## Tagged Questions

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### a question of local field

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 …
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### Lipschitz map of the circle onto a triangle

Assume that $f$ is (Euclidean) $L-$biLipchitz mapping of the unit circle onto a triangle $\Delta(A,B,C)$. Can we find a $10000 L$ bi-lipchitz extension of $f$ onto the whole plane. …
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### Why do knot cobordisms result in functoriality with respect to knot homologies so often?

Why do knot cobordisms result in functoriality with respect to knot homologies so often?
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### Surfaces ruled over elliptic curves

Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose $E$ …
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### Interpreting numerical double integration as a matrix multiplication

I have a convex optimization problem of finding a function Q(x,y) as below: Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the questi …
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### 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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### repeated application of binomial distribution on a set of random variables

I have four solutions which are termed: A1, A2, A3, A4. These are actually the results of a searching algorithm. I know that A1 is the best solution, A2 is next to A1, A3 is next t …
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### decomposition of the injective hull of a torsion free module

Let $R$ be a ring, $\Sigma$ be a multiplicatively closed subset of $R$. $M$ is an $R$-module. Denote the injective hull of $M$ by $E(M)$. $M$ is $\Sigma$-torsion if for any $m$ …
A knot in S^3 is small if its complement does not contain a closed incompressible surface. Is it a generic property for knots, meaning that among all knots with less than $n$ cross …