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.

Digital Collections in Regional Public Library “P. R. Slaveikov” – Veliko Tarnovo in the Context of the National Program for Preservation and Promotion of Literary Heritage

Nowadays the great public libraries in Bulgaria are gaining the appearance of digital centers which provide new informational resources and services in the digital space. The digital conversion as a way of preservation is one of the important priorities of Regional Public Library in Veliko Tarnovo. In the last few years we persistently search for possible ways of financing by national and foreign programs in this direction. In the beginning the strategy was oriented to digitalization of the funds with most urgent conversion – these of the local studies periodicals from 1878 till 1944 year. The digitalization of funds will create conditions of laying the basement of full text database of Bulgarian periodical publications. The technology that is offered gives opportunities for including other libraries in the Unified index, which can develop it into a National Unified index of periodical publications. The integrated informational environment that is created is an attractive, comfortable and useful place for work in home or at work for researchers, historians, art experts, bibliographers. The library readers use very actively all informational services of the library internet page and work competently with the on-line indexes provided there, they find the necessary title, which can be demanded later for usage in home or in the library, using electronic means again.

Optimization of Rational Approximations by Continued Fractions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

The Distributed System of Databases on Properties of Inorganic Substances and Materials

The principles of organization of the distributed system of databases on properties of inorganic substances and materials based on the use of a special reference database are considered. The last includes not only information on a site of the data about the certain substance in other databases but also brief information on the most widespread properties of inorganic substances. The proposed principles were successfully realized at the creation of the distributed system of databases on properties of inorganic compounds developed by A.A.Baikov Institute of Metallurgy and Materials Science of the Russian Academy of Sciences.

Structuring of Ranked Models

Prognostic procedures can be based on ranked linear models. Ranked regression type models are designed on the basis of feature vectors combined with set of relations defined on selected pairs of these vectors. Feature vectors are composed of numerical results of measurements on particular objects or events. Ranked relations defined on selected pairs of feature vectors represent additional knowledge and can reflect experts' opinion about considered objects. Ranked models have the form of linear transformations of feature vectors on a line which preserve a given set of relations in the best manner possible. Ranked models can be designed through the minimization of a special type of convex and piecewise linear (CPL) criterion functions. Some sets of ranked relations cannot be well represented by one ranked model. Decomposition of global model into a family of local ranked models could improve representation. A procedures of ranked models decomposition is described in this paper.

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.

Preserving Cultural Heritage Using Open Source Collection Management Tools

Open source software (OSS) popularity is growing steadily and many OSS systems could be used to preserve cultural heritage objects. Such solutions give the opportunity to organizations to afford the development of a digital collection. This paper focuses on reviewing two OSS tools, CollectionSpace and the Open Video Digital Library Toolkit and discuss on how these could be used for organizing digital replicas of cultural objects. The features of the software are presented and some examples are given.

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.