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We considerably improve upon the recent result of [34] on the mixing time of Glauber dynamics for the 2d Ising model in a box of side L at low temperature and with random boundary conditions whose dis...
This paper deals with the veri cation and the synthesis of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that ...
We observe that Clay-Rolfsen’s obstruction of bi-orderability, which uses the classical Alexander polynomial, is not strengthened by using the twisted Alexander polynomials for finite representations ...
Counting Euler characteristics of the discriminant of the quadratic equation in terms of Newton polytopes in two different ways, G. Gusev ([Gus]) found an unexpected relation for mixed volumes of tw...
For a finite group G, (semi-)Mackey functors and (semi-)Tambara functors are regarded as G-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if G is trivial, they agree with th...
We prove constructively that for any finite-dimensional commu-tative ring R and n  dim(R) + 2, the group En(R[X,X−1]) acts transitively on Umn(R[X,X−1]). In particular, we obtain that for...
We interpret the coefficients of the cyclotomic polynomial in terms of simplicial homology.
The scope of refinable functions in wavelet theory is focused to localized functions. In our paper we like to widen that scope, in particular we show that all polynomial functions are refinable. This...
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type folia-tion.
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.
We use the method of steepest descents to study the root distribution of the Ehrhart polynomial of the d-dimensional cross-polytope, namely Ld, as d ! 1. We prove that the distribution function of the...
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. ...
A necessary and sufficient condition for the triviality of the Milnor monodromy of a central hyperplane arrangement is given. This is a consequence of a Thom-Sebastiani type result, where the sum of h...
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
The Tutte polynomial G(X, Y ) of a graph G is a classical invariant,important in combinatorics and statistical mechanics. An important feature of the Tutte polynomial is the duality for planar graphs...

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