The strip of minimum width covering a centrally symmetric set of points

In this paper the following is proved: let be a centrally symmetric set of points, such that the distance between any pair of points is at least 1 and every three of them can be covered by a strip of width 1. Then there is a strip of width √2 covering . Supported by CONACYT, SNI 38848     

Bohr’s strip for vector valued Dirichlet series

Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series , converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr’s strip for a Dirichlet series with coefficients a _n in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series. The first, second and third authors were supported by MEC and FEDER Project MTM2005-08210.     

A Novel Insight into the Perfect Phylogeny Problem

One of the classical problem in computational biology is the character compatibility problem or perfect phylogeny problem. A standard formulation of this problem in terms of two closely related questions is the following. Given a data set consisting of a finite set X and a set

Hyperbolic Equations with Non-analytic Coefficients

We prove that the Cauchy problem for a hyperbolic, homogeneous equation with coefficients depending on time, is well posed in every Gevrey class, although in general it is not well-posed in provided the characteristic roots satisfy the condition

Maximal partial packings of $${Z_2^n}$$ with perfect codes

A maximal partial Hamming packing of is a family of mutually disjoint translates of Hamming codes of length n, such that any translate of any Hamming code of length n intersects at least one of the translates of Hamming codes in . The number of translates of Hamming codes in is the packing number, and a partial Hamming packing is strictly partial if the family does not constitute a partition of . A simple and useful condition describing when two translates of Hamming codes are disjoint or not disjoint is proved. This condition depends on the dual codes of the corresponding Hamming codes. Partly, by using this condition, it is shown that the packing number p, for any maximal strictly partial Hamming packing of , n = 2 ^m −1, satisfies . It is also proved that for any n equal to 2 ^m −1, , there exist maximal strictly partial Hamming packings of with packing numbers n−10,n−9,n−8,...,n−1. This implies that the upper bound is tight for any n = 2 ^m −1, . All packing numbers for maximal strictly partial Hamming packings of , n = 7 and 15, are found by a computer search. In the case n = 7 the packing number is 5, and in the case n = 15 the possible packing numbers are 5,6,7,...,13 and 14.      

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder in a product Riemannian manifold . It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabi on complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature. Dedicated to Professor Manfredo P. do Carmo on the occasion of his 80th birthday.     

ON FRT– CLIFFORD ALGEBRAS

We study the q-Clifford algebras

Operator Space Embedding of Schatten p-Classes Into Von Neumann Algebra Preduals

Let X₁ and X₂ be subspaces of quotients of R OH and C OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of (equipped with its natural operator space structure) into with a QWEP von Neumann algebra. Received: June 2006, Revision: June 2007, Accepted: September 2007     

On the existence of solutions to a special variational problem

In this paper we establish an existence and regularity result for solutions to the problem

Inequalities for the Volume of the Unit Ball in \mathbb {R}^{n}, II

We present several sharp inequalities for the volume of the unit ball in ,

On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem

We consider the problem

Brake orbits type solutions to some class of semilinear elliptic equations

We consider a class of semilinear elliptic equations of the form

Sufficient conditions for the convexity of the level sets of ground-state solutions

Let Ω be a bounded convex domain in . We consider constrained minimization problems related to the Euler-Lagrange equation

A spinorial analogue of Aubin’s inequality

Let (M, g, σ) be a compact Riemannian spin manifold of dimension ≥ 2. For any metric conformal to g, we denote by the first positive eigenvalue of the Dirac operator on . We show that

Infinitely many solutions of some nonlinear variational equations

The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem

On automorphisms of the symmetrized bidisc

We characterize the group Aut for the symmetrized bidisc

Properties of global decaying solution to the Cauchy problem of nonlinear evolution equations

We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations,

Morse indices and the number of maximum points of some solutions to a two-dimensional elliptic problem

In this note, we consider the problem