0
votes
0answers
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
1answer
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
votes
0answers
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
1answer
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
votes
0answers
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
0answers
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
0answers
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
1answer
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
1answer
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
0answers
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 ...
0
votes
1answer
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
0answers
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 $\exists$ ...
0
votes
0answers
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
1answer
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
votes
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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 $\mathbb{R}^n$ ...
0
votes
0answers
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
0answers
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
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
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
1answer
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
1answer
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
0answers
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
0answers
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 ...
0
votes
0answers
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
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
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
1answer
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
0answers
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
2answers
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
0answers
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
0answers
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
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
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
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 ...
-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
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
0answers
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
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
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
1answer
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
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
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 ...

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