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.

A Cognitive Science Reasoning in Recognition of Emotions in Audio-Visual Speech

In this report we summarize the state-of-the-art of speech emotion recognition from the signal processing point of view. On the bases of multi-corporal experiments with machine-learning classifiers, the observation is made that existing approaches for supervised machine learning lead to database dependent classifiers which can not be applied for multi-language speech emotion recognition without additional training because they discriminate the emotion classes following the used training language. As there are experimental results showing that Humans can perform language independent categorisation, we made a parallel between machine recognition and the cognitive process and tried to discover the sources of these divergent results. The analysis suggests that the main difference is that the speech perception allows extraction of language independent features although language dependent features are incorporated in all levels of the speech signal and play as a strong discriminative function in human perception. Based on several results in related domains, we have suggested that in addition, the cognitive process of emotion-recognition is based on categorisation, assisted by some hierarchical structure of the emotional categories, existing in the cognitive space of all humans. We propose a strategy for developing language independent machine emotion recognition, related to the identification of language independent speech features and the use of additional information from visual (expression) features.

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Grid-enabling Satellite Image Archive Prototype for UA Space Grid Testbed

* The work is partially supported by the grant of National Academy of Science of Ukraine for the support of scientific researches by young scientists No 24-7/05, " Розробка Desktop Grid-системи і оптимізація її продуктивності ”.

Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15