The magnetism of rare earth intermetallics RFe4Al8

Hyperfine Interactions - The YFe4Al8 and ErFe4Al8 intermetallics were studied by57Fe Mössbauer spectroscopy between 2 K and room temperature. The spectra are consistent with iron occupying 8f...     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations

Optimal explicit Runge–Kutta methods consider more stages in order to include a particular spectrum in their stability domain and thus reduce time-step restrictions. This idea, so far used mostly for real-line spectra, is generalized to more general spectra in the form of a thin region. In thin regions the eigenvalues may extend away from the real axis into the imaginary plane. We give a direct characterization of optimal stability polynomials containing a maximal thin region and calculate these polynomials for various cases. Semi-discretizations of hyperbolic–parabolic equations are a relevant application which exhibit a thin region spectrum. As a model, linear, scalar advection–diffusion is investigated. The second-order-stabilized explicit Runge–Kutta methods derived from the stability polynomials are applied to advection–diffusion and compressible, viscous fluid dynamics in numerical experiments. Due to the stabilization the time step can be controlled solely from the hyperbolic CFL condition even in the presence of viscous fluxes.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

High pressure mössbauer studies of magnetic actinide systems

Due to the wider radial extent of 5f electrons when compared to their 4f counterparts, intermetallics of the light actinides show a broad spectrum of magnetic properties ranging from the localized magnetism of the lanthanides to the itinerant magnetism often found in transition metal compounds. One parameter which strongly influences the magnetic character of the compound is the actinide-actinide separation which can experimentally be varied by the application of high pressure. The question of 5f electron delocalization will be reviewed with respect to Moesshauer high pressure data on NpCo₂si₂, NpAl₂, NpOs₂ and new results will be presented of NpAs. The connection of hyperfine parameters with results of X-ray diffraction studies will be discussed.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

Rigorous Generalization of Young's Law for Heterogeneous and Rough Substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameters.     

High order linear initial-value problems and Schauder bases

In this paper we approximate the solution of a linear initial-value problem, making use of a Schauder basis for certain Banach space associated with such a differential problem. In addition, we apply that results in order to calculate numerically the response from a structure modelled by a three degree-of-freedom mass–damper–spring system.     

Mathematical problem solving: an evolving research and practice domain

Research programs in mathematical problem solving have evolved with the development and availability of computational tools. I review and discuss research programs that have influenced and shaped the development of mathematical education in Mexico and elsewhere. An overarching principle that distinguishes the problem solving approach to develop and learn mathematics is to conceptualize the discipline as a set of dilemmas or problems that need to be explored and solved in terms of mathematical resources and strategies. In this context, relevant questions that help structure and organize this paper include: What does it mean to learn mathematics in terms of problem solving? To what extent do research programs in problem solving orient curricular proposals? What types of instructional scenarios promote the students’ development of mathematical thinking based on problem solving? What type of reasoning do students develop as a result of using distinct computational tools in mathematical problem solving?