On the Best Approximation of the Infinitesimal Generator of a Contraction Semigroup in A Hilbert Space

Let A be the infinitesimal generator of a strongly continuous contraction semigroup in a Hilbert space H. We give an upper estimate for the best approximation of the operator A by bounded linear operators with a prescribed norm in the space H on the class Q2={x∈D(A2):∥A2x∥≤1}, where D(A2) denotes the domain of A2.This work was supported by the Russian Foundation for Basic Research (project no. 15-01-02705), the Program for State Support of Leading Scientific Schools of the Russian Federation (project no.NSh-9356.2016.1), and by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and the Ural Federal University)

Metric Fourier approximation of set-valued functions of bounded variation

We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.Comment: 26 pages, 1 figur

ON THE BEST APPROXIMATION OF THE INFINITESIMAL GENERATOR OF A CONTRACTION SEMIGROUP IN A HILBERT SPACE

Let $A$ be the infinitesimal generator  of a strongly continuous contraction semigroup in a  Hilbert space $H$.   We give an upper estimate for the best approximation of the operator $A$ by bounded linear operators with a prescribed norm  in the space $H$ on the class $Q_2 = \{x\in \mathcal{D}(A^2) : \|A^2 x\| \leq 1\}$,  where $\mathcal D(A^2)$ denotes the domain of $A^2$

Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces

Utilization of fly ashes formed during the combustion of solid fuel

The fly ash definition, fly ash classification and the quantity of fly ash formed are described. The influence of Reftinskaya power station fly ash on density and strength of Portland cement is presented.В работе рассмотрено понятие зол-уноса, их классификация, основные объемы образующегося продукта. Приведены результаты эксперимента по изучению влияния золы-унос Рефтинской ГРЭС на плотность и прочность портландцемента класса ЦЕМ I 42,5Н

Эффективность и безопасность клинического применения сухого экстракта листьев плюща в лечении заболеваний органов дыхания у детей

Data of morbidity of respiratory diseases in children at Sankt-Petersburg are given in the article. The authors described significance and current features of respiratory diseases in children, showed a role of mucostasis in poor course and importance of mucoactive therapy in community-acquired and in-hospital respiratory pathologies. Results of post-marketing clinical trial of mucoactive efficacy of Prospan in 180 children of 6 months to 17 years of age with wide-spread respiratory diseases have been presented in the article. High mucolytic and bronchodilating activity and good safety profile of Prospan, which is dry extract of ivy leaves, have been demonstrated. No interaction was noted between Prospan and other medications used in the treatment of respiratory diseases in children. Therapy with dry extract of ivy leaves was safe in children with most prevalent co-existing pathology including early age children.В статье представлены данные о распространенности болезней органов дыхания (БОД) среди детей Санкт-Петербурга, определены значение и особенности современного течения БОД у детей. Показана роль мукостаза в неблагоприятном течении бронхолегочных заболеваний, обоснована необходимость мукоактивной терапии и целесообразность ее применения в амбулаторной и госпитальной терапии. Представлены данные постмаркетингового клинического исследования мукоактивной эффективности препарата Проспан (сухого экстракта листьев плюща – СЭЛП) в лечении наиболее распространенных заболеваний бронхолегочной системы у 180 детей в возрасте от 6 месяцев до 17 лет. Подтверждена высокая муколитическая и бронходилатационная эффективность препарата при высоком профиле безопасности. Не выявлено взаимодействие с другими лекарственными средствами, применяемыми в комплексной терапии БОД у детей. Отмечена безопасность применения СЭЛП в лечении детей с наиболее распространенной сопутствующей педиатрической патологией, в том числе и в раннем возрасте

Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions

AbstractWe prove that the kernels of the Baskakov–Durrmeyer and the Szász–Mirakjan–Durrmeyer operators are completely monotonic functions. We establish a Bernstein type inequality for these operators and apply the results to the quasi-interpolants recently introduced by Abel. For the Baskakov–Durrmeyer quasi-interpolants, we give a representation as linear combinations of the original Baskakov–Durrmeyer operators and prove an estimate of Jackson–Favard type and a direct theorem in terms of an appropriate K-functional

Stability, pseudostability and quasistability of vector trajectorial lexicographic optimization problem

Lower bounds of stability, pseudostability and quasistability radii of lexicographic set in vector combinatorial problem on systems of subsets of finite set with partial criteria of more general kinds have been found

Microsilica as component of organic-mineral modifier for fine-aggregate concrete

Currently, modern heavy concrete including fine-aggregate ones are systems containing basic and additional components. Their production is not complete without the use of various mineral and organic additives. Such widespread additives include microsilica and various types of polymers. The effective use of additives, based on microsilica with polymers, allows creating heavy concretes with high performance properties. This topic is of a high relevance, so the research works were conducted to study the properties of fine-aggregate concrete, containing microsilica as an active mineral additive in the organic-mineral modifier composition in the Institute of new materials and technologies of Ural Federal University. This paper is devoted to the selection of composition of the organic-mineral modifier, based on the microsilica of OJSC 'Chelyabinsk Electrometallurgical Works'. © Published under licence by IOP Publishing Ltd