# All Questions

100,101 questions
344 views

### Surfaces that are 'everywhere accessible' to a randomly positioned Newtonian particle with an arbitrary velocity vector

Consider an idealized classical particle confined to a two-dimensional surface that is frictionless. The particle's initial position on the surface is randomly selected, a nonzero velocity vector is ...
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### probabilistic knot theory

Take a smooth closed curve in the plane. At each self-intersection, randomly choose one of the two pieces and lift it up just out of the plane. (Perturb the curve so there are no triple ...
1k views

### Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration

This must be an elementary question: could somebody tell me a reference for the Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration? I'm working in the category of pointed ...
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### Are there two non-diffeomorphic smooth manifolds with the same homology groups?

I know that there definitely are two topological spaces with the same homology groups, but which are not homeomorphic. For example, one could take T^2 and S^{1}\vee S^{1}\vee S^{2} (or maybe S^{1}\...
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### Closed form solution to x^(x+1)=(x+1)^x [closed]

From an elementary question in differential entropy for decision sequences... Numerical solutions is: x = 2.293166287408052... The equality is only well defined (with respect to its origination) in ...
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### A few questions on model theory, especially model theory of rings

I have never really read anything proper about model theory, so I have a few questions: Someone told me that a school of logicians managed to give a very short proof of Falting's Theorem using model ...
546 views

### Relationship between universal coefficient theorem and $[K(\mathbb{Z},n), K(G,n)]$?

In short, I'm wondering whether the universal coefficient theorem can be understood/reinterpreted by using maps of Eilenberg-MacLane spaces. This is a wishy-washy idea and I don't have evidence to ...
851 views

### Quantum Computing Complexity?

After reading a recent post on Church's Thesis, I ran into Turing-Church's Strong Thesis, that may be potentially disproven by advances in Quantum Computing. Does anyone know of a good resource that ...
790 views

### Is there a version of Temperley-Lieb using sl(3) rather than sl(2)?

This question is a spin-off from Sammy Black's question on super Temperley-Lieb. Please see there for the background. The short version is that Sammy defines the Temperley-Lieb at index d as the ...
340 views

### What kind of operations does the Tall-Wraith monoid encode?

According to the nLab page, for an algebraic theory V a Tall–Wraith V-monoid is "the kind of thing that acts on V-algebras". Well, it certainly does act on V-algebras, but in which sense is it "the ...
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### What is the most compelling reason to believe Church's thesis? [closed]

Church's thesis states that the Turing machine is a universal model of computation. What is the most compelling argument supporting this assertion?
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### Very strong multiplicity one for Hecke eigenforms

In Invent. math. 116, 645-649 (1994) Dinakar Ramakrishnan proves a theorem which I understand to imply that the following statement (in light of the fact that elliptic curves over $\mathbb{Q}$ are ...
3k views

### Is the set of primes “translation-finite”?

The definition in the title probably needs explaining. I should say that the question itself was an idea I had for someone else's undergraduate research project, but we decided early on it would be ...
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### Sources for exact triangles in triangulated categories.

The other day I came across the statement that in the triangulated category $\mathfrak{KK}$ (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides ...
443 views

### Equivariant Derived Categories via their properties.

There are some ways to define equivariant derived categories of all sorts. But all the ways i know of involve giving a concrete construction. Is the other way around possible? Is there some universal ...
778 views

### properly interpreting Pi_0 in the homotopy exact sequence

Define the lens space L(m,n) as the quotient of S2m+1 by the action of the cyclic group ℤn⊂S1⊂ℂ*. We can create the infinite lens space L(∞,n) by a telescoping construction ...
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Serre's A Course in Arithmetic gives essentially the following proof of the three-squares theorem, which says that an integer $a$ is the sum of three squares if and only if it is not of the form $4^m (... 3answers 340 views ### Multiplication of (0,1) matrices is there an obvious lattice path counting interpretation for multiplying n by n (0,1) matrices ? 3answers 1k views ### Is there a stable algorithm for polynomial division (in several variables)? Suppose you have a homogeneous ideal$I$inside the algebra$\mathbb{C}[x_1,...,x_d]$of complex polynomials in$d$-variables. Can one find a basis for$I$, say$\{f_1,...,f_k\}$, such that every$h \...
466 views

This is probably an easy question. Let C be a category with (finite) products. An internal hom in C category is an object uhom(X, Z) which represents the functor: Y |-----> hom(Y x X, Z) here "...
6k views

### Canonical examples of algebraic structures

Please list some examples of common examples of algebraic structures. I was thinking answers of the following form. "When I read about a [insert structure here], I immediately think of [example]." ...
2k views

### When is a locally convex topological vector space normal or paracompact?

All locally convex topological vector spaces (LCTVS) are completely regular, since their topology is given by a family of semi-norms. I'm interested in conditions that imply that a LCTVS is ...
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### Is no proof based on “tertium non datur” sufficient any more after Gödel?

There are many proofs based on a "tertium non datur"-approach (e.g. prove that there exist two irrational numbers a and b such that a^b is rational). But according to Gödel's First Incompleteness ...
7k views

### japanese/chinese for mathematicians?

I'd like to learn to read math articles in Japanese or Chinese, but I am not interested in learning these languages from usual textbooks. Exist suitable texts, specialized for the needs for reading ...
798 views

### Subgroups of a group generated by a free semigroup

Let $F$ be a free semigroup (say, $2$-generated) which is embedded in a group $G$, and suppose that $G$ (as a group) is generated by $F$. The most simple such situation would be when $G$ is a free ...
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### Ansätze for solving PDEs with wavelets

It is common to solve PDEs with e.g. Fourier and Laplace Transforms. It is often said that Wavelets are a progression compared to them with many nice features. My question: Which Ansätze do you know ...
231 views

### limits of algebraic varieties

I'm looking for a reference which deals with limits of families of algebraic varieties as the degree increases (or at least keywords from this subject). For the kind of example I have in mind, ...
447 views

### Finiteness of Obstruction to a Local-Global Principle

Say that a projective variety V over Q satisfies the local-global principle up to finite obstruction (#) if there are only finitely many isomorphism classes of projective varieties over Q that are not ...
582 views

### Controlling Ultrapowers

Say I start with some a transitive model of a large fragment of ZFC (say enough to run Łoś' Theorem externally) and a specific set x∈M. Now let's say I'm going to pick some M-ultrafilter U on x. ...

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