Gr\"obner Bases and Generation of Difference Schemes for Partial Differential Equations

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gr\"obner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gr\"obner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Algebraic construction and numerical behaviour of a new s-consistent difference scheme for the 2D Navier-Stokes equations

In this paper we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier-Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier-Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier-Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behaviour of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and also with the scheme which is not strongly consistent

Optimization of Physical Training in Special Medical Groups

The article studies the issues of improving the student’s physical training efficiency of special medical groups in universities. On the basis of the data analysis of the complex students survey a number of directions for optimization of physical training in these groups was offered. It is found that at the moment the process of conducting such classes at the University has insufficient individual approach and contains great potential for optimizing the use of special techniques.В статье рассматриваются вопросы повышения эффективности занятий физической культурой студентов специальных медицинских групп в вузе. На основе анализа данных комплексного анкетирования студентов УГМУ предложен ряд направлений оптимизации занятий физкультурой в указанных группах. Выявлено, что на данный момент процесс проведения таких занятий в вузе имеет недостаточный индивидуальный подход и содержит большой потенциал для оптимизации использования специальных методик

The rapeutic physical education for students with disabilities

This article presents the ratio of the number of USMU students with HIA to students with the main health group, distribution by health groups, nosological units, as well as measures of prevention and treatment with physical therapyв данной статье приводится соотношение количества студентов УГМУ с ОВЗ, к студентам с основной группой здоровья, распределение по группам здоровья, нозологическим единицам, а также меры профилактики и лечения средствами ЛФ

Restoration of biomechanics of everyday movement as a means of rehabilitation and prevention of herniated discstribution

The article reveals aspects of herniation of intervertebral discs as a result of violation of normal biomechanics in the pelvic region due to suboptimal daily human movements. The types of these degenerative-dystrophic changes are classified, the causes of their occurrence are analyzed from the point of view of biomechanics and arthrokinematics, and rehabilitation measures are proposedВ статье раскрываются аспекты грыжеобразования межпозвоночных дисков как результата нарушения нормальной биомеханики в тазовом регионе вследствие неоптимальных повседневных движений человека. Классифицируются виды этих дегенеративно-дистрофических изменений, анализируются причины их возникновения с точки зрения биомеханики и артрокинематики и предлагаются возможные стратегии реабилитации. В основном рассматриваются случаи грыжевых дефектов поясничного отдела позвоночник

Comparative characteristics of the health status of 1st year students in different universities of Yekaterinburg

This article provides a comparative description of three major universities in Yekaterinburg. The state of health of 1st year students is compared, and their ratio by health groupsВ данной статье приводится сравнительная характеристика трёх крупных университетов города Екатеринбурга. Сравнивается состояние здоровья студентов 1 курса, и их соотношение по группам здоровья

Therapeutic physical training for arthrosis of the shoulder joints of athletes

This article examines the statistics of the occurrence of arthrosis of the shoulder joints in athletes and its connection with the popularization of various sports, as well as compares the methods of treatment of this diseaseВ данной статье рассматривается статистика возникновения артроза плечевых суставов у спортсменов и связь её с популяризацией различных видов спорта, а также сравниваются методы лечения данного заболевания. Артроз часто является следствием травмы, поэтому в статье будет рассмотрена статистика травм плечевого сустав

Glucocorticoid doping in high performance sport (literature review)

The article presents a literature review devoted to the problem of the use of doping agents in modern sports, namely the use of pharmacological drugs of the group of glucocorticosteroids. Their chemical structure, classification of drugs registered in the Russian Federation, mechanism of action, effect on the body of athletes, as well as possible side effects are considered.В статье представлен обзор литературы, посвящённый проблеме применения допинговых средств в современном спорте, а именно использованию фармакологических препаратов группы глюкокортикостероидов. рассмотрены их химическая структура, классификация средств, зарегистрированных в российской федерации, механизм действия, влияние на организм атлетов, а также возможные побочные эффекты

The use of diuretics as pharmacological doping by athletes in different sports

The article discusses the use of diuretic drugs as pharmacological doping in modern sports. The reasons for the use of diuretics by athletes of different disciplines are described. The percentage of athletes resorting to this type of doping is evaluated. The most popular diuretic used by athletes has been singled out. Undesirable side reactions of a human body for the intake of diuretics are explained.В статье рассмотрена проблема применения диуретических препаратов, как фармакологического допинга в современном спорте. описаны причины употребления диуретиков спортсменами разных дисциплин. Рассмотрено процентное соотношение атлетов, прибегающих к данному виду допинга. определено самое популярное мочегонное средство, используемое спортсменами. объяснены нежелательные побочные реакции со стороны организма на прием мочегонных средств