Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Intelligent Model of User Behavior in Distributed Systems

We present a complex neural network model of user behavior in distributed systems. The model reflects both dynamical and statistical features of user behavior and consists of three components: on-line and off-line models and change detection module. On-line model reflects dynamical features by predicting user actions on the basis of previous ones. Off-line model is based on the analysis of statistical parameters of user behavior. In both cases neural networks are used to reveal uncharacteristic activity of users. Change detection module is intended for trends analysis in user behavior. The efficiency of complex model is verified on real data of users of Space Research Institute of NASU-NSAU.

Existence of Global Solutions to Supercritical Semilinear Wave Equations

∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.

Synthesis Methods of Multiple-valued Structures of Language Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued of coding are considered. The many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neurons diaphragms, and also modification of frequency of following of the transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

Grid-enabling Satellite Image Archive Prototype for UA Space Grid Testbed

* The work is partially supported by the grant of National Academy of Science of Ukraine for the support of scientific researches by young scientists No 24-7/05, " Розробка Desktop Grid-системи і оптимізація її продуктивності ”.

Multiple-Valued Structures of Intellectual Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neuron diaphragms, and also frequency modification of the following transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.