On some Concepts of Residuals

2000 Mathematics Subject Classification: 60E10, 62G15, 62M20

Electromagnetism: Interaction of Simulation and Real Lab Experiment

eLearning at universities is taking an increasingly larger part of academic teaching methodologies. In part this is caused by different pedagogical concepts behind interactive learning system, in part it is because of larger numbers of students that can be reached within one given course and, most important, actively integrated into the teaching process. We present here the development of a novel concept of teaching, allowing students to explore theoretical and experimental aspects of act of magnetic field on moving charge through real experiments and simulation. This problem is not only part of the basic education of physics students, but also element of the academic education of almost all engineers.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.