Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.Comment: a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extende

Technical assistance, neo-colonialism or mutual trade? The experience of an Anglo/Ukrainian/Russian social work practice learning project

Since the collapse of the Soviet Union there has been a steady stream of Western consultants ready to work in Eastern Europe and Russia and share professional and academic expertise and experience. Social work, unknown as a discrete discipline or profession in the Soviet Union, has been a growth area with funding from a variety of sources to help promote East-West partnerships.Social work theory and practice emphasises critical appraisal of policy and embraces issues of power, discrimination and oppression. Social work educators should therefore be especially alert to the complex ethical questions which these kinds of collaborations raise, and adept at finding practical solutions or workable compromises. This article explores these ethical and political issues with reference to a project to develop social work practice learning in a Russian oblast' (region). The project was an ambitious partnership of British, Ukrainian and Russian educators, involving numerous Russian social work and related agencies, and four Russian universities and colleges in one oblast'. The authors use a series of vignettes to help the reader achieve insights into these East-West transactions. The article concludes with a discussion of different interpretations of these dealings, using three prisms: technical assistance, neo-colonialism and mutual trade

Influence of boric anhydride upon the physical and chemical properties of ferrosilicon slag

The authors study the influence of boric anhydride upon the physical and chemical properties of slag in the manufacture of ferrosilicon. It is established that adding boric anhydride to the slag changes its refractory quality and its viscosity and eases pouring slag and metal. Slags with optimal composition and properties are described

Выявление точек «разладки» устойчивых периодов экономических систем при робастном управлении

This article addresses the potential of mathematical and statistical modelling the change point detection in economic systems on the example of UC «RUSAL». Change point prediction of stable or quasi-stable periods of economic systems is necessary for the operational changing of a strategy, tactics and control of the considered economic system. It solves one of the robust control problems, the purpose of which is the synthesis of the regulator that can provide the preservation of output variables of the system within the robust limit for all types of membership functions and the uncertainty of the input data.The developed algorithm is based on the study of the behavior of residuals of regression models by the observed series of the dynamics of some exponent (as a benchmark was chosen the price of ordinary share). This algorithm is applicable for small volume samples, which, as a rule, are the series of dynamics of exponents of economic systems and also, in the study of non-Gaussian observational models.В данной статье продемонстрированы возможности математико-статистического моделирования выявления моментов нарушения устойчивости (точек «разладки») экономических систем (на примере ОК «РУСАЛ»). Прогноз точек «разладки» ус-тойчивых или квазиустойчивых периодов экономических систем необходим для оперативного изменения стратегии, тактики и управления рассматриваемой экономической системы. Это решает одну из задач робастного управления, цель которого - синтез регулятора, способного обеспечивать сохранение выходных переменных системы в рамках робастного предела при всех типах функций принадлежности и неопределенности входных данных.Разработанный авторами алгоритм, основанный на формализованном отражении поведения остатков регрессионных моделей по наблюдаемому ряду динамики определенного показателя (в качестве опорного показателя была выбрана цена обыкновенной акции), применим для выборок малого объема, каковыми, как правило, и являются ряды динамики показателей экономических систем. По мнению авторов, такой алгоритм целесообразен при исследовании отличных от гауссовских моделей наблюдений.

All-optical switching in a vertical coupler space switch employing photocarrier-induced nonlinearity

A novel compact integrated nonlinear optical switch is demonstrated. Using a high-power picosecond pulse of 5-ps pulsewidth and 250-MHz repetition rate, all-optical switching with a contrast ratio of 23 dB has been achieved using an in-fiber input power < 14 dBm (100 pJ/pulse). The switch speed depends on the carrier sweep-out time, which can be reduced to the 10 ps range by either applying a reverse bias or by introduction of carrier recombination centers in the active layer