Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Mathematics Subject Classification: 44A05, 46F12, 28A78

Development of Database for Distributed Information Measurement and Control System

The purpose of this work is the development of database of the distributed information measurement and control system that implements methods of optical spectroscopy for plasma physics research and atomic collisions and provides remote access to information and hardware resources within the Intranet/Internet networks. The database is based on database management system Oracle9i. Client software was realized in Java language. The software was developed using Model View Controller architecture, which separates application data from graphical presentation components and input processing logic. The following graphical presentations were implemented: measurement of radiation spectra of beam and plasma objects, excitation function for non-elastic collisions of heavy particles and analysis of data acquired in preceding experiments. The graphical clients have the following functionality of the interaction with the database: browsing information on experiments of a certain type, searching for data with various criteria, and inserting the information about preceding experiments.

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

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.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Fractional Integration and Fractional Differentiation of the M-Series

Mathematics Subject Classification: 26A33, 33C60, 44A15

On the Optimal Allocations in Economy with Fixed Total Resources

Здравко Д. Славов - В тази статия се разглежда математически модел на икономика с фиксирани общи ресурси, както и краен брой агенти и блага. Обсъжда се ролята на някои предположения за отношенията на предпочитание на икономическите агенти, които влияят на характеристиките на оптимално разпределените дялове. Доказва се, че множеството на оптимално разпределените дялове е свиваемо и притежава свойството на неподвижната точка.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.