Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

Evolutionary Technique of Shorter Route Determination of Fire Brigade Following to Fire Place with the Optimized Space of Search

In this paper the technique of shorter route determination of fire engine to the fire place on time minimization criterion with the use of evolutionary modeling is offered. The algorithm of its realization on the base of complete and optimized space of search of possible decisions is explored. The aspects of goal function forming and program realization of method having a special purpose are considered. Experimental verification is executed and the results of comparative analysis with the expert conclusions are considered.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Multipliers on a Hilbert Space of Functions on R

2000 Mathematics Subject Classification: 42A45.

Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

A Cognitive Science Reasoning in Recognition of Emotions in Audio-Visual Speech

In this report we summarize the state-of-the-art of speech emotion recognition from the signal processing point of view. On the bases of multi-corporal experiments with machine-learning classifiers, the observation is made that existing approaches for supervised machine learning lead to database dependent classifiers which can not be applied for multi-language speech emotion recognition without additional training because they discriminate the emotion classes following the used training language. As there are experimental results showing that Humans can perform language independent categorisation, we made a parallel between machine recognition and the cognitive process and tried to discover the sources of these divergent results. The analysis suggests that the main difference is that the speech perception allows extraction of language independent features although language dependent features are incorporated in all levels of the speech signal and play as a strong discriminative function in human perception. Based on several results in related domains, we have suggested that in addition, the cognitive process of emotion-recognition is based on categorisation, assisted by some hierarchical structure of the emotional categories, existing in the cognitive space of all humans. We propose a strategy for developing language independent machine emotion recognition, related to the identification of language independent speech features and the use of additional information from visual (expression) features.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Distributed Genetic Algorithm Implementation by Means of Remote Methods Invocation Technique – Java RMI

The aim of this work is distributed genetic algorithm implementation (so called island algorithm) to accelerate the optimum searching process in space of solutions. Distributed genetic algorithm has also smaller chances to fall in local optimum. This conception depends on mutual cooperation of the clients which realize separate working of genetic algorithms on local machines. As a tool for implementation of distributed genetic algorithm, created to produce net's applications Java technology was chosen. In Java technology, there is a technique of remote methods invocation - Java RMI. By means of invoking remote methods it can send objects between clients and server RMI.

Projective Methods of Image Recognition

We propose a method for image recognition on the base of projections. Radon transform gives an opportunity to map image into space of its projections. Projection properties allow constructing informative features on the base of moments that can be successfully used for invariant recognition. Offered approach gives about 91-97% of correct recognition.

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Kneser and Hereditarily Kneser Subgroups of a Profinite Group

2000 Mathematics Subject Classification: 20E18, 12G05, 12F10, 12F99.