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

Solution of an infinite system of differential equations.

We consider an infinite system of differential equations of the second order. Existence and uniqueness questions are discussed in the Hilbert space. We obtain a result which enables the investigation of optimal control and differential game problems described by such a system

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

Academic Motivation of Master Students Studying Pedagogical Science: Case of KFU

The relevance of the study is due to the contradiction between the objective need for developing the academic motivation of Master students by means of research-oriented education and the insufficient development of the corresponding didactic conditions. The purpose of this paper is to identify the research-based learning potential in the development of Master students academic motivation and reasoning the didactic conditions promoting its effective implementation. In order to achieve it, the following tasks were solved: to reveal the essence of academic motivation and its features among Master’s students studying “Pedagogical science”; to promote theoretically and experimentally the didactic conditions for the effective implementation of the motivational potential of research-oriented learning. To identify the features of academic motivation, the methodology “Scale of Academic Motivation” was used.Research results: the essence of academic motivation as a set of motives that are the reason for the conscious inclusion of a student in educational activities is revealed; the features of the academic motivation of Master students studying Pedagogical science were revealed (the conscious choice of the program of training by the vast majority of students; different students’ background – previous education, work experience, age, that determines the polymotivation of educational activity with the dominance of internal motivation). It is shown that the motivational potential of researchoriented teaching of students is associated with its main characteristics: the purpose, content, nature of studying and research activities, features of results evaluation. Didactic conditions were experimentally promoted that enhance the motivational potential of research-oriented learning (taking into account the characteristics and levels of development of the corresponding types of students’ motivation; creating real opportunities for free choice of research topics for Master students; using work in pairs as a form of organizing educational and research activities; using a complex of stimulating methods for evaluating the study results). Perspective paths for study of the students’ academic motivation are indicated

Nonlocal aspects of λ\lambda-symmetries and ODEs reduction

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE $\mathcal{Y}$ is used here to recover $\lambda$-symmetries of $\mathcal{Y}$ as nonlocal symmetries. In this framework, by embedding $\mathcal{Y}$ into a suitable system $\mathcal{Y}^{\prime}$ determined by the function $\lambda$, any $\lambda$-symmetry of $\mathcal{Y}$ can be recovered by a local symmetry of $\mathcal{Y}^{\prime}$. As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to $\mathcal{Y}^{\prime}$.Comment: 13 page

Means of expression of incentive modality in Tatar and English languages

The relevance of the investigated problem is caused by the need to improve the functional approach to understanding the nature of the content incentive modality. The aim of the study is to identify the means of expression incentive modality in the Tatar and Russian languages, their similarities and differences. The leading approach to the study of the problems is selected descriptive-comparative method with its components - observation, comparison and generalization. The findings suggest that, in both languages there are corresponding counterparts, causing typological commonality; the most frequent way of expressing incentive modality in the English language are modal verbs and modal words, in Tatar - modal words as part of a complex predicate, the use of which depends on the context. Article Submissions may be useful in lecture courses on linguistics, in special courses on the problems of modality, as well as in the practice of teaching the Tatar and English languages.Keywords: language, translation, bilingual, incentive modality, means of expression, typological intention