Evolutionary Clustering of Complex Systems and Processes

In a paper the method of complex systems and processes clustering based use of genetic algorithm is offered. The aspects of its realization and shaping of fitness-function are considered. The solution of clustering task of Ukraine areas on socio-economic indexes is represented and comparative analysis with outcomes of classical methods is realized.

Evolution of Sets Systems and Homotopy Groups of Spheres

Симеон Т. Стефанов, Велика И. Драгиева - В работата е изследвана еволюцията на системи от множества върху n-мерната евклидова сфера S^n. Установена е връзката на такива системи с хомотопичните групи на сферите. Получени са някои комбинаторни приложения за многостени.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

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.