Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem

Онтологическое проектирование интеллектуальных систем учебного назначения

Application of the ontological approach to the design of intelligent systems for educational purposes is considered in the paper

Онтологическое проектирование интеллектуальных систем учебного назначения

Application of the ontological approach to the design of intelligent systems for educational purposes is considered in the paper. Ключевой проблемой высшего образования является несоответствие между возможностями традиционных подходов к обучению и тем объёмом фактических знаний и навыков, которыми должен обладать современный выпускник учебного заведения