# All Questions

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### What is an explicit example of a sequence converging to two different points? [closed]

In principle a sequence in a non-Hausdorff space can converge to two points simultaneously. Can anyone give me an explicit example of the above? Or tell me any method of generating such kinds of ...
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### Kahler differentials and Ordinary Differentials

What's the relationship between Kahler differentials and ordinary differential forms?
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### Principal Bundle with given Curvature

Hey, For personal exercising purposes I try to give a proof, that a U(1)-principal-bundle has curvature $\alpha$ iff the cohomology class of $\alpha$ is integral: By the Cech-deRham-isomorphism a ...
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### Next (Restricted) B-Smooth Number Problem?

Given a bound, $B$, and a list of (small) primes $(p_0, p_1, \dots, p_{n-1})$ is there an efficient algorithm to find the next number greater than $B$ that can be expressed as a product of primes from ...
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### map between $C^*$-algebras with special properties, why is $f(a^2)=f(a)^2$ for all $a\in A$?

Let $A$ and $B$ unital $C^\ast$-algebras, $f:A\to B$ a linear, bounded map such that $f(a^*)=f(a)^*$ for all $a\in A$, $f(1_A)=1_B$ and $f(a)f(b)=0$ for all $a,b\in A_{sa}$ with $ab=0$. Follows ...
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### A particular interesting elliptic curve

Given the elliptic curve $E:y^2=x^3-4x+4$. (a) How to prove that the group of rational points $E(\mathbb{Q})$ is generated by $P=(2,2)$. (b) If we consider the piece of curve on the region ...
Does anyone recognize this problem? There are $2p$ equations and $2p$ unknowns, and it feels like a classic, but I've never encountered it before: Given $d_1, d_2, \ldots d_p$, find $a_1, a_2, \ldots ... 1answer 54 views ### How to write a given rank matrix with some constraints? I want to write down an$m\times n0/1$matrix such that every row is distinct and every column is distinct. If I want to write with only rows or columns distinct, I could just pick$m$or$n$... 0answers 45 views ### How many techniques are there to test colliniarity of n points? [on hold] How many techniques are there to test coliniariry of n points? For example, suppose we have 4 points A, B , C, D. How many ways can it be tested that they are collinear? 0answers 37 views ### is graph coloring problem in general np-complete?(solvable) [on hold] graph coloring problem Hi, i tried to find an algorithm for this problem and i want to make sure. i found it with this knowledge. 1.is graph coloring problem in general to find the ... 0answers 84 views ### Can someone explain some of the steps in this paper clearly? I'm having trouble understanding the steps this paper makes to come to the conclusion$p_{f}(d) \sim e^d\sqrt{d}$Marek Wolf, First occurrence of a given gap between consecutive primes, preprint, ... 0answers 193 views ### How algebraic is the holonomy map? Let$G$be either a compact, simple, simply-connected Lie group, or a simply-connected complex reductive group (so either$SU(n)$or$SL(n,\mathbb{C})$, for instance), or even complex affine. I don't ... 0answers 27 views ### Box counting dimension of the graphs of functions on$\mathbb R \rightarrow \mathbb R$[on hold] Generally speaking box counting techniques are applied to fractals defined by some iterative process, but what about functions? Has the concept of box counting dimension been investigated on the graph ... 0answers 38 views ### Derived Deformations of associative algebras Let$k$be a field (if necessary for my question, we can assume its characteristic to be zero). In the non derived context, we can then define deformations of an associative algebra$S$as follows: ... 1answer 273 views ### soft: Reference/ Suggested Read: Homological Algebraic techniques in PDEs I was reading this article on wikipiedia and was interested by the apparent link between Homological Algebra and PDEs. What is an accessible reference which showcases the link between these topics? ... 0answers 41 views ### Egyptian fractions similar to Erdos-Straus conjecture It is known that the Erdos-Straus conjecture is about writing$4/n$as three unit fractions. My question is that if it is known that if$a>4$$$\frac an=\frac1{x_1}+\frac1{x_2}+\cdots+\frac1{x_k} ... 0answers 86 views ### reference for groupoid cohomology In nLab (groupoid cohomology) says: "Under the homotopy hypothesis theorem, plain (non-internal) groupoid cohomology is the same as the cohomology of homotopy 1-types." Are there references for ... 1answer 248 views ### Integral formula for \int_{0}^{\infty}e^{-3\pi x^{2}}((\sinh \pi x)/(\sinh 3\pi x))\,dx by Ramanujan The following is a re-post from MSE because I did not get any answer even after offering a bounty. Towards the end of G. N. Watson's (one of the joint authors of famous book "A Course of Modern ... 0answers 41 views ### Decomposition of polynomial ring as S_n-module [migrated] I want to whether there is a containment relation between the S_n-modules \mathbb{C}S_n and \mathbb{C}[x_1,\ldots ,x_n]. Is it true that \mathbb{C}[x_1,\ldots ,x_n] contains an isomorphic copy ... 3answers 212 views ### Lower bounding the probability that \gcd(t,N)≤B, for a random t and fixed (large) N \newcommand{\Prb}[1]{\mathcal{P}_{#1}} I have the following number theory problem, related to Odlyzko's improvement on Shor’s factoring algorithm (see this cstheory.sx question for details). Let ... 0answers 130 views ### When did people know that all real polynomials of degree greater than 2 are reducible? [migrated] Admittedly, this may not be a research level question, but I am deeply curious about this. Let f(x) \in \mathbb{R}[x], and write d = \deg f. It is well known that if \deg f > 2, then f is ... 1answer 82 views ### About a closed strucure on profunctors Let Prof the bicategory with profunctors (on small categories), arrows are like D: \mathscr{A} \dashrightarrow \mathscr{B} and this means that D: \mathscr{A}^{op} \times \mathscr{B}\to Set. ... 0answers 41 views ### asymptotic behavior of the solution of an ordinary differential equation I am a civil engineer with basic mathematics skills and need help for the following - perhaps simple - problem. Consider the following autonomous system of two non-linear ordinary differential ... 2answers 204 views ### Does the ring generated by the odd power sum symmetric functions have a name? Let \Lambda be the ring of symmetric functions and recall the power sum symmetric function p_i = \sum x_1^i + x_2^i + \dots generate this ring. Let \tilde\Lambda be the ring generated by the odd ... 1answer 518 views ### Why is it so hard to prove Toeplitz' conjecture? I'm a layman in mathematics, so please excuse me in advance for anything in this question that may be inappropriate :D. Well: Four years ago, I was reading (and working to solve the puzzles on) ... 0answers 122 views ### Hochschild Cohomology of the Quantum Torus I would like some advice on how to compute directly, or by a higher powered method the Hochschild Cohomology groups of the quantum torus using the stated complex I have found. I think there are ... 3answers 255 views ### “Most Similar Vector Problem” on an Integer Lattice? I am currently working on problem that I think could be expressed as an integer lattice problem. Given u \in \mathbb{R}^n and a bounded integer lattice L = \mathbb{Z}^n \cap [-M,M]^n I would like ... 4answers 379 views ### SO(4) (& SO(n)) characterization? I believe it is the case that any finite subgroup of SO(3) (the 3 \times 3 orthogonal matrices of determinant 1) is either a cyclic group C_n, or a dihedral group D_n, or one of the groups ... 1answer 121 views ### Tor-amplitude [0, 1] in the setting of intersection theory on a regular surface? The question is coming from Definition 1.5 in Deligne's Expose X in SGA 7 on intersection theory. Let X be a connected regular scheme of dimension 2 and Y \subset X a reduced divisor that ... 3answers 343 views ### Do cotangent bundles have “bounded geometry”? I have often heard the phrase "a manifold M has bounded geometry" thrown around without ever seeing a precise definition of what this means. Apparent examples are compact manifolds and ... 1answer 172 views ### reference on Dirichlet theorem on primes in arithmetic progression I appreciate if you could help me to find a reference (and a proof). Combining Dirichlet theorem on primes in arithmetic progression with Chebotarev densitiy theorem, we know that given two positive ... 0answers 64 views ### Proofs needed for observations regarding prime-partitionable numbers Below is the definition of a prime-partitionable integer taken from W. Holsztynski, R. F. E. Strube, Paths and circuits in finite groups, Discr. Math. 22 (1987) 263-272 and is apparently the same in ... 3answers 183 views +50 ### Terminology for polygons As you may know term "polygon" might mean few different things and its meaning has to guessed from context. By some reason I have to use few of these meaning in one place. So I converge to the ... 1answer 175 views ### History of unstable formulas [on hold] There are many equivalent definitions for stability, one of them being that being unstable is equivalent to the existence of a formula having the order property. While intuitively it makes sense that ... 2answers 1k views ### Distributing points evenly on a sphere I am looking for an algorithm to put n-points on a sphere, so that the minimum distance between any two points is as large as possible. I have found some related questions on stackoverflow but ... 1answer 62 views ### examples of completely positive order zero maps to demonstrate a theorem I'm interested explicit examples which can be used to demonstate the theorem: Theorem: Let A and B C^*-algebras and \phi:A\to B be a completely postive map of order zero. Set ... 2answers 175 views ### Hausdorff Dimensions of Limit set of subgroups of SL(2,Z) In a recent paper by Bourgain, Sarnak, Gamburd [1] talks about subgroups of SL(2,\mathbb{Z}). Let \Lambda be a finitely generated non-elementary subgroup of SL(2,\mathbb{Z}) with Hausdorff ... 1answer 268 views ### Particular case of Beal's Conjecture Is it known that there exist no coprime positive integers A, B and C such that A^3+B^4=C^3? This is a particular case of Beal's Conjecture. 2answers 187 views ### Asymptotics of a recurrence relation The sequence (a_n)_{n \ge 0} satisfies, a_0 = a_1 = 1 and the recursion relation:$$a_n = \sum\limits_{k=0}^{[n/2]} \frac{a_k}{(n-2k)!}$$where,$[x]$is the nearest integer to$x$not exceeding ... 2answers 99 views ### Reference for (co)limit-preserving functor$X\mapsto R^X$Fix a commutative ring$R$. There's a contravariant functor from finite sets to finite$R$-algebras sending$X$to$R^X$. Viewed as a covariant functor$\text{set}^{op}\to R\text{-alg}$, this functor ... 2answers 83 views ### Existence and characterization of transitive matrices? We call a matrix$M \in \mathbb{R}^{d \times d}$transitive if it satisfies the following: For any three vectors$u, v, w$in$\mathbb{R}^d$. If$u^T M v > 0$and$v^T M w > 0$then$u^TMw ...
Let $\mathbb{F}$ be the field of size 2. Say I have functions $p_1,\ldots,p_m : \mathbb{F}^n \to \mathbb{F}$ each with high degree $\approx n$ as (multilinear) polynomials, and another function \$s : ...