Preface

Preface

Preface     

Existence theory for nonclassical entropy solutions of scalar conservation laws

We establish a general existence theory for the Cauchy problem associated with a scalar conservation law in one-space dimension. The flux-function is assumed to be nonconvex and we consider nonclassical entropy solutions selected by a kinetic relation. To solve the Cauchy problem, we construct a sequence of approximate solutions using a wave-front tracking scheme. The main difficulty is deriving a uniform estimate on the total variation of the approximate solutions. This is achieved here by introducing a generalized total variation functional, which is decreasing in time and, additionally, reduces to the standard total variation functional when the solutions contain only classical shocks. This functional seems sufficiently robust to be useful for systems as well.Received: June 3, 2002; revised: November 12, 2002     

A-priori upper bounds for the set covering problem

A matrix M∈R^n×n is said to be a column sufficient matrix if the solution set of LCP(M,q) is convex for every q∈Rⁿ. In a recent article, Qin et al. (Optim. Lett. 3:265–276, 2009) studied the concept of column sufficiency property in Euclidean Jordan algebras. In this paper, we make a further study of this concept and prove numerous results relating column sufficiency with the Z and Lypaunov-like properties. We also study this property for some special linear transformations.     

RELATIVELY WEAKLY COMPACT SETS IN THE DEN JOY SPACE

Some topological Properties of the completion H of the Denjoy space are studied. In particular sufficient conditions for a subsets of H be relatively compact and characterizations for a subsets of H be restively weakly compact are given.     

Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.     

Evaluation of the enantiomeric selectivity in the chiral ligand-exchange chromatography of amino acids by a computational model

The chromatographic resolution of enantiomeric amino acids is accomplished on a reversed phase column using aqueous mobile phase containing the chiral reagent N,N-dimethyl-S-phenylalanine-Cu(II). The separation is a result of the whole interaction between the diastereomeric complex surface and the mixed stationary phase realized by the dynamic coating of the RP-18 carbon chains layer. The elution order seems to be related to the different water coordination capability on copper ion in the formation of the mixed ternary complexes.