On nonstationary flow through porous media

Summary Saturated-unsaturated flow of an incompressible fluid through a porous medium is considered in the case of time-dependent water levels. This corresponds to coupling the mass conservation law with a continuous constitutive condition between water content and pressure. An existence result for the corresponding weak formulation is proved. Finally we study the limit as the constitutive relation degenerates into a maximal monotone graph.This work was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 123 (Heidelberg).On leave from: Istituto di Analisi Numerica del C.N.R., Corso C. Alberto 5 - I 27100 Pavia (Italy).     

Optimal Salesmen's Compensation Plans: A Multiperiod Approach

Conditions to induce an income maximizing salesman to allocate his time among product lines so as to maximize the firm's long-run profits are derived. These conditions highlight the need to take explicitly into account the carryover effects of salesmen's activities in determining the relative importance of the commission rates to be paid for the various product lines.     

A spectral study of transition-metal complexes on a chelating ion-exchange resin containing aminophosphonic acid groups

The coordination mode of a commercial chelating ion-exchange resin, ES 467, containing aminomethylphosphonic acid groups anchored on a macroporous styrenedivinylbenzene copolymer, with several metal ions, such as chromium(III), cobalt(II), nickel(II), copper(II) and zinc(II) has been studied with the aid of IR, ligand field and ESR spectra. The chelating group of ES 467, aminomethylphosphonic acid, appears to bind different metal ions mainly through oxygen atoms of the phosphonic acid group, though, in the case of those species containing low-loading of metal ions, the secondary amine nitrogen atom also appears to take part in coordination. Most of the metal ions studied seem to be present as six-coordinated species in the polymeric matrix, whereas cobalt(II) species show electronic spectra which are consistent with the presence of both four-coordinated (tetrahedral) and six-coordinated (octahedral) structures of these species. The distribution coefficients for cobalt(II), nickel(II), copper(II) and zinc(II) have been determined and it appears that the resin ES 467 binds copper(II) ions selectively. An attempt has been made to find a possible relationship between the selectivity of the chelating resin and the stereochemistry of the adsorbed metal ions.     

Solving the uncapacitated multi-facility Weber problem by vector quantization and self-organizing maps

The uncapacitated multi-facility Weber problem is concerned with locating m facilities in the Euclidean plane and allocating the demands of n customers to these facilities with the minimum total transportation cost. This is a non-convex optimization problem and difficult to solve exactly. As a consequence, efficient and accurate heuristic solution procedures are needed. The problem has different types based on the distance function used to model the distance between the facilities and customers. We concentrate on the rectilinear and Euclidean problems and propose new vector quantization and self-organizing map algorithms. They incorporate the properties of the distance function to their update rules, which makes them different from the existing two neural network methods that use rather ad hoc squared Euclidean metric in their updates even though the problem is originally stated in terms of the rectilinear and Euclidean distances. Computational results on benchmark instances indicate that the new methods are better than the existing ones, both in terms of the solution quality and computation time.