### Book

## Математическое моделирование социальных процессов

Free bulging process is an experimental technique which can be used to characterize a sheet material in conditions of biaxial tension during hot forming. Analytical and semi-analytical models of this process are usually based on the hypothesis offering certain relations between the geometrical characteristics of a bulge during forming. The paper presents an original relation between a specimen thickness at the dome pole and the dome height which is used at the semi-analytical method for simulation of free bulging process. In order to obtain this relation, the finite-element computer simulation results were generalized. The influence of the material constants on the geometrical parameters of the bulge was studied. It was shown that the sheet thickness corresponding to a specific dome height is dictated by the strain rate sensitivity index of the material. The equation describing the influence of the strain rate sensitivity index on the dome apex thickness is presented.

Currently, the tasks of ensuring the quality and stability of the provided IT services are extremely topical. In the operation of the composite applications, the problem of increasing the effectiveness of incident management is a complex technical problem, the solution of which requires the use of the simulation methods. In the work, the integration platform Ensemble of InterSystems Company was considered as a basis for designing integration solutions. Given the architectural features of the integration platforms, a mathematical model of the incident management process in the Ensemble integration platform is proposed. This mathematical model was used to develop algorithms for identifying and classifying incidents. The results of the work can be used in the design and development of incident management information systems, as well as in organizing the work of technical support services for IT companies

We consider the problem of manipulability of social choice rules in the impartial anonymous and neutral culture model (IANC) and provide a new theoretical study of the IANC model, which allows us to analytically derive the difference between the Nitzan-Kelly index in the Impartial Culture (IC) and IANC models. We show in which cases this difference is almost zero, and in which the Nitzan-Kelly index for IANC is the same as for IC. However, in some cases this difference is large enough to cause changes in the relative manipulability of social choice rules. We provide an example of such cases.

Nowadays the random search became a widespread and effective tool for solving different complex optimization and adaptation problems. In this work, the problem of an average duration of a random search for one object by another is regarded, depending on various factors on a square field. The problem solution was carried out by holding total experiment with 4 factors and orthogonal plan with 54 lines. Within each line, the initial conditions and the cellular automaton transition rules were simulated and the duration of the search for one object by another was measured. As a result, the regression model of average duration of a random search for an object depending on the four factors considered, specifying the initial positions of two objects, the conditions of their movement and detection is constructed. The most significant factors among the factors considered in the work that determine the average search time are determined. An interpretation is carried out in the problem of random search for an object from the constructed model.The important result of the work is that the qualitative and quantitative influence of initial positions of objects, the size of the lattice and the transition rules on the average duration of search is revealed by means of model obtained. It is shown that the initial neighborhood of objects on the lattice does not guarantee a quick search, if each of them moves. In addition, it is quantitatively estimated how many times the average time of searching for an object can increase or decrease with increasing the speed of the searching object by 1 unit, and also with increasing the field size by 1 unit, with different initial positions of the two objects. The exponential nature of the growth in the number of steps for searching for an object with an increase in the lattice size for other fixed factors is revealed. The conditions for the greatest increase in the average search duration are found: the maximum distance of objects in combination with the immobility of one of them when the field size is changed by 1 unit. (that is, for example, with 4x4 at 5x5) can increase the average search duration in e^1,69≈5,42. The task presented in the work may be relevant from the point of view of application both in the landmark for ensuring the security of the state, and, for example, in the theory of mass service.

The article includes the observation of the cluster analysis of medical data on the example of the cardiac data. One of the main effective and commonly used Data Mining methods that applied to the large amounts of information (for example, mathematical economics) are clustering methods: the search for signs of similarity between objects in the study of the subject area and the subsequent merger of objects into subsets (clusters) according to the established affinity. The main purpose of the investigation is to examine the hypothesis of the possibility of diagnosing the patient health status, as well as identifying his pathologies, using the analysis of electrocardiogram (ECG) series and the allocation of similar clusters based on the results of this analysis. However, the subject of clustering techniques implementation to the ECG on the grounds of similarity of forms have not previously been extensively investigated. In the model of the heart, which is used in this study, the state of the heart is taken as a fixed oscillatory process of the phenomenon of the FPU auto-return. But, on the other hand, since the heart is an self-oscillating system and it has no need to start the oscillations by obtaining the energy of “perturbation”, the concept of FPU autoreturn is introduced in the study of the heart. The mathematical modeling of the heart work by using a decomposition of the Fermi-Pasta-Ulam (FPU) was investigated. The formal description of the mathematical model of the heart as a system of connected cells myocytes is presented. This represents a single oscillatory degree of freedom described by a system of coupled nonlinear differential equations of the second order equation of Van der Pol. Cluster analysis bases on the search of similar clusters of Fourier spectrum which are received by FPU recurrence. The current results that are obtained show that the hypothesis is confirmed. In mathematical modeling of the FPU heart modeling, which is based on the forms of Fourier spectra, were identified. Subsets were identified, among which various subsets of both forms of Fourier spectra with pathologies and forms of the Fourier spectrum of healthy people were formed. From this study it follows that the cluster analysis of the electrocardiogram may refer this ECG to any cluster and thereby diagnose the state of cardiac health of the patient.

Describes the history of establishment of the scientific field of "artificial intelligence", describes the main directions of its development and scope of mapping the three main strategic approaches to creation of intellectual systems: the technology of expert systems, neural network technology and technologies of evolutionary modelling. Theoretical bases and examples of the development of intelligent systems and examples of their application to the data mining, in Economics, in business, in psychology, in sociology and other fields. The book builds and expands the worldview of the graduates, improving his ranking in life. At the same time, the book is a comprehensive guide to mastering technologies for creating neural network intelligent systems and their applications for solving a wide range of problems encountered in many fields of human activity. For students of higher educational institutions.

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives.

The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting.

The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the development fields discussed, to demonstrate their mathematical complexity and, more importantly, to encourage mathematicians to contribute to the further success of such practical applications as weather forecasting and climate change projections. Written by leading experts in the field, the book provides an attractive and diverse introduction to areas in which mathematicians and modellers from the meteorological community can cooperate and help each other solve the problems that operational weather centres face, now and in the near future.

Readers engaged in meteorological research will become more familiar with the corresponding mathematical background, while mathematicians working in numerical analysis, partial differential equations, or stochastic analysis will be introduced to further application fields of their research area, and will find stimulation and motivation for their future research work.

This article is talking about state management and cultural policy, their nature and content in term of the new tendency - development of postindustrial society. It mentioned here, that at the moment cultural policy is the base of regional political activity and that regions can get strong competitive advantage if they are able to implement cultural policy successfully. All these trends can produce elements of new economic development.