Characteristic Elements of Unimodular -lattices

Characteristic elements have been useful in the classification of unimodular lattices over the integers. This article gives an explicit formula for characteristic elements of a lattice in terms of a basis for the lattice and the dual of that basis.     

Remarks on my paper: packing of incongruent circles on the sphere

The paper [3] contains an upper bound to the weighted density of a packing of circles on the unit sphere with radii from a given finite set. This bound is attained by many packings and has applications to problems of solidity. In the present note it is shown that a certain condition imposed on the set of admissible radii can be removed by modifying the original proof of the theorem.     

Generalized Greatest Common Divisors,Divisibility Sequences,and Vojta’s Conjecture for Blowups

We apply Vojta’s conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements generalize earlier results and conjectures. We also discuss the relationship between generalized greatest common divisors and the divisibility sequences attached to algebraic groups, and we apply Vojta’s conjecture to obtain a strong bound on the divisibility sequences attached to abelian varieties of dimension at least two.     

Error of Asymptotic Formulae for Volume Approximation of Convex Bodies in

 We estimate the error of asymptotic formulae for volume approximation of sufficiently differentiable convex bodies by circumscribed convex polytopes as the number of facets tends to infinity. Similar estimates hold for approximation with inscribed and general polytopes and for vertices instead of facets. Our result is then applied to estimate the minimum isoperimetric quotient of convex polytopes as the number of facets tends to infinity. Received 16 July 2001     

Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface

In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by ε the period, the diffusion coefficient is scaled as ε². The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when ε goes to zero. First, there is a global homogenized problem as in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunction. Received: January 10, 2001; in final form: July 9, 2001?Published online: June 11, 2002     

Polyhedral results for two-connected networks with bounded rings

We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “ring”) does not exceed a given length K.?We present here a new formulation of the problem and derive facet results for different classes of valid inequalities. We study the separation problems associated to these inequalities and their integration in a Branch-and-Cut algorithm, and provide extensive computational results. Received: September 1999 / Accepted: February 2002?Published online May 8, 2002     

Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations

This paper is devoted to study a class of systems of nonlinear Schrödinger equations: \(\left\{\begin{array}{rcl} -\Delta u+u-u^{3}=\epsilon v, \\ -\Delta v+v-v^{3}=\epsilon u, \end{array}\right.\) in \(\mathbb{R}^{n}\) with dimension n = 1,2,3. Our main result states that if \(\mathcal{P}\) denotes a regular polytope centered at the origin of \(\mathbb{R}^{n}\) such that its side is greater than the radius, then there exists a solution with one multi-bump component having bumps located near the vertices of \(\xi\mathcal{P}\), where \({\xi\sim \log(1/\varepsilon)}\), while the other component has one negative peak.     

Steady States of Anisotropic Generalized Newtonian Fluids

We consider the stationary flow of a generalized Newtonian fluid which is modelled by an anisotropic dissipative potential f. More precisely, we are looking for a solution of the following system of nonlinear partial differential equations

一类带有三维核的多点边值问题解的存在性(英文)

In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.     

Gelfand-Kirillov Dimension and Local Finiteness of Symmetrizations of Associative Superalgebras

In this work we extend to superalgebras a result of Skosyrskii [Algebra and Logic, 18 (1) (1979) 49–57, Lemma 2] relating associative and Jordan structures. As an application, we show that the Gelfand-Kirillov dimension of an associative superalgebra coincides with that of its symmetrization, and that local finiteness is equivalent in associative superalgebras and in their symmetrizations. In this situation we obtain that having zero Gelfand-Kirillov dimension is equivalent to being locally finite.Partially supported by MCYT and Fondos FEDER BFM2001-1938-C02-02, and MEC and Fondos FEDER MTM2004-06580-C02-01.Partially supported by a F.P.I. Grant (Ministerio de Ciencia y Tecnología).