# All Questions

**-2**

votes

**0**answers

86 views

### lower bound for $\#\{n \mid n\leq x\text{ and }2n-1,2n+1\text{ are not prime}\}$ [closed]

I'm searching for upper and lower bounds and a good estimate for the function $f$ ($f(x)\sim x$ for $x\to\infty$), which is counting the numbers $n\leq x$, s.t. $2n+1$ and $2n−1$ aren't prime (see ...

**6**

votes

**2**answers

336 views

### Quasi-affineness of the base of a $\mathbb{G}_a$-torsor

Let $\mathbb{G}_a$ be the additive group over an algebraically closed field $k$ of any characteristic. Let $X \to Y$ be a $\mathbb{G}_a$-torsor of $k$-schemes (of finite type - in case that is ...

**-4**

votes

**1**answer

163 views

### A question about group topologies on $\Bbb Z$ [closed]

Let $\mathcal T$ be a group topology on $\Bbb Z$ such that the set of all neighborhoods of $0$ has a countable neighborhood base but not a finite base. And let $U$ be a neighborhood of $0$.
Is there ...

**0**

votes

**0**answers

60 views

### Reference request: How you can reach any point in the vector space of vector fields generated by Lie brackets

By a Theorem of Chow, you can reach any point in the vector space of vector fields generated by Lie brackets.
Do you know any reference for this theorem?

**0**

votes

**0**answers

53 views

### Factoring a semiprime is easier than matrix multiplication? [closed]

I'm currently dealing with complexity estimates of various algorithms and the connected mathematical problems. Up until now, I had in mind that problems such as integer factorization and the discrete ...

**0**

votes

**0**answers

104 views

### Can ramification be “seen” at smooth subcurves?

This is a follow-up question to this. Though it's a differnt question, therefore I decided to open a new question so that we don't lose track. I hope that's okay.
Let $f: X \to Y$ be a finite, ...

**3**

votes

**0**answers

162 views

### Relationship between fragments of the axiom of choice and the dependent choice principles

The dependent choice principle ${\rm DC}_\kappa$ states that if $S$ is a nonempty set and $R$ is a binary relation such that for every $s\in S^{\lt\kappa}$, there is $x\in S$ with $sRx$, then there ...

**0**

votes

**0**answers

46 views

### Approximating the probability of an event by finite-dimensional distributions [migrated]

Let $(X(t))_{t\ge 0}$ be a stochastic process on $\mathbb{R}^d$, say an Ito diffusion (with continuous sample paths). Let $A\subset \mathbb{R}^d$ be a measurable set and $t>0$. Does the following ...

**-1**

votes

**0**answers

90 views

### Find out acceptance rate / selectiveness of conference [closed]

In general, how can I find out the acceptance rate of a conference, and whether it's highly refereed or not?
For example, say I encounter a conference like the FPSAC. Is it highly selective, or does ...

**3**

votes

**2**answers

319 views

### Zigzags and contractibility of categories

Let $\mathbf{C}$ be a small category and $\mathbf{C}'$ its hammock localization in the sense of Dwyer and Kan. I am looking for a proof (or counterexample) of the following assertion:
If there is ...

**4**

votes

**1**answer

159 views

### orthogonal group in characteristic 2

Let $O(2,\mathbb{Z}_2)$ be the orthogonal group of order two matrices. On $\mathbb{Z}_2$ there should exist just one odd quadratic form, hence the stabilizer subgroup $O^-$ of an odd quadratic for ...

**3**

votes

**1**answer

167 views

### Preimage of smooth curves under morphism of smooth varieties

Let $f: X \to Y$ be a finite, surjective morphism of smooth, projective, irreducible varieties over $\mathbb{C}$ and let $y \in Y$.
Can I find a smooth curve $C \subseteq Y$ with $y \in C$ such ...

**4**

votes

**1**answer

252 views

### Are constant connection coefficients uniquely determined by the (1,3) curvature coefficients?

Suppose that on a certain coordinate system the coefficients $\Gamma^i_{jk}$, $i,j,k=1,\cdots, n$, of a linear connection are constant. We do not require compatibility with a metric, however I am ...

**0**

votes

**1**answer

90 views

### rational sections of logarithmic differentials on a curve

Let $C$ be a smooth projective curve over a field $k$ of characteristic zero and $S$ a reduced divisor on $C$ (so just a collection of points). Consider the sheaf of logarithmic differentials ...

**1**

vote

**1**answer

105 views

### homotopy type of the cone of a loop space

I read somewhere that for, a path connected CW complex $X$, there is a homotopy equivalence of pairs between $(P_1X,\Omega X)$ and $(C\Omega X,\Omega X)$ where $P_1X$ denotes the set oh paths ...

**8**

votes

**1**answer

198 views

### Integers with a large prime divisor in short intervals

For an integer $n$, denote by $P^+(n)$ the largest prime divisor of $n$. Then we have the following:
There exists some $c>0$, such that for all $x$ sufficiently large the number of integers ...

**0**

votes

**0**answers

107 views

### Measure concentration for law of large numbers

The classical law of large numbers states that
$$\frac{\sum_{i=1}^k X_i}{k} \rightarrow \mathbb{E} X_1$$
for iid $X_1, X_2, \ldots$ with bounded $L^1$ nrom.
I was wondering that is it possible to ...

**5**

votes

**2**answers

222 views

### Matching number and chromatic number

If $G$ is a (finite) graph, denote with $\mu(G)$ the size of any maximum matching in $G$ (this number is also called the "matching number" of $G$).
For odd integers $n$ we have $n=\chi(K_n) = ...

**0**

votes

**0**answers

63 views

### Linkage between homotopy equivalence and identification of algorithms

I vaguely recall that someone says there is linkage between homotopy equivalence and identification of algorithms which may be isomorphic or morphism or something like that,the algorithm may be ...

**7**

votes

**0**answers

138 views

+50

### Saturated Ultrapowers

I posted it on MSE and didn't receive any comments or answers, so I thought I would post it here.
(See http://math.stackexchange.com/questions/895549/keisler-order-saturated-ultrapowers)
Keisler's ...

**0**

votes

**0**answers

78 views

### Relation between modulus of smoothness and reflexivity

Baillon proved that if $X$ is a Banach space with $\rho'_X(0)<\frac{1}{2}$, then $X$ has the fixed point property (by $\rho_X(t)$
we denote the modulus of smoothness). My questions are as ...

**5**

votes

**0**answers

138 views

### Ultracoproducts and Cartesian products

Let $X$ be a metrizable compact topological space, let $\mathcal U$ be an ultrafilter, and denote by $X^{\mathcal U}$ the ultracopower of $X$ with respect to $\mathcal U$.
As a C$^*$-algebraist, I ...

**-1**

votes

**0**answers

42 views

### Morphism of curves with special ramification

Let $\varphi: C_1 \to C_2$ be a finite morphism of integral, projective curves over a field of characteristic $0$. Let $n_i: \tilde{C_i} \to C_i$ be the normalization and let $\tilde{\varphi}: ...

**4**

votes

**2**answers

177 views

### What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?

In certain intuitionistic frameworks the extreme value theorem cannot be proved. Depending on the exact framework, counterexamples can be constructed as well; see for example pp. 294-295 in
...

**4**

votes

**0**answers

139 views

### Atlas of a manifold as a Sheaf

--Hopefully this question does not dublicate another--
In this question Tom Goodwillie pointed out, that the 'atlas part' of
the definition of a smooth manifold can be redefined in terms of
sheaves. ...

**2**

votes

**1**answer

174 views

### vector bundles on $\mathbb{C}[x,y,z]/(x y - z^k)$

Let $A = \mathbb{C}[x,y,z]/(x y - z^k)$. In fact $A$ is the ring of $\mu_k$ invariants: $A = \mathbb{C}[u,v]^{\mu_k}$ where $g \in \mu_k$ acts by $g(u,v) = (g u, g^{-1} v)$.
This allows one to ...

**-1**

votes

**0**answers

35 views

### Existence of a limit [closed]

Let x(n) be a real sequence such that
x(n+1) <= x(n) + 1/n^2
Prove that lim x(n) exists.
I've tried to prove it using the delta-epsilon definition, limit superior and inferior, cauchy ...

**0**

votes

**0**answers

83 views

### A special Lie subalgebra

Motivated by comments of the following post A question on involutions on the Lie algebra of vector fields we ask the following question:
Let $L$ be a Lie algebra. We consider the Lie subalgebra ...

**2**

votes

**0**answers

87 views

### When do limits and colimits of infinity-categories commute?

This is a question for someone who read (or wrote) enough of Lurie's HTT to know a reference. Suppose $D,E$ are small "diagram" $(\infty,1)$-categories, and $\mathcal{C}$ is a stable infinity-category ...

**0**

votes

**0**answers

18 views

### Find the probability generating function of a GW process [migrated]

Consider a Galton-Watson process with offspring distribution
$Possion(1)$. That is, $\textbf{p}(k) = \frac{e^{-1}}{k!}$. Given this information, and that $P(z) = ...

**2**

votes

**2**answers

127 views

### How to define the input of computable function or Turing machine over real numbers

Computation or computability over $\mathbb{N}$ can be extended to computation or computability over $\mathbb{R}$ or even computation or computability over $\mathbb{C}$.The following is a formal ...

**2**

votes

**1**answer

224 views

### Does every mathematics article have a DOI (Digital Object Identifier)?

Most articles nowadays have DOI's. I am looking for a list of mathematics journals in which some (or all) articles lack this piece of metadata.
I don't have access to MathSciNet, but even if I had, a ...

**10**

votes

**1**answer

1k views

### ICM 2014 streaming video

Is there a possibility to watch ICM 2014 opening ceremony and the big talks online?
I hope there is since it was possible for the previous meeting.

**2**

votes

**0**answers

43 views

### Some Questions from Reading on Wave Front Set from Hormander's Linear PDE Vol. 1

In Hormander's Linear PDE Vol. 1 (pg 252-253, before the definition of wave front set is introduced), Lemma $8.1.1$ says that if $\phi \in C_{0}^{\infty}$ and $v \in \mathcal{E}^{\prime}$, then ...

**3**

votes

**3**answers

89 views

### Are there any results on well-quasi-ordering of languages?

There are a number of papers that I can find about well-quasi-orders in formal lnaguage theory, by Kunc, de Luca, D'Alessandro, and Varricchio, among others. I am interested, however, in well-quasi ...

**21**

votes

**1**answer

591 views

### What is the analogue of simple prime closed geodesic for prime numbers?

The prime geodesic theorem (of Margulis?) states that on a compact surface of (constant?) negative curvature, the number of prime closed geodesics of length at most $L = \log x$ is approximately ...

**0**

votes

**1**answer

68 views

### Probability of k overlapping subsets in N trials

Ok, here is what I am attempting to find an answer to:
I draw M uniformly random subsets of size K from the set of numbers $\Omega=\{1, \dots, N\}$ (where uniformly random means that each unique ...

**0**

votes

**1**answer

67 views

### A Modified Birkhoff-von Neumann Theorem [closed]

Sorry for having two open MO posts.
Let "stochastic" matrix be the matrix whose rows sum to one and deterministic matrix be a stochastic matrix whose all rows consist of a one and zero.
For example ...

**1**

vote

**0**answers

41 views

### Decomposition of polynomials with three variables

We use $\bigtriangleup _i$ to denote either multiplication or addition.
Suppose we have a polynomial $P(x,y,z)$ over some algebraic closed field such that:
There are $Q(x), W_1(x,y),W_2(x,z)$ ...

**2**

votes

**3**answers

99 views

### Conformal invariance of Brownian motion in higher dimensions

We know for planar Brownian motion, that conformal maps composed with Brownian motion are also Brownian motion (preserve distribution).
Does it follow for higher dimensions?
I think it follows for ...

**0**

votes

**0**answers

113 views

### connections and curvature

Let $(M, g)$ be a Riemannian manifold. Is it possible to construct two different affine (or metric) connections, say $\nabla$ and $\nabla'$, which induce the SAME curvature tensor, i.e. $R(X, ...

**1**

vote

**0**answers

53 views

### Estimating convolutions of powers

I would like an asymptotic estimate of
$$
\sum_{y \in \mathbb{Z}^d} \frac{1}{|y-a_1|^{d-1} \ldots |y-a_n|^{d-1}}
$$
that does not involve any infinite summation. In order to lighten the notation, I ...

**1**

vote

**1**answer

121 views

### Is there a “Bipartite” Szemeredi-Trotter theorem?

One version of the Szemeredi-Trotter theorem states the following:
Given a set of $L$ lines in the plane, the number of points incident to at least $k$ lines is bounded above by a constant times $L/k ...

**3**

votes

**1**answer

70 views

### Density of $\Gamma(N)$ in $\mathrm{Sp}_{2g}(\mathbb{Z}_{\ell})$ where $\ell \not | N$

Let $\mathrm{Sp}_{2g}$ denote the symplectic group of $2g \times 2g$ matrices for some $g \geq 1$, and let $\Gamma(N)$ be the level-$N$ principal congruence subgroup of $\mathrm{Sp}_{2g}(\mathbb{Z})$. ...

**0**

votes

**0**answers

75 views

### A question about ordinal numbers and sub-theories of ZF

A number of set theories have been investigated which were obtained from ZF by restricting in various ways, or even deleting, some of the axioms of ZF-such as Power set, Aussonderung, Infinity, ...

**0**

votes

**1**answer

40 views

### average number of cycles and closed walks length k in incomplete directed graph

I asked this question before, but formulation was poor. I've deleted previous question and reformulate it again.
Let graph $G=(N,p)$ is finite simple incomplete directed graph of size $N$ (multiple ...

**1**

vote

**1**answer

147 views

### Density with infinite cardinals [on hold]

Let κ ≤ µ infinite cardinals.
and lat D(µ, κ) = min{|D| : D ⊆ [µ]^κ ∧ (∀y ∈ [µ]^κ)(∃x ∈ D)(x ⊆ y)}
D(µ, κ) is called the density of κ-sets of µ.
1) Suppose κ = cf(µ) < µ. prove that D(µ, κ) > ...

**3**

votes

**2**answers

193 views

### Is the ideal of functions vanishing at a set complementable in $C(X)$?

Let $X$ be a compact Hausdorff topological set, and $Y$ be its closed subset. Is the ideal of functions vanishing on $Y$
$$
I=\{f\in C(X):\ \forall y\in Y\ f(y)=0\}
$$
complementable (as a closed ...

**0**

votes

**0**answers

29 views

### Logarithmic Units [closed]

A graph has its values and uncertainties listed in a table like this:
3.03 0.07
3.46 0.04
3.76 0.03
The values (first column) are the logarithm of what ...

**1**

vote

**0**answers

55 views

### Convex Optimization related problem

Suppose two non-negative convex functions $f$ and $g$ be given.
We want to solve the following optimization
$$\max_{g\leq\epsilon}f.$$
Now suppose that both $f$ and $g$ can be upper-bounded by a ...