# All Questions

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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**

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**0**answers

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 ...

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**1**answer

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
$$
...

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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 $\exists$ ...

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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 ...

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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 ...

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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**

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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 ...

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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 = ...

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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**

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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 ...

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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**

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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

**1**answer

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 $\mathbb{R}^n$ ...

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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 ...

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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 ...

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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 $\Pr(f(X)\neq X)<\epsilon$ ...

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**0**answers

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**

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**1**answer

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

**1**answer

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 ...

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**0**answers

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**

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**0**answers

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 ...

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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 ...

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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

**1**answer

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**

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**1**answer

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 ...

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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**

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**2**answers

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**

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**0**answers

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 ...

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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.
...

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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 ...

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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: ...

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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 ...

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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**

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**0**answers

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**

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**0**answers

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

**0**answers

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 ...

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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 ...

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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

**1**answer

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 ...

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votes

**1**answer

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

**1**answer

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

**1**answer

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 ...

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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 ...

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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
$$\sup_{x,y}A(x,y)=\sup_x A(x,x)?$$

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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**

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**1**answer

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**

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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

**3**answers

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 ...

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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?