# All Questions

**0**

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2 views

### What is the AAN algorithm for computing the fast DCT, and does it work for arbitrary or even-sized input vectors?

I'm trying to implement a faster DCT algorithm for an image perceptual hashing library I maintain in Rust. I based my original implementation on listing2.c from ...

**0**

votes

**1**answer

16 views

### SU(2) and differential forms

I am a physicist with some background in differential geometry and I apologize for any possible unprecise terminology.
Consider the Lie group $SU(2)$ and its tangent space $su(2)$ forming a tangent ...

**0**

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8 views

### Isomorphism in a derived category of chain complexes with rational coefficients

Let $C$ be the category of quasi-projective schemes over a base field $k$ (maybe I will need some assumptions on $k$). Let $Ab(C_{\tau})$ be the category of Abelian sheaves on a site $C_{\tau}$, where ...

**0**

votes

**1**answer

13 views

### p-groups and 2-generated abelian images

Let $p$ be a prime number. Is there a finite nonabelian $p$-group $G$ such that any finite epimorphic $2$-generated image of $G$ is abelian?

**2**

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**0**answers

18 views

### Algebraic theory of smooth functions: 2-truncated?

Recall that an algebraic theory (in the sense of Lawvere) is a category $\mathcal{C}$ which is closed under taking finite products, and whose set of objects can be identified with the set ...

**-3**

votes

**0**answers

46 views

### Formula to sum 1/sqrt(i) [on hold]

Is there a formula to calculate the sum of 1/$\sqrt i$ for n numbers?
My application repeatedly calculates $\sum\limits_{i=k}^{k+m} \frac{1}{\sqrt i}$ , for different values of k and m.
It spends ...

**-1**

votes

**0**answers

32 views

### knots complements and geometry

Let $K$ be a knot in $S^{3}$. If I understand correctly the complement $S^{3}-K$ is an Eilenberg Maclane space. Is $S^{3}-K$ always a hyperbolic 3-manifold ?

**3**

votes

**1**answer

48 views

### Geometric dominating set: NP-complete?

Let $G=(V,E)$ be a geometric graph, a graph embedded in the plane whose edge lengths are
the Euclidean distance between its endpoint vertices.
Say that a set of vertices $D \subseteq V$ is a geometric ...

**1**

vote

**1**answer

29 views

### Lyndon–Hochschild–Serre spectral sequence for not normal subgroup

Is there analog of 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 ...

**1**

vote

**0**answers

28 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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votes

**1**answer

33 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

**0**answers

52 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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votes

**0**answers

44 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 ...

**4**

votes

**1**answer

29 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 ...

**-2**

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**0**answers

24 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

**0**answers

71 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

**0**answers

73 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 = ...

**-1**

votes

**0**answers

36 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\{
...

**23**

votes

**0**answers

213 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

**0**answers

38 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

**0**answers

55 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 ...

**5**

votes

**1**answer

119 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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**0**answers

35 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

**0**answers

161 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**

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**0**answers

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

**0**answers

27 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 ...

**12**

votes

**1**answer

163 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

145 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 ...

**1**

vote

**0**answers

21 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

**0**answers

65 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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52 views

### Numbers summing to distinct integers

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

**0**answers

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

116 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

**1**answer

198 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

**0**answers

28 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

**2**answers

218 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

**0**answers

65 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

11 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**

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**0**answers

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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votes

**0**answers

33 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

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

**0**answers

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 ...

**-8**

votes

**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

38 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

45 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

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

146 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

59 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

79 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 ...