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Groups with polynomial geodesic growth
Geodesic growth virtually nilpotent group with virtu-ally cyclic abelianization
2010/12/13
We study the geodesic growth function for finitely gen-erated groups, and we show that there is a strong relation be-tween virtually cyclic groups and the existence of generating sets
for which geode...
Let A {1, . . . ,N} and P1, . . . , Pℓ 2 Z[n] with Pi(0) = 0 and deg Pi = k for every 1 i ℓ.We show, using Fourier analytic techniques, that for every ε > 0, there necessarily exists...
A new look at nonnegativity on closed sets and polynomial optimization
closed sets nonnegative functions nonnegative polynomials semidefinite
2010/11/26
We first show that a continuous function f is nonnegative on a closed set K Rn if and only if (countably many) moment matrices of some signed measure d = fdμ with supp μ = K, are all positive semid...
A polynomial bracket for the Dubrovin--Zhang hierarchies
polynomial bracket Dubrovin--Zhang hierarchies
2010/12/14
We define a hierarchy of Hamiltonian PDEs associ-ated to an arbitrary tau-function in the semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds.We prove that the eq...
A formula for the HOMFLY polynomial of rational links
formula for the HOMFLY polynomial rational links
2010/12/3
In this paper we give an explicit formula for the HOMFLY polynomial of a rational link (in particular, knot) in terms of a special continued fraction for the rational number that defines the given lin...