, and $n$ indeterminates ...
-1
votes
0answers
146 views

A Small Discussion I want to have with Professional Mathematicians [on hold]

My professor is a really learned man, having written and published more than 18 research papers within 20 years. Hence I greatly admire him and value his opinion. He is, of course, a PhD in ...
0
votes
0answers
17 views

minimal entropy approximation of a discrete random variable

Let $X$ be a $\mathbb{N}$-valued random variable. Define $$ H^\epsilon_n(X) = \inf_f H(f(X)) $$ where $f$ runs over all functions $\mathbb{N} \to \mathbb{N}$ such that $\Pr(f(X)\neq X)<\epsilon$ ...
0
votes
0answers
25 views

How to show validity in classical logic? [on hold]

Firstly, I would like to know what does it mean to be a valid expression in classical logic. Secondly, How do we show validity of a formula (in sequent calculus) such as: (∀x A → ∃B) → ∃x(A → B) As ...
11
votes
1answer
128 views

A congruence involving binomial coefficients

The following open problem was shown to me by Maxim Kontsevich. I state it in a different but equivalent form. Let $a(n)$ be the sequence at http://oeis.org/A131868, that is, $$ a(n) ...
2
votes
1answer
79 views

book about string theory a la Von Neumann

Can we summarize string theory (in its actual state) in some principles and fundamental equations like electromagnetism, general relativity, quantum mechanics and classical mechanics ? I am looking ...
0
votes
0answers
18 views

Signs associated to self-dual simple objects in a fusion category

Every self-dual simple object $X$ in a fusion category can canonically be assigned a number $a$, from its "snake" associator element: The square of $a$ equals Muger's "squared dimension" of $X$, an ...
-4
votes
0answers
62 views

Algebraic Curves: Exercise 2.17 (William Fulton) [on hold]

Let $V=V(Y^2-X^2(X+1))\subset\mathbb{A}^2$, e $\overline{X}, \overline {Y}$ the residues of $X,Y$ in $A(V)$ its coordinate ring; let $z= \dfrac{\overline{Y}}{\overline{X}}\in K(V)$. Find the pole sets ...
0
votes
0answers
27 views

Bound from distinct integer summation

We want to find $r$ positive integers $\{a_i\}_{i=1}^r$ such that of atmost $(2s+1)^r$ values obtained from $$\sum_{i=1}s_ia_i$$ where $s_i\in\{-s,-s+1,\dots,0,\dots,s-1,s\}$, we insist on some ...
0
votes
0answers
10 views

Bits of precision matrix reconstruction

We have a real rank $r$ matrix $M\in\{0,1\}^{n\times n}$. Suppose we have diagonalized using $LMR=D$. I want to recover a real matrix $\widetilde{M}$ such that maximum absolute entry of ...
-2
votes
1answer
111 views

Direct image of structural sheaf

I am sorry if my question is not of high level!! Let $\pi:X\rightarrow Y$ be a double cover where $X$ and $Y$ are projective smooth curves. Is it true that $R^1\pi_*\mathcal O_X=0$ ? Why ? Thanks ...
4
votes
1answer
191 views

Formal group law over $\mathbb{F}_p$

Let $p$ be a prime. For each $n > 0$ there is a unique 1-dimensional commutative formal group law $F$ over $\mathbf{Z}$, $F(X, Y) = X + Y + \dots \in \mathbf{Z}[[X, Y]]$, whose logarithm function ...
1
vote
0answers
27 views

Enumerating matrices function of ranks

Is there an expression/approximate expression for number of real matrices $M\in\{0,1\}^{n\times n}$ of rank $r\leq n$?
4
votes
2answers
185 views

how to calculate the sum of remainders of N?

I'm trying to sum the remainders when dividing N by numbers from 1 up to N $$\sum_{i = 1}^{N} N \bmod i$$ It's easy to write a program to evaluate the sum if N is small in O(N) but what if N is large ...
-1
votes
0answers
64 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
0answers
10 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. ...
-3
votes
0answers
56 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
0answers
31 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
0answers
39 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
0answers
66 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
0answers
81 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
-8
votes
0answers
62 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
0answers
37 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
0answers
42 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
0answers
35 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
1answer
142 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
1answer
57 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
1answer
55 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
1answer
78 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
0answers
111 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
0answers
34 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
0answers
21 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
1answer
23 views

Reorder rows and columns to find as close to block diagonal structure in a non-symmetric sparse matrix [on hold]

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
0answers
123 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 ...
11
votes
3answers
244 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
0answers
15 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?

15 30 50 per page