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.

Technology-Enhanced Learning: Review and Prospects

This paper is a reflection on the history and future of technology-enhanced learning. Over the last century various new technologies were introduced in education. Often, educational revolutions were proclaimed. Unfortunately, most of these new technologies failed to meet the high expectations. This paper reviews the rise and fall of various "revolutionary" learning technologies and analyses what went wrong. Three main driving factors are identified that influence the educational system: 1) educational practice, 2) educational research, and 3) educational technology. The role and position of these factors is elaborated and critically reviewed. Today, again many promising new technologies are being put in place for learning: gaming, social web, and mobile technologies, for example. Inevitably, these are once again proclaimed by its supporters to revolutionise teaching and learning. The paper concludes with identifying a number of relevant factors that substantiate a favourable future outlook of technology-enhanced learning.

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.