# All Questions

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 ...
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 ...
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 ...
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?
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 ...
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 ...
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 ?
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 ...
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 ...
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 ...
33 views

36 views

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...

15 30 50 per page