# All Questions

**3**

votes

**2**answers

78 views

### Polynomial invariants for unoriented links

I have seen that usually one finds polynomial invariants for oriented links (for example the Jones polynomial, the Hompfly polynomial). Does anyone know what polynomial invariants exist for ...

**0**

votes

**0**answers

28 views

### SVD of sum of a symmetric matrix and a banded matrix [on hold]

The SVD of the sum of a symmetric square matrix and an appropriately sized identity matrix can be written as following:
$A^TA + \lambda I = V(\Sigma + \lambda I)V^T$
where $\Sigma$ contains the ...

**0**

votes

**0**answers

47 views

### How to prove that the set of maximal elements of a set of prime ideals is finite

Let $A$ be a subset of ${\rm Spec}(R)$ with $R$ noetherian
Are there any techniques to prove that ${\rm max}(A)$ (ie the set of maximal elements of $A$) is finite?
I'm looking for equivalent ...

**-2**

votes

**0**answers

17 views

### What is the most efficient algorithmic implementation of maximum overlap discrete wavelet transform? [on hold]

What is the most efficient algorithmic implementation of maximum overlap discrete wavelet transform (MODWT)?

**6**

votes

**0**answers

126 views

### A generalization of SOCA

Roughly speaking, SOCA (Semi Open Coloring Axiom) says that for an open coloring of the unordered pairs over an uncountable separable metric space you can always find an uncountable homogeneous subset ...

**3**

votes

**1**answer

90 views

### Weak convergence in $W^{1,p}_0$

Note from the answerer : this question stems from this article.
I ask this question in http://math.stackexchange.com/questions/1206617
I have a bounded sequence $(u_n)$ from $W^{1,p}_0(\Omega)$ so ...

**1**

vote

**0**answers

25 views

### embdedding standard models of PA into nonstandard models [migrated]

Maybe it's well known to experts, but is there always an embedding $f$ of the standard model of Peano arithmetic into a nonstandard model? By Peano arithmetic I mean its first-order version, with the ...

**1**

vote

**0**answers

52 views

### Notions of consistency / heterogeneity in sets of vector values?

The problem
Let us consider a row vector u of size $n\in\mathbb{N}$, containing only binary values (0,1):
$$u=(u_1 \cdots u_n), n\in\mathbb{N}$$
$$\forall i \in \{1\ldots n\}, u_i \in\{0,1\}$$
I ...

**-2**

votes

**0**answers

123 views

### How to prove a certain theorem about algebraic function fields [on hold]

This question concerns a point from the book
David Goldschmidt, Algebraic Functions and Projective Curves, 2001 (link).
Let $K$ be a finitely generated extension of $k$ of transcendence degree ...

**8**

votes

**1**answer

269 views

### Must we know $MU^*(X)$ in order to compute $Ell^*(X)$?

Let $Ell^*(X)$ be the elliptic cohomology theory (associated to a given elliptic curve $E$) of a nice space $X$.
Recall the Landweber-Ravenel-Stong construction:
$MU^*(X) \otimes_{MU^*} R \simeq ...

**3**

votes

**0**answers

114 views

### Counting number of points in a lattice with bounded length

I am interested in counting number of lattices using the following theorem.
The following is Theorem IV (page 412) in Chapter VIII of "An introduction to the geometry of numbers (second printing, ...

**6**

votes

**2**answers

139 views

### Reference for proof that consistency of $\omega_1$-Erdos cardinal implies Con(Chang's Conjecture)

What is a good source for Silver's proof (or a more modern version) that Con($\exists \omega_1$-Erdos cardinal) implies Con(Chang's Conjecture)?
Silver's original proof seems to have never been ...

**3**

votes

**0**answers

112 views

### Does the higher cohomology of a quasi-coherent sheaf on a Stein manifold vanish?

It is a well-known result in algebraic geometry that if $X$ is an affine scheme and $\mathcal{F}$ is a quasi-coherent sheaf on $X$, then the higher cohomologies of $\mathcal{F}$ vanish, i.e.
$$
...

**3**

votes

**0**answers

56 views

### Which compact topological spaces are homeomorphic to their ultrapower?

It is well known that for any compact metric space $(X, d)$, and any ultrafilter $\mu$ there is a map $i_\mu:\prod_\mu (X, d) \to (X_d)$ in the category of metric spaces and Lipschitz maps where ...

**-1**

votes

**0**answers

42 views

### Problems concerning meromorphic 1 form on Riemann surface [on hold]

1. For a compact Riemann surface $X$, let the genus of $X$ be the dimension of the space of holomorphic one forms on $X$. How to compute the genus of the Riemann sphere and a complex torus.
2. ...

**15**

votes

**4**answers

592 views

### Thales' semicircle theorem in higher dimensions

Thales semicircle theorem says that an angle inscribed in a semicircle is a right angle.
Q1. Does a cone with apex on a hemisphere and encompassing the circular base
have a solid angle ...

**0**

votes

**0**answers

49 views

### Derivative of Log_p map

If $\mathscr{M}$ is a $(d-dimensional)$ Riemann Manifold and $p$ is a point therein. What is the derivative of $Log_p$ function?

**7**

votes

**0**answers

138 views

### The bifunctoriality of co/limits

I recently noticed that there are two senses in which colimits are functorial, and I'm curious about their interplay.
Let $C$ be a cocomplete category. Then, on the one hand, for any diagram ...

**0**

votes

**0**answers

29 views

### regularity of non-local linear elliptic equation

$\alpha\in (0,1)$, $u$ satisfies:
\begin{equation*}
b\cdot \nabla u(x)+\sum_{i=1}^d \int_{R} \left[u(x+se_i)-u(x)-s\mathbb{I}_{\{|s|\leq ...

**16**

votes

**0**answers

400 views

### Enriques surfaces over $\mathbb Z$

Does there exist a smooth proper morphism $E \to \operatorname{Spec} \mathbb Z$ whose fibers are Enriques surfaces?
By a theorem of, independently, Fontaine and Abrashkin, combined with the ...

**0**

votes

**0**answers

32 views

### Optimal bound in $L^2$ product on compact Kahler manifold

Let $X$ be a compact Kahler manifold of dimension $n$, equipped with a Kahler metric of volume $1$. There exists a constant $C \geq 1$ such that for any smooth functions $f,g$ on $X$ we have
$$
\int_X ...

**2**

votes

**0**answers

30 views

### How is the structure of spectrum in cap-sets with no strong increments unrealistic if density is too large?

I am reading this excellent paper by Bateman and Katz on improved bounds on the cap set problem.
Let A be a set in $\mathbb{F}_3^n$ containing no 3-term arithmetic progression and let $A(x)$ denote ...

**-1**

votes

**0**answers

24 views

### Variance under time-scaling of sample measurements [on hold]

I am struggling with explain something I read in a Whitepaper. The essence is as follows.
Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X ...

**0**

votes

**0**answers

72 views

### Does a (non-closed) differential 1-form define a curve? [on hold]

I am trying to understand under what conditions the following procedure properly defines a curve. Take a manifold $M$ with a (non-closed) 1-form $B$ and an exact 1-form $dA$. Define the functions ...

**1**

vote

**0**answers

16 views

### When does a symmetric Poisson manifold decompose into homogeneous pieces?

When people study representations, they pay a lot of attention to the irreducible ones. This is justified by the fact that, roughly speaking, every unitary representation decomposes into a direct ...

**1**

vote

**1**answer

68 views

### Polyhedra containing hexagones only [on hold]

It is well-known that Euler's theorem gives raison d'être to polyhedra containing exactly 12 pentagons if they are connected by 3 in a vertex. The number of hexagons may be arbitrary (in fact >1). In ...

**-3**

votes

**0**answers

41 views

### why the split extension of a quasicyclic $2$-group $C$ by the cyclic group is not finite by abelien [on hold]

Let $G$ be split extension of a quasicyclic $2$-group $C$ by the cyclic group of ordre 2 generated by the inversion automorphism of $C$ it is clear that $G$ is abelien by (finite cyclic) but why $G$ ...

**1**

vote

**1**answer

38 views

### Can real-valued Markov processes with continuous surjective sample paths admit a non-trivial “forward-invariant” set?

I have both a more general question (concerning stopping times), and then a more specific application (as described in the title).
Let $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t \geq 0},\mathbb{P})$ be ...

**3**

votes

**1**answer

137 views

### Toral rank conjecture

In 1985, S.~Halperin conjectured in the topological context of maximal free torus actions on topological manifolds, that:
If $X$ is a topological space, then $$\dim H^*(X;\mathbb Q)\geq 2^{rk(X)}.$$
...

**1**

vote

**2**answers

209 views

### Root in positive Weyl chamber

Let $\mathfrak{g}$ be a complex simple Lie algebra. We fix a Cartan subalgebra $\mathfrak{t}\subset \mathfrak{g} $. Let $R\subset \mathfrak{t}^*$ the set of roots. We fix $\Pi\subset R$ the set of ...

**2**

votes

**0**answers

64 views

### Lower boundedness of the Ricci curvature [on hold]

I know that this is going to be slightly vague, but it's itching me: why is lower boundedness of the Ricci curvature required by some of the very important theorems in Riemannian geometry? The ...

**2**

votes

**0**answers

89 views

### Geometry of rings and semi-rings

Basically, I wonder whether a theory similar to geometric group theory has been or could be developed for rings and semirings.
One direction would be the following. Consider $\mathbb{N}$ (with the ...

**15**

votes

**1**answer

480 views

### Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?

I know $\sum_{k=1}^{n} \sin(k)$ is bounded by a constant. How about $\sum_{k=1}^{n} \sin(k^2)$?

**1**

vote

**1**answer

94 views

### Dense symmetric unitary integer matrix?

Can someone give me a nontrivial example of a symmetric unitary integer matrix? I'm looking for something as dense as possible (i.e., not too many 0's); 5 <= size <= 8 would be ideal.

**1**

vote

**0**answers

73 views

### Square-free sieve over number fields

I am trying to work on extending various methods to study square-free values of polynomials (or more generally, $k$-free values) over general rings of integers, and a literature review has yielded ...

**5**

votes

**1**answer

176 views

### $\mathcal S(\mathbb R^n) \hat \otimes_\pi \mathcal S(\mathbb R^m) \simeq \mathcal S(\mathbb R^{n+m})$?

If $S(\mathbb R^n)$ is the Scwartz space of smooth rapidly decaying functions equipped with the topology generated by the family of semi-norms
$$\mathcal N_p (\varphi)= \sum_{|\alpha|, |\beta| \leq p} ...

**-4**

votes

**0**answers

232 views

### Proof theory and the generalized Riemann hypothesis [on hold]

Is there a disproof of the following?
CONJECTURE: Let $\chi$ be a Dirichlet character modulo $q$. Let $\varepsilon$ be a positive number with $0 < \varepsilon < \frac{1}{2}$. Let $T$ be a ...

**1**

vote

**0**answers

79 views

### What is $\int (1-e^{-x})^n dx$? [on hold]

For my purposes, $n$ is a non-negative integer, and $x > 0$. I didn't know how to evaluate this integral, so I plugged it into Mathematica. It told me the solution is
$(-1)^n B(e^x; -n, n+1)$
I ...

**4**

votes

**0**answers

45 views

### Is there a generalization of Polya urns to continuous outcome event?

Take for example the simplest model where there are n blue balls and m white balls in an urn. Then, in a first step realization, a white one has been drawn and then c + 1 of this colour had been put ...

**3**

votes

**0**answers

117 views

### Is surjectivity for morphisms of schemes local on the domain?

It is said so in Knutson's book 'algebraic sapces' in several places for different topologies on schemes, see Chapt. I, 2.19 for Zariski top, 3.13 for flat top., 4.11 for etale topology.
But this ...

**0**

votes

**0**answers

47 views

### Number of “small” subsets to a “large” set [migrated]

For the following we assume the axiom of choice.
Let $X$ be a set of cardinality $l$ for some infinite cardinal number $l$, and let $p(X)$ be the number of subsets of $X$ that have cardinality ...

**2**

votes

**0**answers

24 views

### Conditions for monotone function to take maximal chains to maximal chains surjectively

Suppose that $P$ and $Q$ are graded posets (with rank function $r$) and suppose that all maximal chains of $P$ and $Q$ have length $n$.
Let $f:P \to Q$ be a surjective monotone function such that ...

**5**

votes

**1**answer

151 views

### Scotts Theorem for one ended Fuchsian groups

in Peter Scott's work "Subgroups of Surface groups are almost geometric" is proven that for a closed surface $S$ and any fin. gen. subgroup $U$ of $G:=\pi_1(S,x)$ there exists a finitely sheeted ...

**1**

vote

**1**answer

108 views

### Subgroups generated by opposite root groups

Suppose $\mathbf{G}$ is a connected reductive (possibly non-split!) group over a field $F$, $\mathbf{S} \leq \mathbf{G}$ a maximal split subtorus and $\mathbf{Z} \leq \mathbf{G}$ its centralizer. For ...

**0**

votes

**3**answers

216 views

### orbit space of $\mathbb{Z}_p$ action over complex projective space by permuting the homogeneous coordinates

$Z_p$:=cyclic group of order $p$.
I want to understnd $H_\ast(\mathbb{C} P^{n}/Z_{n+1};Z)$ with $(n+1)$ being a prime number,and the action is given by permuting the homogeneous coordinates.
For ...

**1**

vote

**0**answers

146 views

### In set theory, is there a name for a function which maps the empty set to zero and all the others to one? [on hold]

I would like to avoid inventing something which might be standard.
Thus, I'am asking if there is a name for a function which is defined as $f$:
Let $S$ be any set, then $f(S)=0$ if $S$ is empty and ...

**6**

votes

**2**answers

348 views

### Texts about Dwork's work

I want to ask about references to papers, that probably exist, which explain the articles of Bernard Dwork starting from "The rationality of the zeta function of an algebraic variety" to "On the ...

**3**

votes

**2**answers

215 views

### A problem with pointwise stabilizer subgroups of fixed-point subspaces II

Definitions: Let $W$ be a representation of a group $G$, $K$ a subgroup of $G$, and $X$ a subspace of $W$.
Let the fixed-point subspace $W^{K}:=\{w \in W \ \vert \ kw=w \ , \forall k \in K \}$.
Let ...

**11**

votes

**1**answer

568 views

### Applications of set theory in physics

In the introduction of the paper "Links between physics and set theory", the following quote of Eris Chric is stated:
...

**4**

votes

**1**answer

130 views

### Simply connected Lie groups homeomorphic to R^n are solvable

I have found the following claim in many proofs "Simply connected Lie groups homeomorphic to $\mathbb{R}^n$ are solvable". But the universal covering of $SL(2,\mathbb{R})$ satisfies the hypothesis of ...