# All Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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Consider a Galton-Watson process with offspring distribution $Possion(1)$. That is, $\textbf{p}(k) = \frac{e^{-1}}{k!}$. Given this information, and that $P(z) = ... 2answers 127 views ### How to define the input of computable function or Turing machine over real numbers Computation or computability over$\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 ... 1answer 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 ... 1answer 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. 0answers 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 ... 3answers 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 ... 1answer 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 ... 1answer 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 ... 1answer 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 ... 0answers 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$Q(x), W_1(x,y),W_2(x,z)$... 3answers 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 ... 0answers 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, ...
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 ...