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The study's relevance is due to the need to achieve a fundamental theoretical understanding of the type of professional teacher training and preparation that is demanded by society, government, and the professional teacher community so that teachers can effectively act as character educators. Such an understanding will make it possible to institute supporting norms and regulations so that teachers can develop and practice the necessary professional skills and personal behaviors when performing as learning and character development facilitators. Before we can solve this problem, we need a clear description of the normative image of the teacher as a character educator. The article presents the progress and results of our study, which was designed to determine the essential characteristics of the contemporary normative image of the teacher as a character educator. The research methodology of the study combined personality, activity, value-based, systems, and synergetic approaches. Research methods included a contextual analysis of regulations, comparisons, systematizations, interpretations, and generalizations. The article presents the rationale and results of a contextual analysis of the two basic professional standards governing teachers and specialists in character education. Ten criteria provided the basis for comparison, subsequent systematization, and interpretation of the data, including the consideration and acceptance of the personal and unique individual traits of students; the factors that determine the formation of the value systems of students; the personal qualities of students; factors that stimulate the development of self-organizational and self-management skills as well as personal self-development; the formation of the character education system and space; conducting group work and team building as well as establishing relationships; the design and organization of the character education work and various types of activities, and so on. Our analysis enables us to conclude that, given the existing regulations that govern the domain of character education, the normative image of the teacher as a learning and development facilitator can so far only be described as rather ambiguous and inconsistent. In addition, current provisions that frame the professional dimension of character education in Russia have failed to establish an adequate room for agency as an important modifier of the teacher's ability to take initiative and exercise more effective instructional strategies across the functional areas and particular activities of character education. [Translated by Kenneth Cargill.]

In this survey, some interesting generalizations of the theory of Co-semigroups and their applications are presented. The survey is divided into three parts: 'Integrated semigroups,' 'Csemigroups,' and 'Applications.' Different approaches to the theory are discussed. The content presented is taken from articles of the last 20 years and also contains some results of the authors. Various applications are presented; most of them concern ill-posed Cauchy problems. Keywords and phrases: semigroup, integrated semigroup, C-semigroup, Cauchy problem, differential equation. AMS Subject Classification: 47D60, 47D62, 65Y20, UDC 517.986.7 CONTENTS Introduction 514 Chapter 1. Integrated Semigroups 519 1.1. Exponentially Bounded Integrated Semigroups 527 1.2. Local Integrated Semigroups 542 1.2.1. Local integrated cosine families 543 Chapter 2. C-Semigroups [...]

An important role in studying the classical Cahn-Hilliard problem [5] is played by its singular-limit problem, the so-called Melin-Sikerk free boundary problem, which, at present allows one to only numerically describe the instability of the crystallization process. The purpose of this work is to prepare the material for deducing the singular-limit problem for the essentially asymmetric model [8, 21]., UDC 517.957.6 CONTENTS 1. Two Cases of Specific Energy Expansion 2. Studying Interphase Zone References 1. Two Cases of Specific Energy Expansion In accordance with [5, 8, 21], we assume [...]

The problem presented below is a singular-limit problem of the extension of the Cahn-Hilliard model obtained via introducing the asymmetry of the surface tension tensor under one of the truncations (approximations) of the inner energy [2, 5-8, 10, 12, 13]., UDC 517.957.6 CONTENTS 1. Expansion of Specific Energy in Three-Dimensional Case 2. Studying Interphase Zone in Two-Dimensional Case 3. Passage to Two-Dimensional Free Boundary Problem 4. A More General Case [...]

A certain one-phase problem with free boundary is studied. The local (in time) solvability of this problem is proved; moreover, the general method elaborated is applied in a more concrete case. For this purpose, a new change of variables and the parametrization of the boundary are introduced, and the problem studied is reduced to a problem in a constant domain., UDC 517.957.6 CONTENTS 1. Introduction 2. Change of Variables, Parametrization of Boundary, Reduction of Problem to a Problem in a Constant Domain 3. Example. Change of Variables and Parametrization of [...]