Труды выдающихся ученых МГУ

The monograph presents the principles of operation of robotic networks on the example of the Global Network of Robot Telescopes MASTER (Mobile Astronomical System of Robot Telescopes). The first chapter tells a brief history of the appearance of robotic optical telescopes in the world. The next four chapters are devoted to the principles of operation of individual robotic observatories and their interaction as part of a network united by a common goal and management. The next six chapters of the book are devoted to the most striking astrophysical discoveries made by the MASTER network in the study of extreme processes in the Universe.

In real time, it is possible to observe the formation or collision of relativistic stars and relativistic processes occurring near them. After the discovery of the polarization of its own optical radiation, the MASTER network became the world leader in early observations of gamma-ray bursts — the most powerful electromagnetic explosions in the universe. Its robots independently produced the first in the history of astronomy localization of the source of gravitational waves with optical accuracy. The MASTER network is a leader in the operational search for extragalactic sources of high-energy neutrinos. At the same time, its telescopes constantly carry out a regular survey of the sky and have discovered thousands of explosions in the universe and even potentially dangerous asteroids and comets. All the largest telescopes in the world have observed objects discovered by the MASTER system.

The book is devoted to the issues of modern multidimensional calculus of variations. The central place in it is occupied by the presentation of the original methods developed by the author for the explicit finding of multidimensional extremals of functionals and the study of their topological properties. The book is unique in that it presents a solution to the spectral multidimensional Plateau problem in a form accessible to a wide range of specialists.

For mathematicians specializing in topology, global calculus of variations, functional analysis, theory of differential equations, Lie groups and algebras. It can serve as the basis for special courses and special seminars.

For the first time, the book systematically outlines the mathematical foundations of the coming digital economy (2020-2050), which represents the sixth great Kondratiev cycle (BCC) in the development of the world economy. The first part of the book is devoted to the analysis of the Schumpeter-Kondratiev innovation—cyclical theory of long-term economic development, which is most suitable for forecasting non-equilibrium and unstable economic development. Mathematical models for describing and calculating the trend trajectory of economic development within a single BCC are presented. A nonlinear model of macroeconomic dynamics is also presented, taking into account the interaction of trend and cyclical fluctuations, which most adequately describes this theory.

In the second part of the book, mathematical models are given that have shown their effectiveness in practice and are intended for short- and medium—term forecasting of crisis phenomena in the economy - bifurcation points and disruption in recession. Long-term forecasting models are based on an information model for calculating and predicting technological progress depending on the speed of information production. It is also shown that in the digital age, the main driving force will be the symbiosis of "man + intelligent machine (IM)", in which a person plays a leading role. The third part of the book presents examples of modeling and forecasting of national, regional and global projects implemented in the digital era: the Chinese megaproject "one belt, one road" and the Russian project to expand and modernize the high-speed railway network of Siberia and the Far East and their impact on the economies of the Eurasian continent; innovative breakthrough strategies in the development of the Russian economy; the revolutionary role of the widespread use of IT in the digital age to change the upward trend of global demographic dynamics to a downward one. All of these models were developed by the authors and verified for the fifth information BCC (1982-2018).

The book is intended for students, postgraduates and researchers interested in mathematical modeling and forecasting the long-term development of nonequilibrium and unstable processes of world dynamics.

The book presents modern fast direct and iterative methods for solving systems of linear algebraic equations with a large number of unknowns and sparse ill-conditioned matrices. Such systems arise in the grid method for solving boundary and initial-boundary value problems for partial differential equations. The main part of the book is devoted to the construction, justification and algorithmic implementation of methods, as well as the construction of various types of preconditioners, the use of which allows to increase the efficiency of iterative methods. At the end of each chapter, information is provided that complements its content and allows the reader to navigate through a structured list of cited publications. The book contains three appendices, one of which is a summary of information from linear algebra used in various chapters. The book includes a large number of algorithms implementing these methods, and a detailed subject index.

The book will be useful to specialists who use existing effective grid methods to solve differential equations, and to researchers engaged in the development of new methods. It will be useful for university students and postgraduates specializing in numerical methods and applied mathematics.

Keywords: direct methods, iterative methods, convergence, preconditioning, grid equations, systems of linear equations, sparse matrices

The book of selected works by P. Ya. Galperin is the most complete collection of his publications and speeches covering a wide range of fundamental and applied problems of psychology. The publication introduces the teaching of P. Ya. Galperin about orientation activity as a function of the psyche, ideas about its development in philo-, anthropo- and ontogenesis, the theory of gradual formation of mental actions and concepts, the concept of different types of orientation activity.

Of particular interest is the planned-stage formation as a method of studying mental processes, creative thinking and the problem of the relationship between learning and development.

The monograph examines the scientific status of sociology, acutely debated by representatives of various sociological schools. The milestones of the development of sociological science in Russia and in the USSR are investigated. The author offers his understanding of the theory and structure of sociology, its role and place in the system of social sciences and humanities.

The history of our country has proved the destructiveness of myth-making as the basis of social reconstruction. The monograph presents significant tools of sociological science for overcoming social myth-making.

The conclusions of the book are closely related to the ideas of the work "Social myth-making and social practice", published by the publishing house "Norma" in 2000.

The monograph is intended for sociologists, philosophers, economists, political scientists and readers interested in the problems of studying modern life