# All Questions

**-4**

votes

**0**answers

35 views

### If Linear equations solution is inconsistent? [on hold]

Hello,
If my Linear equation system's martix is inconsistent.
There is no point to check homogenus system's solution, and I can safely say that the asked system has no solutions. Or am I wrong?

**1**

vote

**0**answers

77 views

### When can the rank of a submodule be bigger than the rank of the module itself? [migrated]

It is well known that the dimension of a subspace is less than or equal to the dimension of the vector space it is contained in. The same is true e.g. for modules over a principal ring.
I am looking ...

**1**

vote

**0**answers

30 views

### References to study Weak and Strong Topologies and aproximations on function spaces of manifolds

I´m studing weak and strong topologies and aproximations on the function space $C^{\infty}(M,N)$ of two manifolds $M$ and $N$. I´m using the book Differential Topology of Morris Hirsch but it is a ...

**-4**

votes

**0**answers

63 views

### Graph theory and topology [on hold]

I have related topological ideals with vertex magic totallabeling in graph theory. Is there any possibility to relate vertex magic totallabeling with generalized topology in a very interesting way? ...

**11**

votes

**2**answers

805 views

### When does Vopěnka's principle hold?

Vopěnka's principle (VP) is the statement that, given any proper class $\{\mathcal{A}_\eta: \eta\in ON\}$ of first-order structures in the same language, there are some $\alpha\not=\beta$ with ...

**3**

votes

**1**answer

418 views

### learning Deligne-Lusztig theory

Can someone give me a roadmap for learning Deligne-Lusztig theory? (Except for the original article by Deligne and Lusztig)
Edit: You may assume knowledge of representation theory of finite groups ...

**5**

votes

**2**answers

146 views

### Common roots of polynomial and its derivative

Suppose $f$ is a uni-variate polynomial of degree at most $2k-1$ for some integer $k\geq1$. Let $f^{(m)}$ denote the $m$-th derivative of $f$. If $f$ and $f^{(m)}$ have $k$ distinct common roots ...

**2**

votes

**0**answers

207 views

### A question about Weil restriction

Let $\pi:\tilde{C}\rightarrow C$ be a ramified cover between two smooth curves. And consider a group scheme $\mathcal G$ over $\tilde{C}$, I have found two definitions for Weil restriction:
...

**0**

votes

**0**answers

177 views

### Is dimension invariant under blow-ups?

Let $X'\rightarrow X$ be a blow-up of a finitely dimensional scheme $X$ in a center $D$.
Under which assumptions one has $\dim X'=\dim X$? Do you know a proof or a reference for a proof? Do you know ...

**-1**

votes

**0**answers

45 views

### Is any model category simplicially enriched?

Let $\mathcal{M}$ be a model category. Let $F\: : \: \mathcal{M}\to\mathcal{M}^{\boldsymbol{\Delta}}$ be a functorial cosimplicial frame. Then the function complex between two objects ...

**0**

votes

**1**answer

80 views

### “Diagonalizing” an associative algebra

Consider the associative algebra A with generators $T_i$ and rule $T_i*T_j=\Sigma_kC^{ij}_k*T_k$. Even if it makes no sense for a fusion ring (my momentary pet :-) to change basis it is still possible ...

**2**

votes

**1**answer

56 views

### Interval topology and order convergence topology

Throughout this post, let $(P,\leq)$ be a poset. The interval topology $\tau_i(P)$ on $P$ is generated by
$$\{P\setminus\downarrow x : x\in P\} \cup \{P\setminus\uparrow x : x\in P\},$$
where ...

**-2**

votes

**0**answers

26 views

### Definition of equi-absolute continuity [on hold]

Could someone provide (or point me to) a definition of equi-absolute continuity for functions defined on an open bounded subset $\Omega \subseteq\mathbb{R}^n$? I only managed to find a definition for ...

**3**

votes

**1**answer

80 views

### Create matrix containing values in [0,1] where sum of all diagonals and anti-diagonals is fixed

The problem I am facing sounds at first glance pretty simple. However, as very often, it seems more complicated than I first assumed:
I want to calculate a matrix $P = (p_{j,k}) \in \mathbb{R}^{n ...

**0**

votes

**0**answers

55 views

### Action of semidirect products of cyclic groups

Is there anything known about group actions of $C_{p}\rtimes C_{p}^{*}$ on the ring of real polynomials $\mathbb{R}[X_{1},\ldots,X_{n}]$, where $C_{p}$ denotes the cyclic group of order $p$ and $p$ is ...

**5**

votes

**0**answers

159 views

### Are Bökstedt's THH manuscripts available?

In many papers dealing with topological Hochschild homology, the original unpublished manuscripts by Bökstedt are cited. To name one example, in McClure and Staffeldt's On the topological Hochschild ...

**3**

votes

**1**answer

137 views

### When does an irreducible unitary real representation remain irreducible after complexifying it?

Consider a unitary real representation of a Lie group $G$ over a real Hilbert space $\mathcal{H}_\mathbb{R}$
\begin{equation}
\rho:G\rightarrow U(\mathcal{H}_{\mathbb{R}})
\end{equation}
Taking the ...

**-4**

votes

**0**answers

20 views

### Normal distribution [on hold]

To solve such a question
$\int_{-\infty}^{\infty}\ln{x}\frac{1}{\sqrt{2\pi}\sigma}\exp(-(x-\mu)^2/2\sigma^2)dx$.
It is easy when $\ln{x}$ is replaced by $x$ or $x^2$, but now I have no clue at all. ...

**1**

vote

**0**answers

33 views

### Green's function for fractional Laplacian

Consider the fractional differential equation
\begin{align}
D_{|x|}^\alpha u(x) +bu(x)=f(x)
\end{align}
with $0<\alpha<2$ on an unbounded domain. Instead of $D_{|x|}^\alpha$ one also often sees ...

**-2**

votes

**0**answers

33 views

### Problem on cohomology [on hold]

I am studying the book "Local Cohomology" written by M. R. Brodmann & R. Y. Sharp.
In exercise 2.2.9 in the page 28, asked to complete the proof of 2.2.8(iii) via proving
...

**7**

votes

**1**answer

318 views

### Explicit counter example to Vopěnka's principle in the constructible universe?

Vopěnka's principle is a large cardinal axiom which has many equivalent formulations. One of them, which I find especially appealing, is the following: if the universe is satisfies Vopěnka's principle ...

**0**

votes

**2**answers

139 views

### étale cohomology via Cech cocycles for a quasi-projective scheme

I am looking for the explicit reference to the fact that for a quasi-projective scheme a class in the étale cohomology of a sheaf of a certain degree can by computed using Cech cocycles.

**-1**

votes

**0**answers

41 views

### Hopf formula for the direct product of groups [on hold]

Let $G$ be a finite group with free presentation $1 \rightarrow R \rightarrow F \rightarrow G \rightarrow 1$. Then, we have well known Hopf formula $H_2(G,\mathbb{Z})=(R \cap [F,F])/[F,R]$.
Now, ...

**3**

votes

**2**answers

230 views

### Topologies for which $\mathcal{M}(X)\otimes \mathcal{M}(Y)$ is dense in $\mathcal{M}(X\times Y)$

Are there complete TVS topologies for which $\mathcal{M}(X)\otimes \mathcal{M}(Y)$ is dense in $\mathcal{M}(X\times Y)$
This question is strongly linked to
is the space of all borel measures on ...

**0**

votes

**0**answers

26 views

### Grouplike elements in dual weak Hopf algebras

It is said in D. Nikshych's paper On the structure of weak Hopf algebras (arXiv:math/0106010) that if $A$ is a finite dimensional weak Hopf algebra, then a functional $\gamma$ in the dual (weak Hopf) ...

**0**

votes

**1**answer

46 views

### Lebesgue covering dimension for locales

A space $(X,\tau)$ is said to have Lebesgue covering dimension $\leq n$ (for some $n\in\mathbb{N}$) if every open covering $\cal U$ has a refinement $\cal V$ such that for every $x\in X$ the set ...

**-2**

votes

**0**answers

22 views

### Find points which form angle X from a triangle formed by 2 other points [on hold]

Here's a diagram (I can't post images)
Diagram
Given angle ACB, angle CAD, position C, and position E, and given that angle ADB equals angle ACB, find position D.

**5**

votes

**1**answer

120 views

### Synthetic projective definition of cubic curves

In a synthetic (Pappian) projective plane, one can define a conic in various clever ways not referring to coordinates. For instance, if $f$ is a projectivity from the pencil of lines through a point ...

**1**

vote

**0**answers

81 views

### Matrix norm on $L^p$ operator algebras

I have a question about the framework of $L^p$ operator algebras ($1<p<\infty$), i.e. norm-closed subalgebras of $B(L^p(X,\mu))$ for some measure space $(X,\mu)$ (see e.g. ...

**4**

votes

**0**answers

85 views

### A digraph related to permutations

A finite sequence of distinct real numbers of length $n$ determines a linear order of $\{1,\ldots,n\}$, by mapping position to rank; call this the permutation of the sequence.
Consider the following ...

**0**

votes

**0**answers

38 views

### To determine whether an ideal is prime using Macaulay 2 [on hold]

I am new to Macaulay2, it seems to me that I cannot use it to determine whether an ideal in the polynomial ring over complex number is prime or not, because when I use the isPrime function, I got the ...

**0**

votes

**0**answers

45 views

### An inequality regarding expectation of random variables [on hold]

Let $X,Y$ be positive-valued, well-behaved random variables. Further, let $g(\cdot) \ge 0$ and $f(\cdot)\ge 0$ be two functions and $E(\cdot)$ denotes expectation operator.
I am trying to prove the ...

**2**

votes

**0**answers

115 views

### When is it appropriate to name something a 'fundamental lemma'? [on hold]

The term 'fundamental lemma' refers to many results in mathematics. I don't know too many results referred to by that name, but I am familiar with, for example, the 'fundamental lemma of sieve theory' ...

**4**

votes

**1**answer

51 views

### Largest regular $k$-simplex inscribed in a $d$-cube, $k < d$

The largest (by edge length) regular simplex inscribed in a unit cube
is well known in $\mathbb{R}^2$ and $\mathbb{R}^3$:
Image sources:
left: NMSU,
right: Mathworld.
A recent ...

**0**

votes

**1**answer

70 views

### Is the following “section-wise” defined function measurable in the product space?

I asked this question in mathstackexchange a couple of days ago. Almost right after posing it a partial (affirmative) answer came to my mind in the following form
Proposition: Assume that ...

**4**

votes

**1**answer

272 views

### Finite field “contour” sum

Let $\Bbb{F}_q$ be a finite field. Choose a non-square $\delta \in \Bbb{F}_q^*$
and form the quadratic extension $\Bbb{F}_q\big( \sqrt{\delta} \, \big)$. For
an element $z \in \Bbb{F}_q\big( ...

**2**

votes

**2**answers

48 views

### Volume of a region given by a Constraint Satisfaction Problem

I have a Linear Constraint Satisfaction Problem i.e. I have variables $ x_1, x_2,...,x_m$, with corresponding domains $D_1,D_2,...,D_m $ satisfying linear constraints $C_1, C_2,...,C_n$ with $n ...

**3**

votes

**0**answers

91 views

### Deformation of vector bundle on projective space with same Hilbert polynomial as multiple of structure sheaf

Let $E$ be a vector bundle on projective space ${\bf P}^n$ whose Hilbert polynomial is the same as $\mathcal{O}^{{\rm rank}(E)}$.
Does there exist a vector bundle over ${\bf P}^n \times {\rm ...

**1**

vote

**0**answers

67 views

### Determining the primitive ideal space of C-star algebras

Is there a general way of finding a primitive ideal space of $C^*$-algebra?
For example, if $C^*$-algebra is given by the universal $C^*$-algebra generated by two self-adjoint unitary elements, how ...

**0**

votes

**0**answers

45 views

### Morphism of modules of sections and pullback bundles

I'v asked this question on StackExchange but unfortunately nobody answered. I thought that maybe it would be more apropriate to post it here:
so suppose that we have a morphism $\theta: \Gamma(B,E_1) ...

**0**

votes

**0**answers

35 views

### Betti numbers over unital rings [closed]

Is the following statement correct?
Given a manifold M. If H_1(M,Z) is a finite cyclic group, then the first R-betti number b_1(M,R) is bounded from above by 1 for every unital ring R.

**2**

votes

**1**answer

70 views

### Functions that are easy to compare to a norm

Let $X$ be a subset of $\mathbb{R}^d$, let $\|\cdot \|_p$ be a norm with $1\leq p\leq\infty$, and let $f:\mathbb{R}^d\to\mathbb{R}$ be a function. I'm trying to find examples of $X$, $p$, and $f$ for ...

**0**

votes

**0**answers

70 views

### Help finding paper: De Concini, Kac - Quantum Groups at roots of 1

I am looking for a specific paper, that I have found very difficult to trace.
C. De Concini, V. Kac - Quantum Groups at roots of 1
Specifically, the paper is cited as follows (on De Concini's ...

**5**

votes

**0**answers

79 views

### The Maximum Number of Lines Contained in the Point Set of a Finite Projective Plane

Consider a finite projective plane of order $q$. Define $f(m)$ to be the maximum number of lines completely contained in any point set of size $m$, where $1 \leq m \leq q^2+q+1$. I would like to ...

**2**

votes

**0**answers

64 views

### Mean on compact metric spaces

Let $X$ be a compact metric space. A $k$ mean on $X$ is a continuous map $f:X^{k}\to X$ which is identity on the diagonal and is invariant under all $k$-permutations. For details, See the following ...

**5**

votes

**2**answers

80 views

### “Relative cone types” for groups relative to some collection of subgroups

It is a well known fact that an infinite hyperbolic group contains an element of infinite order (see e.g. Bridson, Haefliger, Metric spaces of non-positive curvature, Prop. 2.22 on p. 458)
I am ...

**0**

votes

**0**answers

18 views

### Weak continuous convergence of operators [migrated]

Let $T_n$ and $T$ be linear maps from Banach space $X$ to a Banach space $Y$.
Suppose $T_n$ satisfies $T_nx \to Tx$ (convergence in the $Y$ norm) for all $x \in X$.
Let $x_n \rightharpoonup x$ in ...

**0**

votes

**0**answers

26 views

### Morphisms between lax wedges

In the paper
BOZAPALIDES, S., Les fins cartésiennes
the following definition of a lax wedge for a 2-functor $S\colon \mathcal{A}^{op}\times \mathcal{A}\to \mathcal B$ between 2-categories is ...

**1**

vote

**0**answers

22 views

### Question about the characteristics of semimartingales

Let $D=D([0,1,R)$ be the space of cadlag (right-continuous with left limits) functions defined on [0,1] and $X:=(X_t)_{t\in [0,1]}$ be the canonical process on $D$, i.e. $X_t(x)=x(t)$ for all $x\in ...

**4**

votes

**2**answers

148 views

### First collision time of $n$ random walkers on a cycle

My question is somehow related to the one here First Collision Time for k Random Walkers on a Torus but, unfortunately, the answer does not cover my concern.
My problem is: consider $n$ walkers on ...