The article discusses the projects of the upcoming post-industrial society, in particular, the projects of mathematization of the effective formation of public consciousness, it is emphasized that these projects are of particular importance for the current political situation in the world. The article describes the main results obtained by the authors to ensure the formation of public consciousness with the help of media projects, in particular, it talks about mathematical models that allow you to calculate the audience's interest in media projects and the psychological impact of the journalist's personality on the audience, suggests a methodology for preparing media projects on the air, taking into account ensuring the greatest interest of the audience in the project. The article proposes to use models for the effective formation of public consciousness when designing the relationship "robot - human".

Keywords: public consciousness, media projects, robots, human, mathematical models

Civil-legal attitudes of the population determine the degree of its participation in the socio-political processes of society development. The aim of this work is to create a cognitive model that reflects the structure of civil-legal attitudes of the population of the Rostov region, depending on the socio-demographic (age) differences. The object of the study is the civil- legal attitudes in the consciousness of the population of the Rostov region, differentiated by age (youth, the population of economically active age, the older generation). The subject research field includes certain aspects of the structures of civil-legal attitudes of the population of the Rostov region, depending on the belonging to different socio-demographic groups of the population. The methodological basis for the development and research of the considered substantive models is a system analysis in combination with a cognitive approach. In the framework of the study, the cognitive model of civil-legal attitudes of residents of the Rostov region, allowed to identify three components, the degree of severity of each of which has an age determination. To the greatest extent, age differentiation affects the value-semantic, normative and situational components of the cognitive model, which indicates an increasing mental distance between the strata of the older and younger generation of representatives of the Don region. At the same time, there are practically no generational imbalances in the institutional component, which characterizes the role of the state in the formation of the legal and civil field.

Keywords: cognitive model, age groups, civil-legal attitudes, socio-demographic differentiation of regional society, constructs of consciousness of different age groups, value-normative structure of the society

The article deals with the process of spraying immiscible liquid media with a disk spray. A mathematical model for determining the dispersion characteristics of spraying is proposed.

Keywords: liquid, atomization, flow, speed, dosing

Article is devoted multidimensional integrated operators with homogeneous kernels and oscillating in factors of a special kind. The operators representing the sum of the composed are studied: the initial integrated operator with a homogeneous kernel, the operator with осциллирующим in factor and a homogeneous kernel. For the given operators the concept of a symbol, of which terms is defined the criterion neterovosti and the formula of calculation of an index is received. The task in view decision is based on a reduction of the multidimensional integrated equation to infinite diagonal system of the one-dimensional equations.

Keywords: Integral operators with homogeneous kernels,integral operators with oscillating factors, multidimensional integral equations