On variational aspects of some nonconvex nonsmooth global optimization problem

The paper is devoted to study a global optimization problem for a class of nonsmooth, nonconvex and non-locally Lipschitz functionals on a vector-valued reflexive Banach space. The existence of an element which is both a global minimizer and a solution of the associated hemivariational inequality is proved under some unilateral growth restrictions imposed on nonlinearities and under the assumption that an appropriately modified version of the Hedberg truncation procedure can be applied.On leave from his original institute.     

On commuting operators solving Gleason's problem

We prove the uniqueness of commuting operators solving Gleason's problem for certain spaces of functions analytic in the unit ball.

     

On solving the maximum clique problem

The Maximum Clique Problem (MCP) is regarded here as the maximization of an indefinite quadratic form over the canonical simplex. For solving MCP an algorithm based upon Global Optimality Conditions (GOC) is applied. Furthermore, each step of the algorithm is analytically investigated and tested. The computational results for the proposed algorithm are compared with other Global Search approaches.     

On solving a nonlinear matrix eigenvalue problem

Journal of Mathematical Sciences -     

On solving the multi-period single-sourcing problem under uncertainty

We present a framework for solving the strategic problem of assigning retailers to facilities in a multi-period single-sourcing product environment under uncertainty in the demand from the retailers and the cost of production, inventory holding, backlogging and distribution of the product. By considering a splitting variable mathematical representation of the Deterministic Equivalent Model, we specialize the so-called Branch-and-Fix Coordination algorithmic framework. It exploits the structure of the model and, specifically, the non-anticipativity constraints for the assignment variables. The algorithm uses the Twin Node Family (TNF) concept. Our procedure is specifically designed for coordinating the selection of the branching TNF and the branching S3 set, such that the non-anticipativity constraints are satisfied. Some computational experience is reported. D. Romero Morales: The work of this author was supported in part by the National Science Foundation under Grant No. DMI-0355533 The work of the first three authors has been partially supported by the grants TIC2003-05982-C05-05 and SEC2002-00112 from MCyT, Spain     

On some aspects of multivariate polynomial interpolation

The purpose of this paper is to present some aspects of multivariate Hermite polynomial interpolation. We do not focus on algebraic considerations, combinatoric and geometric aspects, but on explicitation of formulas for uniform and non-uniform bivariate interpolation and some higher dimensional problems. The concepts of similar and equivalent interpolation schemes are introduced and some differential aspects related to them are also investigated. This revised version was published online in June 2006 with corrections to the Cover Date.     

On some algorithmic aspects of hypergraphic matroids

Hypergraphic matroids were studied first by Lorea [23] and later by Frank et al. [11]. They can be seen as generalizations of graphic matroids. Here we show that several algorithms developed for the graphic case can be extended to hypergraphic matroids. We treat the following: the separation problem for the associated polytope, testing independence, separation of partition inequalities, computing the rank of a set, computing the strength, computing the arboricity and network reinforcement.     

On some dynamical aspects of NIP theories

We investigate some dynamical features of the actions of automorphisms in the context of model theory. We interpret a few notions such as compact systems, entropy and symbolic representations from the theory of dynamical systems in the realm of model theory. In this direction, we settle a number of characterizations of NIP theories in terms of dynamics of automorphisms and invariant measures. For example, it is shown that the property of NIP corresponds to the compactness property of some associated systems and also to the zero entropy property of automorphisms. These results give a correspondence between some notions of tameness in model theory and ergodic theory. Moreover, we study the concept of symbolic representation and consider it in some well known mathematical objects such as the circle group, Bohr sets, Sturmian sequences, the structure \((\mathbb {Z},+,U)\), and random graphs with a model theoretic point of view in mind. We establish certain characterizations for stability theoretic dividing lines, such as independence property, order property and strict order property in terms of associated symbolic representations. At the end, we propose some applications of symbolic representations and these characterizations by giving a proof for a classical theorem by Shelah and also introducing some invariants associated to the types and elements of models.     

On Tamir's algorithm for solving the nonlinear complementarity problem

Some comments concerning Tamir's algorithm for solving the nonlinear complementarity problem are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On solving large instances of the capacitated facility location problem

We present two sets of results pertaining to the solution of capacitated facility location problems that are large, especially with regard to the number of customers. One set of results relates to customer aggregation, while another set of results concerns the judicious selection of variable-upper-bounding (VUB) constraints to include in the initial integer-programming formulation.     

On some method for solving a nonlinear heat equation

Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation.     

Numerical methods of singular integral equation for solving some problem in fluid dynamic

Consider a contact problem of two different layers under certain conditions. The aim of this work is obtaining the stress potential function between the two layers and obtaining the solution numerically using two different method Toeplitz matrix method and Product Nystrom method Numerical results are considered and the error, in each case, is computed.     

On two particular cases of solving the normal Hankel problem

The normal Hankel problem is one of characterizing all the complex matrices that are normal and Hankel at the same time. The matrix classes that can contain normal Hankel matrices admit a parameterization by real 2 × 2 matrices with determinant one. Here, the normal Hankel problem is solved in the case where the characteristic matrix of a given class is an order two Jordan block for the eigenvalue 1 or ?1.     

On some aspects of Bäcklund transformations

The Painlevé differential equations (P₂-P₆) possess Bäcklund transformations which relate one solution to another solution either of the same equation, with different values of the parameters, or another such equation. We review a method for deriving difference equations, the discrete Painlevé equations in particular, from Bäcklund transformations of the continuous Painlevé equations. Then, we prove the existence of an algebraic formula relating three inconsecutive solutions of the same Bäcklund hierarchy for P₃ and P₄.     

On some aspects of pedagogy in applied mathematics

This paper, after analysing the meaning of ‘applied mathematics’, seeks to explore and set forth some broad outlines of the pedagogical implications of studies in the application of mathematics.     

Elementary methods for solving the plane harmonic dirichlet problem for some canonical domains

This paper is concerned with an explicit method for solving the Dirichlet problem in the unit circle for piecewise rational boundary values as well as in the half-plane. In the latter case also the solutions to mixed boundary conditions are given explicitly. The method is based on the Milne-Thomson theorem