Self-adjoint local boundary problems on compact surfaces. I. Spectral flow

The paper deals with first order self-adjoint elliptic differential operators on a smooth compact oriented surface with non-empty boundary. We consider such operators with self-adjoint local boundary conditions. The paper is focused on paths in the space of such operators connecting two operators conjugated by a unitary automorphism. The first result is the computation of the spectral flow for such paths in terms of the topological data over the boundary. The second result is the universality of the spectral flow: we show that the spectral flow is a universal additive invariant for such paths, if the vanishing on paths of invertible operators is required. In the next paper of the series we generalize these results to families of such operators parametrized by points of an arbitrary compact space instead of an interval. The integer-valued spectral flow is replaced then by the family index taking values in the $K^1$-group of the base space.Comment: 46 pages. V4: minor changes; version accepted by the Journal of Geometric Analysi

Social engineering: challenges and opportunities

Social engineering as a field of science has undergone a stationary period, after which it has spread with new power in educational activities. The article analyzes the status of social engineer, combining its positions of an engineer and a sociologist. Within the framework of socio-engineering activity it is necessary to mention several directions, such as, management consulting, social construction (design, programming and planning), social engineering studies (analysis, diagnosis and examination), organizational and technological activity. They present the main ground in the field of management of social processes for the qualification of future employees. The authors suppose that socio-engineering activity in enterprises should be an integral part of functional management system, along with economic and technological control of production activity

AGGRETGATE PROFESSIONAL IMAGE

В статье обосновывается теоретико-практическая целесообразность использования в социологической и междисциплинарной теории имиджа понятия «совокупный профессиональный имидж», что актуально в условиях превращение имиджа в ценность и актуальную форму коммуникативной компетенции в структуре современной профессиональной культуры.Теоретическая значимость данной работы заключается в доказательстве на базе систематизации ряда положений отечественной теории имиджа структурно-функциональной симметрии содержания принципа профессионализма и совокупного профессионального имиджа.Практическая направленность полученных в исследовании результатов связана с возможностями их применения в практике формирования профессионально-имиджевой компетенции специалистов. Цель была достигнута через решение следующих задач:1. Обоснован онтологический потенциал принципа профессионализма в качестве основы формулировки понятия «совокупный профессиональный имидж».2. Выявлена логика формирования, а также представлена характеристика структурных элементов совокупного профессионального имиджа и их внутрисистемных связей.3. Сформулировано содержание и выделены функциональные задачи персонального профессионального имиджа.The present article deals with practical and theoretical means of using the notion of “aggregate professional image” in sociologic and intra-disciplinary theory. This is quite urgent now-when image is being transformed to a precious and timely means of communicative competence within the structure of modern professional culture.The theoretical value of this paper is that it has managed to prove on a systematizing base, a number of statements in Russian image theory , structural and functional symmetry principle , combining professionalism and aggregate professional image.The practical trend of results received in the course of the research is connected with possibility to use them in order to form practical and image competence of specialists.It was possible, due to the following:1. Statement of ontologic professionalism potential principle, as a means to determine the notion of “aggregate professional image”.2. Identification of forming logic as well as presentation of aggregate professional image structural elements and their intra-system links.3. Statement of aggregate professional image contents and identification of its functional tasks

Individualization of punishment in the context of the public’s fear of crime

The individualization of punishment is largely formalized and axiomatically limited by the normative prescriptions of the General and Special parts of the Criminal Code of the Russian Federation. Meanwhile, when assigning punishment, judges always consider all the circumstances related to the commission of a crime and the identity of the perpetrator, not to mention consideration of public opinion, social and group victimization, and the fear of the population before criminal manifestations. Unlike in Russia, the foreign criminal justice system for a long time accepts the opinion of ordinary citizens on this matter, focusing on their fears of separate crimes. Sometimes, within the framework of this system, there is a manipulation of the individualization of punishment to demonstrate a preventive effect to society. Based on the above, this article is aimed at generating a discourse on the need to study and consider victimological information in the formation of criminal law policy in general and the individualization of punishment, in particular. The statistical and sociological research methods used in the study allowed obtaining and summarizing information on the indicators of the fear of residents of Gelendzhik and Novorossiysk (2017-2018) regarding ordinary crimes; reflecting the relationship between these data and the types of punishment imposed by the courts for the commission of theft, robbery, hooliganism. Systemic synthesis and analysis allowed identifying a number of patterns in this area, and justifying them. The novelty of the article is that it represents one of the few attempts to fill the gap in scientific knowledge about the mechanism of individualization of punishment as a tool of social protection, implemented through general and private prevention and requiring consideration of political-social and ethnocultural peculiarities. The results of the study allowed to articulate proposals for optimizing the activities of federal and regional coordinating councils for the prevention of offenses

The spectral flow for Dirac operators on compact planar domains with local boundary conditions

Let $D_t$, $t \in [0,1]$ be an arbitrary 1-parameter family of Dirac type operators on a two-dimensional disk with $m-1$ holes. Suppose that all operators $D_t$ have the same symbol, and that $D_1$ is conjugate to $D_0$ by a scalar gauge transformation. Suppose that all operators $D_t$ are considered with the same locally elliptic boundary condition, given by a vector bundle over the boundary. Our main result is a computation of the spectral flow for such a family of operators. The answer is obtained up to multiplication by an integer constant depending only on the number of the holes in the disk. This constant is calculated explicitly for the case of the annulus ($m=2$).Comment: 33 pages, 4 figures; section 9 adde