International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

In the work a mathematical model for the non-stationary motion of liquid homogeneous viscous mixtures through pipelines is constructed. The corresponding integral equations expressing the laws of conservation of mass, momentum and energy are deriving, from which, in turn, we get the corresponding differential equations. The formulation of the initial and boundary conditions is given; the necessary additional relations that close the corresponding system of differential equations are indicated. A numerical algorithm for solving such a system is proposed. The corresponding numerical examples are given.

This paper attempts to provide a transparent and, if possible, a formal hierarchy of the main types of mathematical models used in the description of dynamic processes inside, at first glance, different systems. It is emphasized that the mathematical modeling is a natural and universal environment for effective analysis of system processes of different nature. From our point of view, the term "system analysis" means the methodology for classification of real systems (physical, biological, economic, social, etc.), which is based on the classification of mathematical models that are used to describe these systems.

In the present paper is proposed a classification of the problems and the mathematical models for choosing optimal structural variant while designing a technical system. Algorithms and software models were developed based on known methods for determining the priority of criteria functions. The algorithms and models are implemented in a dialog system for structural optimization. Results are shown from using the software for solving a particular problem.

This paper attempts to provide a transparent and, if possible, a formal hierarchy of the main types of mathematical models used in the description of dynamic processes inside, at first glance, different systems. It is emphasized that the mathematical modeling is a natural and universal environment for effective analysis of system processes of different nature. From our point of view, the term "system analysis" means the methodology for classification of real systems (physical, biological, economic, social, etc.), which is based on the classification of mathematical models that are used to describe these systems.