Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Some Applications of the Graphic Method

There are discussed three groups of problems which are solved with the help of the graphic method.

Models, Techniques and Applications of e-Learning Personalization

In recent years Web has become mainstream medium for communication and information dissemination. This paper presents approaches and methods for adaptive learning implementation, which are used in some contemporary web-interfaced Learning Management Systems (LMSs). The problem is not how to create electronic learning materials, but how to locate and utilize the available information in personalized way. Different attitudes to personalization are briefly described in section 1. The real personalization requires a user profile containing information about preferences, aims, and educational history to be stored and used by the system. These issues are considered in section 2. A method for development and design of adaptive learning content in terms of learning strategy system support is represented in section 3. Section 4 includes a set of innovative personalization services that are suggested by several very important research projects (SeLeNe project, ELENA project, etc.) dated from the last few years. This section also describes a model for role- and competency-based learning customization that uses Web Services approach. The last part presents how personalization techniques are implemented in Learning Grid-driven applications.

On the Automorphism Groups of some AG-Codes Based on Ca;b Curves

*Partially supported by NATO.

An Analysis of Some Relations Among Domain Ontologies

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Applications of the Sufficiency Principle in Acceleration of Neural Networks Trainig

One of the problems in AI tasks solving by neurocomputing methods is a considerable training time. This problem especially appears when it is needed to reach high quality in forecast reliability or pattern recognition. Some formalised ways for increasing of networks’ training speed without loosing of precision are proposed here. The offered approaches are based on the Sufficiency Principle, which is formal representation of the aim of a concrete task and conditions (limitations) of their solving [1]. This is development of the concept that includes the formal aims’ description to the context of such AI tasks as classification, pattern recognition, estimation etc.

Cluster Analysis of Some Clases of Objects by Application of the Test Recognition Algorithms

The paper treats the task for cluster analysis of a given assembly of objects on the basis of the information contained in the description table of these objects. Various methods of cluster analysis are briefly considered. Heuristic method and rules for classification of the given assembly of objects are presented for the cases when their division into classes and the number of classes is not known. The algorithm is checked by a test example and two program products (PP) – learning systems and software for company management. Analysis of the results is presented.

On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55