MHD equilibria with incompressible flows: symmetry approach

We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and in particular a special type of "weak" symmetries.Comment: Accepted for publication in Phys. Plasma

Group classification of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.Comment: 18 Pages. Submitted to Classical and Quantum Gravit

Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the curl of the fluid velocity. A main result of the classification in the kinematic case is that the only equation of state found to be distinguished by admitting extra $n$-dimensional conserved integrals, apart from mass, momentum, energy, angular momentum and Galilean momentum (which are admitted for all equations of state), is the well-known polytropic equation of state with dimension-dependent exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of state are found to arise, and here the main result of the classification is that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's two-dimensional circulation theorem is obtained for a general equation of state.Comment: 24 pages; published version with misprints correcte

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Purpose as a pedagogical category

Раскрыты основные характеристики цели как педагогической категории; обоснованы основные признаки целей обучения, рассмотрены соотношение понятия «цель» со смежными понятиями – «результат», «задача», «функции», средства достижения целейThe main characteristics of the goal as a pedagogical category are disclosed; Substantiated the main features of learning objectives, considered the relationship of the goal with related concepts – result, task, functions, means of achieving goal

S. Y. Batyshev about the law of professional pedagogy

The article deals with the contribution to the development of laws S. Y. Batyshev professional pedagogy; a brief description of the content of the seven laws of professional pedagogy underlying the training of skilled workers; proposed systematization of these laws in two groups according to the criterion of «the leading trends connections»В статье раскрывается вклад С. Я. Батышева в разработку законов профессиональной педагогики; дается краткое описание содержания семи законов профессиональной педагогики, лежащих в основе подготовки квалифицированных рабочих; предложена систематизация этих законов в две группы по критерию «ведущая направленность связей

A differential game of evasion from many pursuers

This paper considers a game problem with many pursuers described by infinite systems of differential equations of second order. On the controls of players geometric constraints are imposed. The aim of the pursuers is to capture the evader,while the aim of the evader is the opposite. The theorem on evasion is proved in this paper

Problem-based learning as a base model in modern vocational education

It is shown that in contemporary cultural conditions problematical becoming the norm of professional activity. The thesis of the predominant role of the principle of problematical in vocational education as an objectively necessary condition for the implementation of the requirements of the competency approachПоказано, что в современных культурных условиях проблемность становится нормой профессиональной деятельности. Обоснован тезис о преобладающей роли принципа проблемности в системе профессионального образования как объективно необходимого условия реализации требований компетентностного подход

Избыточная созданная ценность как метрика результативности и ее определение посредством показателя TEVA

The paper explores the excess value created (EVC) metric, which is an aggregated measure of the financial performance of a company over a multi-period measurement interval. The relevance of the study is due to the demand for practical solutions in the field of financial performance monitoring and incentive compensation, which makes it possible to achieve congruence between the interests of shareholders and the decisions of managers. The aim of the study is to build and justify a periodic financial measure that takes into account not only the current result but also the long-term consequences of management decisions. The scientific novelty of the study lies in the determination of the EVC metric via the TEVA indicator and providing the rationale for the new design of the performance measure. The result of the study is the derivation of formulas for calculating the EVC measure on multi-period and one-period intervals, which are free from restrictions on changes in the capital structure and the cost of capital, allow for a time-varying systematic risk of operating activities and possess the advantage of computational simplicity important for practical applications. The study concludes that the measurement of value created using the EVC indicator determined via TEVA makes it possible to achieve close conformity of the metric constructed to the real-world conditions with the unification of calculations in its retrospective and forecast components based on data available from historical and Pro Forma financial statements and information from the capital market.Автор исследует показатель избыточной созданной ценности (EVC), являющейся агрегированной мерой финансовой результативности деятельности компании на многопериодном интервале измерения. Актуальность исследования обусловлена востребованностью практических решений в сфере контроля результативности и материального стимулирования, позволяющих достичь согласованности между интересами акционеров и решениями менеджеров. Целью исследования является построение и обоснование периодического финансового измерителя, учитывающего не только текущий результат, но и долгосрочные последствия решений менеджмента. Научная новизна исследования состоит в определении показателя EVC посредством показателя TEVA и обосновании новой конструкции измерителя результативности. Результатом исследования является вывод формул для расчета показателя EVC на многопериодном и однопериодном интервалах, свободных от ограничений на изменение структуры и стоимости капитала, допускающих изменяющийся во времени систематический риск операционной деятельности и имеющих преимущество вычислительной простоты, важное для практических применений. Сделан вывод, что измерение созданной ценности с помощью показателя EVС, определенного посредством TEVA, позволяет достичь близкого соответствия построенной метрической конструкции условиям реального мира с унификацией расчетов в ее ретроспективной и прогнозной составляющих на основе данных, доступных из исторической и Pro Forma финансовой отчетности, и информации рынка капитала

A Pursuit Problem in an Infinite System of Second-Order Differential Equations

We study a pursuit differential game problem for an infinite system of second-order differential equations. The control functions of players, i.e., a pursuer and an evader are subject to integral constraints. The pursuit is completed if z(τ) = z˙ (τ) = 0 at some τ > 0, where z(t) is the state of the system. The pursuer tries to complete the pursuit and the evader tries to avoid this. A sufficient condition is obtained for completing the pursuit in the differential game when the control recourse of the pursuer is greater than the control recourse of the evader. To construct the strategy of the pursuer, we assume that the instantaneous control used by the evader is known to the pursuer.Вивчається проблема переслідування в диференціальній rpi для нескінченної системи диференціальних рівнянь другого порядку. Керівні функції гравців, тобто переслідувача та переслідуваного, мають деякі обмеження. Переслідування завершується, коли z(τ) = z˙ (τ) = 0 для деякого τ > 0, де z(t) — стан системи. Переслідувач намагається завершити переслідування, а переслідуваний намагається цього уникнути. Встановлено достатню умову завершення переслідування в диференціальній грі, коли зворотнє управління для переслідувача більше, ніж для переслідуваного. Для побудови стратегії переслідувача вважаємо, що миттєве керування, застосоване переслідуваним, є відомим переслідувачу