Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

Fully adaptive multiresolution finite volume schemes for conservation laws

The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.

     

Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Adsorption of poly(vinyl pyrrolidone) on silica. II. The fraction of bound segments, measured by a variety of techniques

The adsorption of the flexible, linear, and nonionic homopolymer poly(vinyl pyrrolidone) from water and from 1,4-dioxane onto pyrogenic silica was studied. Results are reported for the adsorbed amount as a function of adsorption time, molecular mass, and molecular mass distribution (polydispersity). It is found that the adsorption of fractionated samples can be qualitatively explained by the recent theory of Scheutjens and Fleer. However, the influence of the solvent type is larger than predicted by this theory, and an extension of the model to account for this influence is suggested. The polydispersity effects encountered in adsorption isotherms are satisfactorily accounted for by a theory published by Cohen Stuart, Scheutjens, and Fleer.     

Institutional results of the Argentine Graduate Programme in Radiochemistry

Summary The evolution of radiochemistry at the National Atomic Energy Commission (CNEA) in Argentina is analyzed. The antecedents of the establishment, in 1998, of the Master Programme in Radiochemistry, jointly organized by CNEA and the Buenos Aires Regional Faculty of the National Technological University are revised, and the structure of the Programme is described. On the basis of the thesis works, the initial trends are discussed. Finally, the institutional results of the Programme are described.     

Wetting at a polymer gel–vapor interface; a system not influenced by a long-range van der Waals contribution

The exterior of a cross-linked polymer gel resembles a polymer brush. Such gel including its brush can be swollen by a good solvent. The detachment of the solvent–vapor (L–V) interface from the brush is controlled by the adsorption of polymer segments onto this interface and is to a very good approximation not influenced by long-range van der Waals contributions. A wetting transition in this system coincided with the adsorption–desorption transition for chains onto such L–V interface and has various unusual features. There are several indications that in practice this system should feature a second-order wetting transition.