РЕШЕНИЕ СИНГУЛЯРНОГО ИНТЕГРАЛЬНОГО УРАВНЕНИЯ ТЕОРИИ УПРУГОСТИ С ПОМОЩЬЮ АСИМПТОТИЧЕСКИХ МНОГОЧЛЕНОВ

The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation) based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points) using a method of mechanical quadrature  and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation), which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.Предлагается новый метод приближенного решения одного вида сингулярных интегральных уравнений теории упругости, которые рассматривались ранее другими авторами. Приближенное решение отыскивается в виде асимптотического многочлена невысокой степени (первое приближение), основанного на полиномах Чебышева второго рода. Другие авторы получали решение методом механических квадратур (только в отдельных точках) и хотя использовали также полиномы Чебышева второго рода, однако применяли другую систему узлов, на которых строили нужные формулы. Предлагаемый метод позволяет не только найти приближенное решение для всего промежутка в виде многочлена, но и  вслед за приближенным решением получить остаточный член в виде разложения в бесконечный ряд, коэффициентами которого являются линейные функционалы заданного интегрального уравнения, а базисными функциями – полиномы Чебышева второго рода. Такое представление остаточного члена первого приближения позволяет найти слагаемое бесконечного ряда, начиная с которого будет выполняться заданная точность искомого решения. Этот номер является степенью асимптотического многочлена (второе приближение), который и будет с заданной точностью давать приближение к точному решению. Рассматриваемые многочлены асимптотически стремятся к полиному наилучшего равномерного приближения в пространстве С, построенному для данного оператора. Показана сходимость приближенного решения к точному и  дана оценка погрешности. Предлагаемый алгоритм получения приближенного решения и оценки погрешности хорошо реализуется с помощью вычислительной техники и не требует большой предварительной подготовки при составлении программы

ПРИБЛИЖЕННОЕ РЕШЕНИЕ ОДНОГО УРАВНЕНИЯ ТЕОРИИ КРЫЛА МЕТОДОМ АСИМПТОТИЧЕСКИХ ПОЛИНОМОВ

The method for asymptotic polynomials has been applied to an equation in wing theory which is described with the help of  a singular integro-differential equation. An approximate solution is based on the use of the Chebyshev polynomials of the second kind. Similar solutions were known previously for the spaces C and L2. The paper presents an effective error estimates for the space C, allowing to calculate an error at any point in the reporting period and to determine an extent of the desired polynomial, which will approximate the exact solution in accordance with the given accuracy. Метод асимптотических полиномов применен к уравнению теории крыла, которое описывается сингулярным интегро-дифференциальным уравнением.  Приближенное решение основано на использовании полиномов Чебышева второго рода. Аналогичные решения были известны ранее для пространств С и L2. В статье приводятся эффективные оценки погрешности для пространства С, позволяющие вычислять ошибку в любой точке рассматриваемого промежутка и определять степень искомого полинома, который с заданной точностью будет аппроксимировать точное решение

РЕШЕНИЕ НЕКОТОРЫХ СИНГУЛЯРНЫХ ИНТЕГРАЛЬНЫХ УРАВНЕНИЙ С ПОМОЩЬЮ АСИМПТОТИЧЕСКИХ МНОГОЧЛЕНОВ

The paper proposes a new method for approximate solution of singular integral equations with the Cauchy-type kernel which are taken along the real axis segment. Integration function can be represented as an asymptotic polynomial or infinite series using the Chebyshev polynomials. The remainder has been obtained simultaneously with the approximate solution. Its form makes it possible to determine degree of the polynomial that provides an approximate solution with a given accuracy.Предложен новый способ приближенного решения сингулярных интегральных уравнений с ядром типа Коши, взятых вдоль отрезка действительной оси. Подынтегральная функция может быть представлена в виде асимптотического полинома, либо бесконечного ряда с использованием полиномов Чебышева. Одновременно с приближенным решением будет получен остаточный член, вид которого позволяет определить степень полинома, дающего приближенное решение с заданной точностью

CARACTERÍSTICAS ESPECÍFICAS DAS ORIENTAÇÕES PARA A VIDA ENTRE ESTUDANTES E SUA INTER-RELAÇÃO COM A FORMAÇÃO PROFISSIONAL

O autor deste artigo considera um estudo empírico das orientações de vida dos estudantes e sua inter-relação com a formação profissional. Os principais objetivos do estudo são: conduzir a análise teórica das orientações de vida; compor um bloco de técnicas psicodiagnósticas para estudar orientações de vida entre estudantes de vários programas de estudo ;. O significado prático do estudo consistiu na compilação de um bloco de técnicas de psicodiagnóstico que podem ser usadas para diagnosticar as orientações de vida de uma pessoa e a esfera de valor-significado. Além disso, com base nos dados obtidos, é possível desenvolver suporte corretivo para orientações de vida e características pessoais e pessoais relacionadas da pessoa.El autor de este artículo considera un estudio empírico de las orientaciones de vida de los estudiantes y su interrelación con la formación profesional. Los principales objetivos del estudio son: realizar el análisis teórico de las orientaciones de la vida; componer un bloque de técnicas de psicodiagnóstico para estudiar las orientaciones de la vida entre estudiantes de diversos programas de estudio; La importancia práctica del estudio consistió en compilar un bloque de técnicas de psicodiagnóstico que pueden usarse para diagnosticar tanto las orientaciones de la vida de una persona como la esfera del significado del valor. Además, sobre la base de los datos obtenidos, es posible desarrollar un soporte correctivo para las orientaciones de la vida y las características personales individuales relacionadas de la persona.The author of this paper considers an empirical study of students’ life orientations and their interrelation with professional formation. The major objectives of the study are: to conduct the theoretical analysis of life orientations; to compose a block of psychodiagnostic techniques for studying life orientations among students of various programs of study;. The practical significance of the study consisted in compiling a block of psychodiagnostic techniques that can be used to diagnose both the life orientations of a person and the value- meaning sphere. Also, on the basis of the data obtained, it is possible to develop corrective support for life orientations and related individual-personal characteristics of the person

РАЗРАБОТКА ИМПОРТОЗАМЕЩАЮЩИХ ТЕХНОЛОГИЙ ПРИ ПРОИЗВОДСТВЕ СТРОИТЕЛЬНЫХ МАТЕРИАЛОВ

The paper presents results of investigations on rational usage of mineral resources. In particular, it has shown the possibility to increase a period of raw material serviceability and its application for production of building products depending on chemical and mineralogical composition of the waste. Analysis of the executed investigations shows that import substitution of anthracite, lignite and black coal for local fuels (milled peat and its sub-standard product) is possible in the production technology of porous building materials.A mathematical model for drying process has been developed in the paper. Technology for thermal performance of a sintering machine with calculation of its length at the given pallet speed has been proposed on the basis of the developed model. Once-through circulation of flue gases and heated materials is the main specific feature of belt sintering machines being used in production. In such a case the whole drying process can be divided into two periods: a period of constant drying rate and a period of falling drying rate. Calculations have shown that the drying rate depends on moisture content but it does not depend on heat exchange Bio-criteria, however, heating rate is a function of temperature and Biq. A mechanism of moisture transfer using various drying methods is the same as in an environment with constant temperature and so in an environment with variable temperature. Application of the mathematical model provides the possibility to save significantly power resources expended for drying process.The paper gives description of methodology for calculation of technologically important optimum parameters for sintering processes of agglomeration while using milled peat.Представлены результаты исследований по проблеме рационального использования минеральных ресурсов, в частности показана возможность расширения интервала пригодности сырья и его использования для получения строительных продуктов в зависимости от химического и минералогического состава отходов. Анализ проведенных исследований показывает, что в технологии производства пористых строительных материалов возможно импортозамещение антрацита, бурого и каменного угля на местные виды топлива - фрезерный торф и его некондиционный продукт.Разработана математическая модель процесса сушки и на основе ее решения предложена технология тепловой работы агломерационной машины с расчетом ее длины при заданных скоростях движения палет. Прямоточное движение дымовых газов и нагреваемых материалов является основной особенностью применяемых в производстве ленточных агломерационных машин. При этом весь процесс сушки можно разделить на два периода: постоянной и падающей скорости сушки. Результаты вычислений показали, что скорость сушки зависит от влагосодержания, но не зависит от теплообменного критерия Био. Однако скорость нагревания является функцией и температуры, и Biq. Механизм переноса влаги при различных методах сушки один и тот же в среде как с постоянной, так и с переменной температурами. Применение данной математической модели дает возможность значительной экономии энергоресурсов, затрачиваемых на сушку.Приведены методики расчета технологически важных оптимальных параметров процессов агломерации с применением фрезерного торфа

The potential risks and impact of the start of the 2015–2016 influenza season in the WHO European Region: a rapid risk assessment

Background: Countries in the World Health Organization (WHO) European Region are reporting more severe influenza activity in the 2015–2016 season compared to previous seasons. Objectives: To conduct a rapid risk assessment to provide interim information on the severity of the current influenza season. Methods: Using the WHO manual for rapid risk assessment of acute public health events and surveillance data available from Flu News Europe, an assessment of the current influenza season from 28 September 2015 (week 40/2015) up to 31 January 2016 (week 04/2016) was made compared with the four previous seasons. Results: The current influenza season started around week 51/2015 with higher influenza activity reported in Eastern Europe compared to Western Europe. There is a strong predominance of influenza A(H1N1)pdm09 compared to previous seasons, but the virus is antigenically similar to the strain included in the seasonal influenza vaccine. Compared to the 2014/2015 season, there was a rapid increase in the number of severe cases in Eastern European countries with the majority of such cases occurring among adults aged < 65 years. Conclusions: The current influenza season is characterized by an early start in Eastern European countries, with indications of a more severe season. Currently circulating influenza A(H1N1)pdm09 viruses are antigenically similar to those included in the seasonal influenza vaccine, and the vaccine is expected to be effective. Authorities should provide information to the public and health providers about the current influenza season, recommendations for the treatment of severe disease and effective public health measures to prevent influenza transmission

SOLUTION OF SINGULAR INTEGRAL EQUATION FOR ELASTICITY THEORY WITH THE HELP OF ASYMPTOTIC POLYNOMIAL FUNCTION

The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation) based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points) using a method of mechanical quadrature  and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation), which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming

APPROXIMATE SOLUTION OF ONE EQUATION IN WING THEORY USING METHOD FOR ASYMPTOTIC POLYNOMIALS

The method for asymptotic polynomials has been applied to an equation in wing theory which is described with the help of  a singular integro-differential equation. An approximate solution is based on the use of the Chebyshev polynomials of the second kind. Similar solutions were known previously for the spaces C and L2. The paper presents an effective error estimates for the space C, allowing to calculate an error at any point in the reporting period and to determine an extent of the desired polynomial, which will approximate the exact solution in accordance with the given accuracy

SOLUTION OF SOME SINGULAR INTEGRAL EQUATIONS BY MEANS OF ASYMPTOTIC POLYNOMIALS

The paper proposes a new method for approximate solution of singular integral equations with the Cauchy-type kernel which are taken along the real axis segment. Integration function can be represented as an asymptotic polynomial or infinite series using the Chebyshev polynomials. The remainder has been obtained simultaneously with the approximate solution. Its form makes it possible to determine degree of the polynomial that provides an approximate solution with a given accuracy