On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

Electromagnetism: Interaction of Simulation and Real Lab Experiment

eLearning at universities is taking an increasingly larger part of academic teaching methodologies. In part this is caused by different pedagogical concepts behind interactive learning system, in part it is because of larger numbers of students that can be reached within one given course and, most important, actively integrated into the teaching process. We present here the development of a novel concept of teaching, allowing students to explore theoretical and experimental aspects of act of magnetic field on moving charge through real experiments and simulation. This problem is not only part of the basic education of physics students, but also element of the academic education of almost all engineers.

Neural Networks for Modelling of Large Social Systems. Approaches for Mentality, Anticipating and Multivaluedness Accounting

It is consider the new global models for society of neuronet type. The hierarchical structure of society and mentality of individual are considered. The way for incorporating in model anticipatory (prognostic) ability of individual is considered. Some implementations of approach for real task and further research problems are described. Multivaluedness of models and solutions is discussed. Sensory-motor systems analogy also is discussed. New problems for theory and applications of neural networks are described.

Rolle's Theorem for Complex Polynomials with Real Coefficients

Let p(z) be an algebraic polynomial of degree n ¸ 2 with real coefficients and p(i) = p(¡i). According to Grace-Heawood Theorem, at least one zero of the derivative p0(z) is on the disk with center in the origin and radius cot(¼=n). In this paper is found the smallest domain containing at leas one zero of the derivative p0(z).

Personal Work Space and Content Analysis Functionality in a Cultural Heritage Digital Library

The paper presents a different vision for personalization of the user’s stay in a cultural heritage digital library that models services for personalized content marking, commenting and analyzing that doesn’t require strict user profile, but aims at adjusting the user’s individual needs. The solution is borrowed from real work and studying of traditional written content sources (incl. books, manuals), where the user mainly performs activities such as underlining the important parts of the content, writing notes and inferences, selecting and marking zones of their interest in pictures, etc. In the paper a special attention is paid to the ability to execute learning analysis allowing different ways for the user to experience the digital library content with more creative settings.