Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

This paper considers a transmission problem for partial differential equations obtained in the recent paper [M. Neuss-Radu, W. Jäger, Effective transmission conditions for reaction-diffusion processes in domains separated by an interface, SIAM J. Math. Anal. 39 (2007) 687–720] as the effective system modeling a reaction–diffusion process in two domains separated by a membrane. For the analysis of this problem an appropriate function space, which includes the coupling conditions for the concentrations on the interface, is introduced. The transmission conditions for the flux are included in the variational formulation with respect to this function space.The solution of the transmission problem is approximated by using the Galerkin method. Numerically the problem is reduced to a system of ordinary differential equations, where the coupling of the micro- and macro-variables leads to a special structure, distinguishing the variables relevant for the transmission. Results of numerical simulations are illustrating the effect of the microscopic process in the membrane on the macroscopic reaction–diffusion process in the bulk domains.     

Eine gewichtsanalytische Methode zur Bestimmung des Magnesiums als MgNH4AsO4.6H2O

Ohne Zusammenfassung     

Locality and realism in contextual theories

Two types of contextual theories are distinguished and shown to be related. For theories of each type a criterion of locality is formulated which is weaker than the classical requirement of separability at spacelike intervals. The relations between the concepts of locality, realism, and ontic chance are discussed.     

En route from patterns to algebra: comments and reflections

This article is a commentary on the papers in this issue of ZDM on Understanding Generalization in K-12 Algebra. It tries to interpret and understand at least some of the reported phenomena within a constructivist framework. The latter locates meaning not in the external representations but in the individual’s activity on and with them. This activity on the other hand is strongly regulated (but not determined) by social contracts and belief systems. From that, and considerations of the more general mathematical context, various suggestions for further and extended research can be drawn. One special aspect is that generalization processes will have to be complemented by some kind of instruction on the conventional algebraic symbolism and its usage.