# All Questions

**4**

votes

**1**answer

63 views

### metrizable neighborhoods of compact subsets

This is a question about general topology:
Assume we are given a first countable Hausdorff space and a compact subset K.
Is it possible to find a countable basis of open neighborhoods of K ?
...

**0**

votes

**0**answers

18 views

### Coupled recurrence relations for generating functions, involving squared arguments

I'm trying to find a solution for the following system of three equations in terms of three bivariate generating functions.
$G(x,y)=b(x,y) \cdot \left( G(x,y^2) + I(x,y^2) \right) +y ;$
$H(x,y)=x ...

**3**

votes

**2**answers

108 views

### Finite Dimensional Simple nonunital associative Algebras

I have the following problem:
Let K be any field. An finite dimensional associative non-unital algebra A is a vector space A, togeter with a K-biliniear associative operation such that there is NO ...

**0**

votes

**0**answers

22 views

### Optimization problem involving an entrywise function

Let $X$ a $n\times p$ real-valued matrix and $Y$ a $p\times q$ real-valued matrix. Let $\phi:\mathbb{R} \to \mathbb{R}$ a function. What is the appropriate way to deal with the following optimization ...

**0**

votes

**0**answers

156 views

### Holomorphic vector bundles over $\mathbb{CP}^1$ and elliptic curves

Can anyone suggest a good exposition of the classification of holomorphic vector bundles over $\mathbb{CP}^1$? Also does there exist any analytic or more elementary proof of Atiyah's classification of ...

**3**

votes

**1**answer

70 views

### Existence of ind-right adjoint functor for semi-simple category?

I'm just reading a lemma in Yves ANDRE's seminar on finite dimensional motives.
Soit $Σ:Rep_F G→T$ un ⊗-foncteur vers une categorie F-tensorielle T ……
where $G$ is a pro-reductive group scheme, ...

**1**

vote

**2**answers

204 views

### An interpretation of not-Con(PA)

Edit After Andreas Blass answer below and comments below the original post I have changed it to accommodate posters' remarks. I hope it is clear and makes more sense now.
Let $\mathrm{PA}$ be the ...

**-5**

votes

**0**answers

137 views

### Why so much graph theory? [closed]

I am a Computer Science student. In my college, we study many aspects of Discrete Mathematics mainly Graph Theory. I understand that, for a Computer Scientist, it is important to know about graphs, ...

**2**

votes

**1**answer

74 views

### Is barycentric subdivision of a collapsible, regular CW complex collapsible (non-evasive)?

Let $X$ be a finite, regular CW complex, and let $X'$ be its barycentric subdivision (i.e. the order complex of the face poset of $X$). Assume $X$ is collapsible.
Is $X'$ collapsible?
Is $X'$ ...

**6**

votes

**3**answers

408 views

### sum of binary and ternary digits

A problem in group theory (indices of imprimitive groups) gives rise to the following conjectures in number theory. Suppose a positive integer $n$ has binary and ternary expansions ...

**9**

votes

**0**answers

129 views

### Derivation of Blattner's conjecture in the Beilinson-Bernstein picture

On the last page of Schmid's article "Discrete Series", he says
"In the Beilinson-Bernstein picture, discrete series modules are attached to closed $K$-orbits in $X$... the $K_{\mathbb R}$-structure ...

**6**

votes

**1**answer

365 views

### Is there a generalized Birkhoff ergodic theorem?

Is there a Birkhoff ergodic theorem for two measure preserving transformations $T$ and $S$ where $S\circ T= T \circ S$ so that $\frac{1}{n+1}\frac{1}{m+1}\sum_{i=0}^{n}\sum_{j=0}^{m}f \circ T^{i}\circ ...

**0**

votes

**0**answers

24 views

### a generalization of the annihilator of cokernel ideal

Let $R$ be a (commutative, associative, unital) ring, consider a homomorphism of some (finitely generated) free $R$-modules $F\stackrel{A}{\rightarrow}G$. Its basic invariants are the Fitting ideals, ...

**0**

votes

**0**answers

49 views

### Bases of surface groups with length restrictions

This question asks for a generalization of Bases of surface groups following the notation and definitions given therein.
Let $\Gamma_g$ be a surface group of genus $g \geq 2$, $B$ a surface basis of ...

**3**

votes

**1**answer

103 views

### Conditional Form of Rosenthal's Inequality

Rosenthal's Inequality as stated in the book "Martingale Limit Theory and Its Application" by Hall and Heyde states the following:
If $\{S_i, \mathcal{F}_i, 1\leq i \leq n\}$ is a martingale and ...

**1**

vote

**0**answers

35 views

### Handelman's positivstellensatz for symmetric matrix-valued polynomials

For certain classes of sets $S \subseteq \mathbb{R}^n$, there exist algebraic characterizations of real valued polynomials $p: \mathbb{R}^n \rightarrow \mathbb{R}$ that are positive on $S$.
Several ...

**-2**

votes

**0**answers

35 views

### Does the algorithm to construct the edge-colored graphs with this special property have any importance? [closed]

I found a semi-general solution to the following open-ended question and obtained the explicit algorithms to construct the edge-colored graphs with the following special property. But does my solution ...

**0**

votes

**0**answers

72 views

### How do we represent one-way “equality” in mathematical notation? [closed]

Here's an example:
You have 20 dollars
A full coke = 2$
A full coke yields an empty bottle and a bottle cap
4 empty bottles yields a full coke
2 bottle caps yields a full coke
Let full coke = F, ...

**-7**

votes

**0**answers

67 views

### Two graph theory questions, really hurry. Thanks a lot [closed]

Q2: Draw the `breadth-first searches' for the Tower of Hanoi for the cases with 1, 2 and 3 discs. Conjecture a strategy and show using a depth-first search, that this strategy works for 4 discs.
Q3: ...

**3**

votes

**0**answers

115 views

### What do we know about isospectral Cayley graphs?

Let $\Gamma_1=\Gamma_1(G_1,S_1)$ (respectively $\Gamma_2=\Gamma_2(G_2,S_2)$) be a Cayley graph for the group $G_1$ and the finite generating set $S_1$ (respectively $G_2$ and the finite generating set ...

**1**

vote

**0**answers

76 views

### Dislocations,Disclinations Latices, Displacement fields and scaling

I am looking up Frank, and Burger vectors and associated material on dislocation/disclination. It seems straightforward describing a lattice and what dislocation means. It is even possible to restrict ...

**-1**

votes

**0**answers

71 views

### On the lattice of submodules of a module over a simple ring [closed]

We suppose that all rings are left Artinian simple rings and all modules over a ring are of finite length.
Let $M$ be a left module over a ring $R$. By Wedderburn theorem, $R$ is a matrix ring over a ...

**10**

votes

**1**answer

552 views

### Is there an analog of the Birch/Swinnerton-Dyer conjecture for abelian varieties in higher dimensions?

I am wondering if there is a multi-dimensional analog of the
Birch/Swinnerton-Dyer (BSD) conjecture.
The recent famous result inching toward resolution of that conjecture is:
Bhargava, Manjul, and ...

**0**

votes

**0**answers

95 views

### Irreducible action of an algebraic group

Is the following claim true?:
Let $G$ be an algebraic group such that $G^\circ$ is reductive. Suppose $G$ acts irreducibly on $V$. Is it true that $V$ is decomposed (written as direct sum) into ...

**1**

vote

**0**answers

69 views

### Can we classify reductive group schemes over curves

Let $C$ be a smooth quasi-projective connected curve over the complex numbers.
Can one classify all reductive group schemes over $C$?
Certainly, you have the trivial ones (coming from pulling-back ...

**7**

votes

**0**answers

186 views

### Is every continuous function measurable?

This question has already been asked on Math StackExchange here, but was too old to be migrated, and I think will be more appropriate to MathOverflow.
In non-Hausdorff topology it is standard to ...

**-1**

votes

**1**answer

73 views

### Action of rotation group on Matrices [closed]

Is the following assertion true?
Suppose $p, q \geq 3$. Consider the action of $SO(p,\mathbb{R})$ on $p \times q$ matrices by left multiplication. I want to show that $MA = A$, where $M \in ...

**1**

vote

**0**answers

47 views

### Which groups may be obtained as $K$-homology groups?

Recently I asked the following question, about the separability of the underlying $C^*$-algebra in the definition of $K$-homology:
mathoverflow.net/questions/181361
As far as I understood, ...

**3**

votes

**0**answers

55 views

### Semigroups with group like behavior

I'm trying to generalize some results done to groups to the semigroup case. I noticed that the results will not work with a general semigroup, I decided to try to extend the results to the inverse ...

**5**

votes

**2**answers

251 views

### What can be said of the structure of a metric space without isosceles triangles?

This is a question that has been bothering me in the back of my head for quite some time.
Suppose we have a metric space $X$ with metric $\mathrm{d}$. By an isosceles triangle we mean a tuple of ...

**4**

votes

**1**answer

98 views

### Canonical bundle of moduli space of rational curves and automorphisms

Let $\overline{M}_{0,n}$ be the usual Deligne-Mumford compactification of $M_{0,n}$ the moduli space of smooth $n$-pointed rational curves.
The canonical divisor $K_{\overline{M}_{0,n}}$ can be ...

**0**

votes

**0**answers

47 views

### Induced subgraphs on a Laminar family of vertices with constant diameter

$X$ is a family of subsets of $V$. $X$ is called a Laminar family on $V$ if for all $A,B\in X$, either $A\cap B=\emptyset$, $A\subset B$ or $B\subset A$.
Let $X$ be a family of subsets of $V$. A ...

**3**

votes

**0**answers

43 views

### survival of a prime ideal in its Nagata transform

Let $R$ be a Noetherian normal domain with fraction field $K$. Recall that for any ideal $I \subseteq R$, its Nagata transform $T(I)$ is defined as the set of elements $f\in K$ such that $I^n f ...

**4**

votes

**1**answer

106 views

### Ends of quotients of Coxeter Groups

Let C(p,q) be the Coxeter group:
$C(p,q):= \langle a,b,c\hspace{1mm}|\hspace{1mm} a^2,b^2,c^2,(ac)^2,(ab)^p, (bc)^q \rangle$
for integers $p,q$ s.t. $\frac{1}{p}+\frac{1}{q}<\frac{1}{2}$. This ...

**3**

votes

**0**answers

76 views

### Reference request: Optimal $L^p$-decay for nonhomogenous heat equation in $\mathbb R^d$

Let $u$ be a classical solution for the nonhomogeneous heat equation in $\mathbb R_+ \times\mathbb R^d$:
$$
\begin{cases}
\partial_tu(t,x)-\Delta u(t,x) = f(t,x), \\
u(0,x)=u_0(x).
\end{cases}
$$
...

**5**

votes

**0**answers

170 views

### A generalization of real characters on a group

Yesterday I understood that I can't live without this construction:
Let $G$ be a group, $A$ an associative algebra over $\mathbb R$ and $n\in{\mathbb N}$. We consider a sequence of maps ...

**0**

votes

**1**answer

118 views

### Estimating the height required to find a given small value of $|\zeta(s)|$ near the line $\sigma=1$

There are some qualitative theorems of Bohr, Jessen and Titchmarsh (e.g. The Theory of the Riemann zeta function, E.C. Titchmarsh, pages 306-308) proving that there is a $K=K(a,\alpha,\beta)$ such ...

**2**

votes

**0**answers

60 views

### Criterion for the existence of finite locally free resolution

Let $X$ be a projective variety over an algebraically closed field $k$, $S$ be a $k$-scheme, $E$ be a coherent sheaf on $X \times_k S$, flat over $S$. We know that if $X$ is smooth then $E$ has a ...

**-7**

votes

**0**answers

61 views

### 1 person to level 5 in a 3X5 Matrix [closed]

I need to know how many people it would take to get 1 person to level 5 in a 3x5 matrix in a straight matrix I know it would take 120 people... My concern is that the 2nd person everyone gets will be ...

**1**

vote

**0**answers

73 views

### Riemann curvature of $S^1$-principal bundle

Let $(M,g)$ be a Riemannian manifold and $\pi:P \to M$ be $S^1$- principal fiber bundle endowed with a connection $\Gamma$. For every $p\in P$ we have,
$$T_pP \simeq T_pV\oplus\Gamma_p$$
Where $V$ ...

**2**

votes

**0**answers

78 views

### Examples for Markov generators with pure point spectrum

I'm looking at symmetric diffusion Markov generators $L$ with pure point spectrum, i.e. infinitesimal generators of symmetric diffusion Markov semigroups, which are defined on $L^2(\mu)$ where $\mu$ ...

**1**

vote

**0**answers

130 views

### Is there a D-module theory in characteristic p>0

everyone.
In characteristic 0 we have a good theory of D-modules. In particular, we have a formalism of Grothendieck's six operators in the derived category of holonomic D-modules and Riemann-Hilbert ...

**2**

votes

**0**answers

95 views

### subschemes of abelian scheme over artinian basis

Let $R$ be an artinian thickening of a field $k$. Denote with $S=Spec(R)$. Let $A$ be an abelian scheme over $S$. Let $X$ be a closed, reduced, equidimensional subscheme of the special fiber $A_k$. I ...

**1**

vote

**1**answer

59 views

### Definition of homotopy between Kasparov modules

I'm trying to understand the definition of homotopy between Kasparov modules as presented in Blackadar's book on K-theory for operator algebras. $A,B$ will be C*-algebras, while $E$ will denote a ...

**-3**

votes

**1**answer

117 views

### A problem that involves matrix and Lorentz Transformation [closed]

To be clear I address the question in two parts as below. All matrixes involved are real four-dimensional matrixes.
$1.$Let $G$ be the matrix $diag(1,-1,-1,-1)$. $A$ is a matrix satisfying $A G ...

**2**

votes

**1**answer

112 views

### convergence of L-functions of curves

Let $C$ be a smooth projective curve over $\mathbb{Q}$. Its associated L-function is defined by
$$
L(C, s)=\prod_{p \text{ prime}} L_p(C, s),
$$
where, if $p$ is a prime of good reduction, ...

**3**

votes

**1**answer

124 views

### Cancellative semigroup on a distributive lattice

Let $(S,\le)$ be a distributive lattice. Is there a semigroup structure on $S$ such that $S$ is cancellative and always $(x\wedge y)(x\vee y)=xy$?

**4**

votes

**2**answers

164 views

### The unit tangent bundle of 2- or 4-manifolds as a principal $S^{1}$- or $S^{3}$-bundle

What type of obstructions have been studied so that the unit tangent bundle of a Riemannian 2-(4-)manifold have a structure of a principal $S^{1}$-($S^{3}$-)bundle?

**0**

votes

**1**answer

59 views

### Paper on unit disk graphs

I was wondering if anybody knows of a 'link' to the paper by Marathe 1995 et al on analysis of the greedy algorithm for finding a Max independent set in Unit Disk Graphs?

**-2**

votes

**0**answers

60 views

### How to plot 2-D and 3-D Joint numerical range of real symmetric matrices in mathematica? [closed]

I know this question this doesn't belong here. However, I am not getting a satisfactory reply from the mathematica forum. Consider $2\times 2$ real symmetric matrices $\mathbf{A}_1$ and ...