# All Questions

**4**

votes

**1**answer

59 views

### Reference for an unbiased definition of a symmetric monoidal category

In the references I know, a symmetric monoidal category is defined as a monoidal category equipped with some additional data, so in particular the monoidal product is a functor
$$
\mathcal{C}\times ...

**0**

votes

**0**answers

13 views

### About properties of polynomials with common interlacing

Say $\{a_1,a_2,..,a_n\}$ and $\{b_1,b_2,...,b_n\}$ be the real roots of two monic polynomials of degree $n$ which have a common interlacing. (say I have arranged the roots in increasing order)
Can ...

**3**

votes

**1**answer

27 views

### Segal maps for Segal precategories

A Segal precategory is just a simplicial space $X:\Delta^{op} \to sSet$ such that its $0$-th space is discrete (i.e. constant). A Segal category is defined everywhere in the literature as a Segal ...

**-1**

votes

**0**answers

32 views

### weakly etale maps

Let $k$ be an algebraically closed field.
Consider the map $\phi:X:=\mathbb{A}^{1}\times\mathbb{G}^{m}\times\mathbb{A}^{\mathbb{N}}\rightarrow Y:=\mathbb{A}^{\mathbb{N}}$
given by $(\lambda, ...

**-6**

votes

**1**answer

37 views

### Find the probability that the product of these numbers is a multiple of 3 [on hold]

From the sequence of natural numbers randomly select a pair of numbers. Find the probability that the product of these numbers is a multiple of 3.

**-4**

votes

**0**answers

26 views

### What is the idea behind a projection operator?what does it do? [on hold]

I need the idea behind this not the definitions of the examples can someone help?

**4**

votes

**1**answer

37 views

### Computing a transversal of a subgroup $H$ of $G$ in expected $O(|G : H|^2 \log |G : H| + |H|)$ time

I have the book "Handbook of Computational Group Theory", by Derek Holt, and in it is a section on finding the transversal of a subgroup. Recall a transversal of a subgroup $H$ of $G$ is a single ...

**-3**

votes

**0**answers

138 views

### How this conjecture is false and it was published in this journal as a true conjecture? [on hold]

This question is related to my recent question, i accrossed this conjecture in this
pdf :http://www.anubih.ba/Journals/vol.8,no-2,y12/11Ladas-Lugo-Palladino.pdf, page
(05).conjecture 08 as an ...

**0**

votes

**0**answers

6 views

### Laplacian Matrix for weighted Adjacency? [on hold]

I have seen definitions for Laplacian matrix in many resources as follows :
L = D − A
where D and A are the degree and ...

**7**

votes

**0**answers

119 views

### Excellent rings

If A is an excellent commutative ring and G is a finite group of automorphisms of A, is the invariant subring A^G still excellent ? I think this is false -- because if not it would probably be written ...

**5**

votes

**1**answer

28 views

### Evolution operator for a linear parabolic equation

Let $A(t)$ be a smooth family of positive definite operators on a Hilbert space $H$. Consider the operator
$$D:= \frac{d}{dt}+A(t)$$
and let $U(t):H\to H$ be the evolution operator, i.e., $U(0)=I$ and ...

**-4**

votes

**0**answers

36 views

### TOPOLOGY DATA ANALYSIS [on hold]

actually i am PHD student and my research in TOPOLOGY DATA ANALYSIS (TDA)
what I dream about to understand this artcile cran.r-project.org/web/packages/TDA/vignettes/article.pdf may you help me:
1- MY ...

**-2**

votes

**0**answers

51 views

### Relation between Kahler form and Kahler potential [on hold]

Let us consider an example. Take $\mathbb{C}^m$ which is identified with $\mathbb{R}^{2m}$. Now, the Kahler form is given by
$$\Omega = \frac{i}{2} \sum_{i=1}^m dz^i \wedge d\bar{z}^i$$
Now, how can ...

**2**

votes

**0**answers

61 views

### The existence of proper schemes under complection

Let $R$ be a regular local ring, $\hat{R}$ be its completion, $X$ be a proper scheme over $\text{Spec}(\hat{R})$. In what case there exist a proper scheme $Y$ over $\text{Spec}(R)$, such that $X$ is ...

**6**

votes

**1**answer

100 views

### Direct proof that $U$ is an $E_\infty$-space

An immediate consequence of Bott periodicity is that the infinite unitary space is an infinite loop space and so an $E_\infty$-space. I wonder if there is a direct proof (not using $U = \Omega^2 U$) ...

**1**

vote

**0**answers

27 views

### why group completion of configuration space is the iterated suspension space

In Lecture notes in mathematics Vol. 533, The homology of $C_{n+1}$-spaces, $n\geq 0$, F. Cohen, page 226, Corollary 3.3:
$\alpha_{n+1}: C(\mathbb{R}^{n+1};X)\to \Omega^{n+1}\Sigma^{n+1}X$ is a ...

**4**

votes

**0**answers

26 views

### Endomorphism algebras of abelian surfaces with real multiplication

Given an abelian variety $A$ over a field $F$, one may consider the ring of endomorphisms $End(A)$, the ring of $F$-rational maps $A \to A$ respecting the group structure on $A$. We may also consider ...

**-5**

votes

**0**answers

44 views

### Has solution of Brocard's Equation n!=m^2-1 [on hold]

Brocard conjecture in 1904 that the only solution of are n=4,5,7. There are no other solutions with .(Berndt and Galway n.d).Another of Brocard’s conjecture is that there are at least four primes ...

**4**

votes

**0**answers

28 views

### Sobolev-Poincaré inequality for curl-integrable functions

Let $B=B(r)$ denote a ball of radius $r$ in $\Omega \subset \mathbb R^d$ and
$$
u_B := \frac1{|B|}\int_B u \, dx.
$$
The standard Sobolev-Poincaré inequality states that if $u \in W^{1,p}(\Omega)$, ...

**6**

votes

**1**answer

52 views

### Infinite graphs with “similar” Hom-sets

Let $G,H$ be infinite simple undirected graphs with the property that for any graph $X$ we have $|\text{Hom}(X,G)| = |\text{Hom}(X,H)|$. Does this imply that $G$ is isomorphic to a subgraph of $H$, ...

**8**

votes

**0**answers

79 views

### The multiplicative group generated by shifted primes

I am asking for references about the following problem.
In particular, it is still open? If not, what is the state of the art result?
Problem 1. Let $\Gamma$ be the multiplicative subgroup of ...

**3**

votes

**0**answers

33 views

### Sparsifiers for 3-term arithmetic progressions

Let $G$ be a finite abelian group of odd order, let $D\subseteq G$, and $\epsilon \in (0,1)$.
For $S\subseteq G$ define
$$
\Lambda(S) = \frac{1}{|S||G|} \sum_{s\in S}\sum_{g\in G} ...

**0**

votes

**0**answers

17 views

### Stochastic gradient descent interleaved with deterministic optimization

I wish to solve
$\min_{x, y_k} \frac{1}{n} \sum_{k=1}^n f_k(x, y_k)$.
where $f_k$ are all smooth and convex.
Using standard stochastic gradient descent (SGD), each iteration I sample a k from $\{1, ...

**1**

vote

**2**answers

116 views

### Algebraic groups “generated” by a Lie algebra element

Here is a definition which I invented and which I would like to understand better.
Let $ A $ be a complex affine algebraic group. Let $ X \in \mathfrak g $ be an element in its Lie algebra. We say ...

**11**

votes

**0**answers

66 views

### Quickest and/or most elementary proof of “principal iff splits completely”?

Let $L$ be the Hilbert class field of a number field $K$, and let $\mathfrak{p}$ be a prime ideal of $K$. Then $\mathfrak{p}$ splits completely in $L$ if and only if $\mathfrak{p}$ is a principal ...

**1**

vote

**0**answers

13 views

### Find paths in a graph that any 2 vertices can be reached through N of them

Given a undirected weighted graph.
I would like to find a finite set of paths (consecutive vertices and edges)
each shorter than L
any two vertices can be reached through at most N(in my case N=4) ...

**5**

votes

**1**answer

64 views

### Iterated sumset inequalities in semigroups

This question is motivated by the following well-known theorems:
Thm (Plünnecke): If $A$ is a finite nonempty subset of an abelian group, then for every $n$ we have $|A^n| \le ...

**1**

vote

**1**answer

82 views

### iterated loop spaces and configuration spaces [on hold]

In the lecture notes by J.P. May, The geometry of iterated loop spaces, Chapter 5, formula (1), (2) and (10), a map
$$
\phi: Hom_T(X,\Omega Y)\to Hom_T(SX,Y)
$$
is defined. And a map
$$
...

**1**

vote

**0**answers

20 views

### Symmetry conjecture for minimal dilatation pseudo Anosov mapping classes

The conjecture is something like the following:
The minimal dilatation among pseudo-Anosov mapping classes on a surface $S_{g,n}$ is realized by $\rho\circ\omega$ where $\omega$ is supported on a ...

**2**

votes

**1**answer

63 views

### References about spectral theory on Hyperbolic space

Can anyone suggest me some books or papers that include details about spectral theory on Hyperbolic spaces or related topics such as scattering theory on Hyperbolic spaces?
After some googling, I ...

**0**

votes

**0**answers

24 views

### Meaning of k-connected directed graphs [on hold]

Is there any existing definition for "k-connected directed graphs"?
Any reference paper?

**-3**

votes

**0**answers

42 views

### If there is in a category $\mathcal{A}$ finite products and equalizers then it has pullbacks [on hold]

My homework consist in showing that "If there is in a category $\mathcal{A}$ finite coproducts and coequalizers then it has pushouts" based on the proof that "If there is in a category $\mathcal{A}$ ...

**-2**

votes

**0**answers

22 views

### simplifying an equation that has infinitesimals [on hold]

I'm trying to understand an equation with infinitesimal changes:
8*X*dX = d(4*X^2)
I think this can be written
$8X\Delta X = \Delta (4(X^{2}))$
I'm guessing going from 8 outside the differential ...

**-3**

votes

**0**answers

49 views

### How to evalute: $\int_0^1 \frac{e^{-ax}}{ax} -\frac{e^{-abx}}{1- e^{-ax}}((1-x)\cos (\pi x) + \frac{3}{\pi} \sin(\pi x)) dx$ and $a, b >0$ [on hold]

How to evalute: $$\int_0^1 \left[ \frac{e^{-ax}}{ax} -\frac{e^{-abx}}{1- e^{-ax}}\left((1-x)\cos (\pi x) + \frac{3}{\pi} \sin(\pi x)\right) \right] dx$$ and $a, b >0$

**-1**

votes

**0**answers

34 views

### how to solve a linear equation (Ax-b)T- lamda(c)? [on hold]

I'm trying to solve an linear optimization problem, it's first order Lagrange condition leas to this equation
$$
(Ax-b)^T A- \lambda C = 0.
$$
Here $A$ is an $m\times n$ matrix, $m>n$, $C$ ...

**6**

votes

**1**answer

122 views

### Question about zeta function of function field in 1 variable over $\mathbb{F}_q$

From my previous question, I know that$$\zeta_X(s) = {{P(u)}\over{(1-u)(1-qu)}}$$for some polynomial $P(u)$ of degree $2g$, where
$X$ is the set of all places of $F$, a function field in one ...

**3**

votes

**3**answers

245 views

### How many primes have the form $(2^p+1)/3$?

Assuming that $p$ is an odd prime. How many primes have the form $(2^p+1)/3$? Is the number finite? Mathematica calculation shows that there are 23 such primes when $p$ ranges over the first 500 ...

**-3**

votes

**0**answers

74 views

### Quotient group of an amalgam [on hold]

If a quotient of a group G is an amalgam then the group G is an amalgam. Is this true or false?
How can we describe a quotient of an amalgam?

**2**

votes

**0**answers

48 views

### Rational curves through a fixed number of points

Let us fix two positive integers $d$, and $N$. Can we determine a third integer $n$ such that given $n$ general points $p_1,...,p_n\in\mathbb{P}^N$ there exists a unique rational curve of degree $d$ ...

**9**

votes

**0**answers

139 views

### On sentences true in all finite groups (revisited)

Let $w$ be a group word with variables $\bar x, \bar y$, where
$\bar x=(x_1,\dots ,x_m)$ and
$\bar y=(y_1,\dots ,y_n).$
I am interested in the following questions.
(1) Is the sentence $(\forall\bar ...

**7**

votes

**1**answer

208 views

### Reference request, zeta function is rational function via Riemann-Roch?

I am looking for a reference to a proof that the zeta function of a function field in one variable over a finite field $\mathbb{F}_q$ is a rational function in $q^{-s}$ by using the Riemann-Roch ...

**-1**

votes

**0**answers

17 views

### Definition of Category of Hypergraphs [migrated]

I have a question concerning the definition of Hypergraphs in category theory, which I adopted from "A category-theoretical approach to hypergraphs" by W.Dörfler and D.A.Waller:
...

**5**

votes

**1**answer

116 views

### Introducing meets while preserving directed closure

A poset $\mathbb{P}$ is called well-met iff every pair of compatible conditions in $\mathbb{P}$ has a greatest lower bound.
Question: Suppose $\mathbb{P}$ is a separative partial order which is ...

**3**

votes

**1**answer

120 views

### Quotients of finitely generated nilpotent groups

I am currently writing my thesis and looking for a reference (or a short proof) to the following fact:
Let $N$ be a finitely generated nilpotent group, and denote its lower central ...

**1**

vote

**0**answers

40 views

### Is the set of singularities of a meromorphic function on a domain in $\mathbb{C}^n$ an analytic variety?

Let $f$ be meromorphic on a domain $D\subset \mathbb{C}^n$ ($n>1$), and let $S\subset D$ be the smallest set such that $f$ is holomorphic on $D\setminus S$. Is the set $S$ an analytic variety?

**0**

votes

**1**answer

80 views

### Moment maps and flat degenerations of toric varieties

We have a flat family of projective varieties with a torus $T$ action, over $\mathbb{A}^1$.
How do the moment map images of the fibers change when we pass from the generic fiber to the special fiber ...

**1**

vote

**0**answers

33 views

### Multivariable polynomial interpolation via evaluations from entrywise powers of a point

I am interested in multivariate polynomial interpolation. Within computational complexity theory, I use it to create efficient reductions between counting problems. In the univariate case, there is ...

**1**

vote

**0**answers

63 views

### Polynomial-time algorithm solving approximately a generalization of the travelling salesman problem [on hold]

Take a graph $G$ and a number of sets of nodes of $G$. The problem is to find the shortest path passing through at least one node in each node set. If each node set consists of only one node, the ...

**-1**

votes

**0**answers

15 views

### graph edge partitioning for isomorphism testing

by a theorem of P. Rowlinson a graph of diameter D is D-walk-regular if and only if it is distance-regular.
See e.g. C. Dalfo, E.R. van Dam, M.A. Fiol, E. Garriga, and B.L. Gorissen,
On almost ...

**-4**

votes

**0**answers

20 views

### Show that the mapping A linear. Lays down rules for adjoint transformation A * [on hold]

Let V n-expansive real vector space with scalar product, a and b given linearly independent vectors from the space V. mapping A: V -> V is given by Regulations Ax = (x, a), * b
Assign eigen values ...