ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL＇S EQUATIONS

This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.     

Synthesis of organofunctional silanes with sterically hindered substituents at silicon atoms

Organofunctional silanes with more sterically hindered substituents at the silicon atom than the typical methoxy (ethoxy) group have lately been frequently used as silane coupling agents, in polymer coupling systems, sol‐gel processes and also as interpenetrating polymer network substrates. New and very efficient synthetic ways leading to organofunctional silanes of the above type with methacryl, amine, chloro and isocyanato functional groups are proposed here. Catalytic transesterification and/or alcoholysis of chloropropyltrialkoxysilanes followed by­nucleophilic substitution has been employed. Copyright © 2001 John Wiley & Sons, Ltd.     

Entropy criterion of random states for granular material in a mixing process

Mathematical assessment of homogenisation progress of the granular material mixing process is presented. The mixing process was realised using a vessel in the form of two partly penetrating horizontal cylinders equipped with two multi-ribbon agitators. The experimental system consisted of three sets of particles of different colour. Random states of the mixed granular material were characterised by the sampling procedure at different moments of the mixing process. Informational entropy as well as the flow of quantum of information were applied to describe the progress of the homogenisation process. Analysis of this process was based on experimental investigations in the form of informational entropy patterns and described by means of the average informational entropy or the quantum of information. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Convergence of algebraic multigrid based on smoothed aggregation

Summary. We prove an abstract convergence estimate for the Algebraic Multigrid Method with prolongator defined by a disaggregation followed by a smoothing. The method input is the problem matrix and a matrix of the zero energy modes of the same problem but with natural boundary conditions. The construction is described in the case of a general elliptic system. The condition number bound increases only as a polynomial of the number of levels, and requires only a uniform weak approximation property for the aggregation operators. This property can be a-priori verified computationally once the aggregates are known. For illustration, it is also verified here for a uniformly elliptic diffusion equations discretized by linear conforming quasiuniform finite elements. Only very weak and natural assumptions on the hierarchy of aggregates are needed. Received March 1, 1998 / Revised version received January 28, 2000 / Published online: December 19, 2000     

Ueber die Analogie des Verhaltens von Emulsionen und des Verhaltens von Fett im Protoplasma

Ohne Zusammenfassung Uebersetzt von J. Matula (Wien). Eine vorl?ufige Mitteilung der in dieser und einer vorhergehenden in dieser Zeitschrift erschienenen Abhandlung niedergelegten Ergebnisse erschien in Science43 (1916).     

A new method for characterizing patterns of neural spike trains and its application

A method for characterizing and identifying firing patterns of neural spike trains is presented. Based on the time evolution of a neural spike train, the counting process is constructed as a time-dependent stair-like function. Three characteristic variables defined at sequential moments, including two formal derivatives and the integration of the counting process, are introduced to reflect the temporal patterns of a spike train. The reconstruction of a spike train with these variables verify the validity of this method. And a model of cold receptor is used as an example to investigate the temporal patterns under different temperature conditions. The most important contribution of our method is that it not only can reflect the features of spike train patterns clearly by using their geometrical properties, but also it can reflect the trait of time, especially the change of bursting of spike train. So it is a useful complementarity to conventional method of averaging.     

On a theorem of Burnside on fixed-point-free automorphisms

We prove that a finite group having a fixed-point-free automorphism in the Fitting subgroup of its automorphism group must be abelian of rather restricted structure. As a consequence, no finite nonabelian group could have a fixed-point-free automorphism in the Frattini subgroup of its automorphism group. Received: 21 April 2007, Revised: 18 May 2007     

Subcritical and fatigue crack growth in anti-plane strain state

Assuming elastic-plastic material behavior the slow growth of Mode III crack under both monotonic and pulsating loadings is considered. Rice's idea of universal R-curve is employed while the mathematical analysis is based on the one-dimensional plasticity model suggested by Kostrov and Nikitin. Motion of a quasi-static Mode III crack is studied and the stable/unstable transition points are found through application of the final stretch failure condition proposed in 1972 by Wnuk. A logarithmic formula for fatigue crack extension rate is derived. Results are compared to other well-known solutions.