## All Questions

224 views

### Help with this Diophantine equation

Note: This question was posted in error, and should be closed as no longer relevant. The correct question is posted at http://mathoverflow.net/questions/131353/help-with-this-sys …
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### Duality between K-theory and K-homology in the non-compact, spin$^c$ case

Let $M$ be a compact spin$^c$ manifold, so that it has a fundamental class $[M] \in K_n(M)$. It is well-known that the cap product with $[M]$ induces Poincare duality isomorphisms …
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### Help with this system of Diophantine equations

A couple hours ago, I'd posted a Diophantine equation question, but realized that I'd committed a rather preposterous blunder deriving it. This is the actual question which I'm tr …
274 views

### Probability $k$ bins are non-empty.

The following problem arises in the analysis of Bloom filters. Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …
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### Why every complex of injectives is homotopically injective (provided that, the injective dimension is finite)?

Let $\scr A$ be an abelian category with exact products and a cogenerator (e.g. $\scr A$ is a category of modules). Let ${\mathbf K}(\scr A)$ be the homotopy category of cochain c …
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### Non-crystallographic cluster algebras

Background Fomin and Zelevinsky have introduced cluster algebras in an influential article. To define a cluster algebra, Fomin and Zelevinsky have defined a mutation of seeds. Her …
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### Circle segment of exact length [closed]

I need to find: a spherical line that passes through the points 0,0 and 8,8 and the distance of the line between those two points must be exactly 12 I imagine the answer will b …
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### What is the perimeter of the figure shown on the coordinate plane? [closed]

What is the perimeter of the figure shown on the coordinate plane? Picture http://imgur.com/r4CNd4y
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### fundamental class is the sum of simplices of triangulation of the manifold?

M is an n-dimensional closed orientable manifold. I find in a book "Intuitively,the fundamental class can be thought of as the sum of the (top-dimension) simplices of a suitable tr …
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### Non-(stable)-triviality of the tautological bundles

This is a question I asked at Math.SE but got no answers: http://math.stackexchange.com/q/396217/7110/ The tautological vector bundle $\gamma_k(\mathbb{K}^N)$ over the Grassmann m …
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### Field of definition of canonical morphism between (congruence) modular curves

Let $\Gamma\subseteq \Gamma'\subset SL_2(\mathbb Z)$ be congruence subgroups, and $X(\Gamma)$, $X(\Gamma')$ be the associated smooth projective modular curves over $\mathbb C$. Th …
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### Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville: “The big experts in the field had already tried to make this approach w …
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### How to simplify this Kampé de Fériet function?

I was dealing with a convolution type integral $$\int^z_0 t^m {}_0F_1(;1;-t) \: {}_2F_3\Big( 1,1;2,m,m+1 ; -a t\Big) \:\mathrm{d}t$$ By applying one of the identities in Exton's …
Let $K$ be a local field with mix char, $k$ residue field. We have an exact sequence $0 \longrightarrow I \longrightarrow G_{K} \longrightarrow G_{k} \longrightarrow 0$ Then we o …
Suppose we are given a commutative ring R with unit-element. Now we have a composition of R as the direct product of two rings $R\cong R_1\times R_2$. It is now straight forward, …