q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Growth of some varieties of Leibniz-Poisson algebras

2010 Mathematics Subject Classification: 17A32, 17B63.

Technology of Storage and Processing of Electronic Documents with Intellectual Search Properties

The technology of record, storage and processing of the texts, based on creation of integer index cycles is discussed. Algorithms of exact-match search and search similar on the basis of inquiry in a natural language are considered. The software realizing offered approaches is described, and examples of the electronic archives possessing properties of intellectual search are resulted.

A Framework for Fast Classification Algorithms

Today, due to globalization of the world the size of data set is increasing, it is necessary to discover the knowledge. The discovery of knowledge can be typically in the form of association rules, classification rules, clustering, discovery of frequent episodes and deviation detection. Fast and accurate classifiers for large databases are an important task in data mining. There is growing evidence that integrating classification and association rules mining, classification approaches based on heuristic, greedy search like decision tree induction. Emerging associative classification algorithms have shown good promises on producing accurate classifiers. In this paper we focus on performance of associative classification and present a parallel model for classifier building. For classifier building some parallel-distributed algorithms have been proposed for decision tree induction but so far no such work has been reported for associative classification.

Selfstructurized Systems

The problems of constructing the selfsrtucturized systems of memory of intelligence information processing tools, allowing formation of associative links in the memory, hierarchical organization and classification, generating concepts in the process of the information input, are discussed. The principles and methods for realization of selfstructurized systems on basis of hierarchic network structures of some special class – growing pyramidal network are studied. The algorithms for building, learning and recognition on basis of such type network structures are proposed. The examples of practical application are demonstrated.

Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

On some Results Related to Köthe's Conjecture

The Köthe conjecture states that if a ring R has no nonzero nil ideals then R has no nonzero nil one-sided ideals. Although for more than 70 years significant progress has been made, it is still open in general. In this paper we survey some results related to the Köthe conjecture as well as some equivalent problems.

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Backlund-Darboux Transformations in Sato's Grassmannian

We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

Analogical Reasoning Techniques in Intelligent Counterterrorism Systems

The paper develops a set of ideas and techniques supporting analogical reasoning throughout the life-cycle of terrorist acts. Implementation of these ideas and techniques can enhance the intellectual level of computer-based systems for a wide range of personnel dealing with various aspects of the problem of terrorism and its effects. The method combines techniques of structure-sensitive distributed representations in the framework of Associative-Projective Neural Networks, and knowledge obtained through the progress in analogical reasoning, in particular the Structure Mapping Theory. The impact of these analogical reasoning tools on the efforts to minimize the effects of terrorist acts on civilian population is expected by facilitating knowledge acquisition and formation of terrorism-related knowledge bases, as well as supporting the processes of analysis, decision making, and reasoning with those knowledge bases for users at various levels of expertise before, during, and after terrorist acts.