On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube [0, ∞)d . The elements of J(χ) can be distinguished among all W -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. Pólya’s theorem can be obtained from the above identity by the specialization χ = 1W , where 1W is the unit character of W.

On a Variational Approach to some Quasilinear Problems

We prove some multiplicity results concerning quasilinear elliptic equations with natural growth conditions. Techniques of nonsmooth critical point theory are employed.

Intelligent Search and Automatic Document Classification and Cataloging Based on Ontology Approach

This paper presents an approach to development of intelligent search system and automatic document classification and cataloging tools for CASE-system based on metadata. The described method uses advantages of ontology approach and traditional approach based on keywords. The method has powerful intelligent means and it can be integrated with existing document search systems.

Model Construction and Research using System Compositional Approach on Natural Hierarchical Neural Networks. Development of Computer Toolbox

System compositional approach to model construction and research of informational processes, which take place in biological hierarchical neural networks, is being discussed. A computer toolbox has been successfully developed for solution of tasks from this scientific sphere. A series of computational experiments investigating the work of this toolbox on olfactory bulb model has been carried out. The well-known psychophysical phenomena have been reproduced in experiments.

Systems Analysis: the Structure-and-Purpose Approach Based on Logic-linguistic Formalisation

Systems analysis (SA) is widely used in complex and vague problem solving. Initial stages of SA are analysis of problems and purposes to obtain problems/purposes of smaller complexity and vagueness that are combined into hierarchical structures of problems(SP)/purposes(PS). Managers have to be sure the PS and the purpose realizing system (PRS) that can achieve the PS-purposes are adequate to the problem to be solved. However, usually SP/PS are not substantiated well enough, because their development is based on a collective expertise in which logic of natural language and expert estimation methods are used. That is why scientific foundations of SA are not supposed to have been completely formed. The structure-and-purpose approach to SA based on a logic-and-linguistic simulation of problems/purposes analysis is a step towards formalization of the initial stages of SA to improve adequacy of their results, and also towards increasing quality of SA as a whole. Managers of industrial organizing systems using the approach eliminate logical errors in SP/PS at early stages of planning and so they will be able to find better decisions of complex and vague problems.

On a Direct Approach to the Solution of Inverse Optical Problems

The evaluation from experimental data, of physical quantities, which enter into the electromagnetic Maxwell equations, is described as inverse optical problem. The functional relations between the dependent and independent variables are of transcendental character and numeric procedures for evaluation of the unknowns are largely used. Herein, we discuss a direct approach to the solution, illustrated by a specific example of determination of thin films optical constants from spectrophotometric data. New algorithm is proposed for the parameters evaluation, which does not need an initial guess of the unknowns and does not use iterative procedures. Thus we overcome the intrinsic deficiency of minimization techniques, such as gradient search methods, Simplex methods, etc. The price of it is a need of more computing power, but our algorithm is easily implemented in structures such as grid clusters. We show the advantages of this approach and its potential for generalization to other inverse optical problems.

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

Early Detection of Emergent Events Based on an Extremal Process Approach

2000 Mathematics Subject Classification: Primary 60G70, 62F03.