A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

Maximal Number of Successors in a Nginar(1) Process

2000 Mathematics Subject Classification: 60J80, 60J20, 60J10, 60G10, 60G70, 60F99.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

The Fuzzy-Neuro Classifier for Decision Support

This paper aims at development of procedures and algorithms for application of artificial intelligence tools to acquire process and analyze various types of knowledge. The proposed environment integrates techniques of knowledge and decision process modeling such as neural networks and fuzzy logic-based reasoning methods. The problem of an identification of complex processes with the use of neuro-fuzzy systems is solved. The proposed classifier has been successfully applied for building one decision support systems for solving managerial problem.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Application of the Artificial Intelligence Algorithms with a Cognitive Graphic as a Tool for a System Analysis of Electrophysiological Processes

Summarizing the accumulated experience for a long time in the polyparametric cognitive modeling of different physiological processes (electrocardiogram, electroencephalogram, electroreovasogram and others) and the development on this basis some diagnostics methods give ground for formulating a new methodology of the system analysis in biology. The gist of the methodology consists of parametrization of fractals of electrophysiological processes, matrix description of functional state of an object with a unified set of parameters, construction of the polyparametric cognitive geometric model with artificial intelligence algorithms. The geometry model enables to display the parameter relationships are adequate to requirements of the system approach. The objective character of the elements of the models and high degree of formalization which facilitate the use of the mathematical methods are advantages of these models. At the same time the geometric images are easily interpreted in physiological and clinical terms. The polyparametric modeling is an object oriented tool possessed advances functional facilities and some principal features.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Branching Stochastic Processes: Regulation, Regeneration, Estimation, Applications

2000 Mathematics Subject Classification: 60J80.

Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses

MSC 2010: 34A08, 34A37, 49N70