An Overview of Modelling Bulgarian Wildland Fire Behaviour by Application of a Mathematical Game Method and WRF-Fire Models

This paper presents the main achievements of the author’s PhD dissertation. The work is dedicated to mathematical and semi-empirical approaches applied to the case of Bulgarian wildland fires. After the introductory explanations, short information from every chapter is extracted to cover the main parts of the obtained results. The methods used are described in brief and main outcomes are listed. ACM Computing Classification System (1998): D.1.3, D.2.0, K.5.1.

Mathematical Models of Domain Ontologies

* This paper was made according to the program No 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project "Intellectual Systems Based on Multilevel Domain Models".

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

About Problems of Decision Making in Social and Economic Systems

The reasons of a restricted applicability of the models of decision making in social and economic systems. 3 basic principles of growth of their adequacy are proposed: "localization" of solutions, direct account of influencing of the individual on process of decision making ("subjectivity of objectivity") and reduction of influencing of the individual psychosomatic characteristics of the subject (" objectivity of subjectivity ") are offered. The principles are illustrated on mathematical models of decision making in ecologically- economic and social systems.

A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

A Mathematical Apparatus for Domain Ontology Simulation. Logical Relationship Systems

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Experience of Development and Application of Expert Systems for Economic Macroparameters Forecasting and Operation

In this article there are considered problems of forecasting economical macroparameters, and in the first place, index of inflation. Concept of development of synthetical forecasting methods which use directly specified expert information as well as calculation result on the basis of objective economical and mathematical models for forecasting separate “slowly changeable parameters” are offered. This article discusses problems of macroparameters operation on the basis of analysis of received prognostic magnitude.

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

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.

Comparison of Multivariate and Univariate Models for Genetic Evaluation of Milk Yield based on Test Day Data

2000 Mathematics Subject Classification: 62H12, 62P99