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Mathematical Remodeling is aimed at transforming mathematical or simulation models of one or different classes (or subsystems forming a studied system) into a model of one predefined unified class. Depending on the goals and specific applications, different interpretations of remodeling are possible. Theoretical model constructed based on its physical meaning, can be quite complicated and is not suitable for further analysis. In this case, an array of input and output training data (which could not be obtained in real conditions) can be generated using the software implementation of the model. Using these obtained values and according to Remodeling concept it is necessary to determine a new model of a given structure with the required accuracy, which can approximate the original model in the best way. The paper presents examples of applying Mathematical Remodeling concept to constructing a dynamic system with a variable structure. Such systems are used to simulate an inertial torque transformer, which is a part of a stepless car transmission. Another example of this approach is the method of estimating freeway section capacity. Feedforward neural networks are used as remodeling classes in both cases. The introduced applications of Mathematical Remodeling approach are in the basis of constructing intelligent transportation systems.

The paper presents an approach to learning based on the implementation of projects under the joint supervision and control of the educational organization and industrial partner. When students carry out projects, collaborative learning technologies are implemented. Periodic joint consultations of students by specialists of different profiles of educational organization and industrial partner help to bring the training closer to the real production process, and upon the completion of the project to get a ready-to-use product. Working in this mode allows students using modern technologies to work on the project, in particular, flexible methodologies of agile development. It helps not to formulate a completely ready technical task for the project, but to adjust it in the process of implementation. Tasks are formulated for a limited time interval of 1–2 weeks, after which the results are evaluated and tasks for the next stage are formed. The paper provides examples of works by students of Lipetsk State Technical University, performed in this format.

Studying technological processes on real production equipment is associated with a large costs of resources: financial, time, etc. Therefore, various types of modeling are actively used to analyze and optimize these processes. With the development of digital technologies, it is possible to collect data about the process directly during the production. This data can be used both for direct control of the process, and for building (adjusting) the model of the process, which allows to get a "digital twin" repeating both the main properties of the modeled object and its current state. Many complex manufacturing processes involve a set of different interconnected models. In this case, the "digital twin" should contain information about the object characteristics, individual models of its functioning, the connections between these models, and the current state. These processes include many stages of metallurgical production. The paper considers complex modeling of the casting process in continuous steel casting unit. The set of models includes a model of the thermal state of the ingot during casting, a model of the stress-strain state, a model of the melt hydrodynamics, structural and concentration models of the ingot. Mathematical models of thermal and stress-strain states and the connections between them are presented. Examples of temperature fields and deformations calculation during the process of casting are given.

Remodeling involves the transition from existing models of the given system to the models of some other class that reveals possibilities for overcoming research difficulties. Takagi- Sugeno (T-S) fuzzy models provide an established approach to description, analysis and synthesis of nonlinear systems. However the potential of transition to fuzzy description on the basis of T- S models is not fully understood and implemented in analysis and synthesis of nonlinear systems. The paper uncovers the peculiarities of the approach to nonlinear system remodeling based on T-S fuzzy models. It demonstrates the scheme of fuzzy remodeling that allows replacing the initial model of the nonlinear system by the T-S fuzzy model equivalent to it in a bounded area of the phase space. The examples illustrating the range of approach applications are given. It is shown that the transition from a nonlinear model to a T-S fuzzy one enables us to solve various analysis and control tasks via the implementation of the apparatus of linear matrix inequalities. The sources of conservatism of fuzzy remodeling, that lie in peculiarities of T-S fuzzy models are emphasized.

In recent years, an increasing number of studies has been undertaken to estimate inequality and to find out its determinants. Most of the works have been executed on income inequality data because wealth is notably harder to estimate. In this study the impact of economic growth and financial development on wealth concentration is examined. There were collected yearly data on Russian economic system covering the period 1995-2014. A set of stochastic difference equations (structural vector autoregression, SVAR) was implemented to represent the dynamics of economic and financial system and their impact on wealth concentration were studied. Our findings suggest that in the short and long run, even if at the very beginning the development of financial system increases the inequality, both dynamics decrease the inequality, while in the middle the two tend to exacerbate the concentration of wealth.

The development of the interval analysis theory and its applications in solving applied problems led to the need to collect, store and extract efficiently interval-significant data in relational databases. Modern relational database management systems (DBMS) either allow to work with built-in data types which however are not friendly for use or provide the ability to create your own user-defined data types in several ways. The article describes the creation of a user-defined data type iInterval, functions and aggregates to work with interval data in MS SQL Server using the Common Language Runtime (CLR).

Class of difference neuro-fuzzy switched models which can describe complex multistage processes is discussed in the article. Two-dimensional fuzzy sets which allow to reduce model parameter’s amount are considered. Numerical algorithm for identifying parameters of two-dimensional fuzzy sets with non-linear centres is proposed.

The paper studies the dynamics of the temperature change of steel ingot during cooling in a continuous casting unit. A mathematical model of ingot cooling is given, including the equation of heat conduction and boundary conditions. The two-dimensional section of the ingot is considered. The developed software simulating the casting process by constructing a thermal field at different times is presented. This program makes it possible to obtain data on the temperature of the slab cut at the output of the continuous casting unit based on the input information about the steel, initial temperatures and break intervals. All information obtained is presented numerically and graphically. The finite element method is used to solve the equations of the mathematical model. Factors affecting the occurrence of slab defects are also analyzed. As such a factor is used the values of the surface temperatures of the ingot in a curved region in the area of the bend and straightening. If the temperature is located in the zone of embrittlement temperatures for a given steel grade, the probability of occurrence of a defect is significant. The adequacy study was carried out by comparing the measured values of temperatures at several points in the casting process with the values obtained by the simulation. The influence of different methods of heat transfer coefficient on the accuracy of the solution is investigated.