Труды выдающихся ученых МГУ

The monograph contains an accessible presentation of the theory of three-dimensional manifolds, which plays a huge role in modern mathematics and mathematical physics. The main emphasis is on algorithmic problems of three-dimensional computer geometry. The publication clearly describes the spectacular and unexpected applications of computers in topology and geometry. The book teaches the competent use of computers to form (and sometimes prove) geometric hypotheses and test them. The application of computer geometry methods to problems of Hamiltonian geometry and physics is shown.

For specialists in computer geometry, for mathematicians, geometricians and topologists. The book can also be used as a textbook for undergraduate and graduate students involved in the creation of modern geometric type algorithms.

The book contains the text of a monograph first published in 1991, the author made stylistic and other changes, and also presents two additional chapters prepared in 2023. In the monograph, argumentation is interpreted as human activity in the interrelation of its various aspects: logical-epistemological, pragmatic, ethical, emotional. In the additional chapters, the correlation of argumentative and manipulative influences is considered.

Keywords: argumentation, theory of argumentation, rhetoric, discussion, protection from manipulation, argumentation, philosophical text

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.

The book outlines the most important questions of the grammar of the Russian language, which are included in the program of the basic and advanced stages of teaching foreign students. Russian Russian as a foreign language departments of Lomonosov Moscow State University, summarizing the long-term practical experience, describes the grammatical structure of the Russian language in a functional and communicative aspect.

The book covers little-known phenomena of Leonardo da Vinci's work - his work in the field of scenography, musical practice, and research into the psychological foundations of visual activity. The leading theme of the book is a historical-semiotic study of the principles of creating iconic ensembles introduced into art by the Italian artistic tradition and, to a decisive extent, by the great master Leonardo da Vinci. The research is based on the methodology of comprehensive historical analysis of textual and iconographic material, fragments and drawings from Leonardo’s notebooks (codes). Illustrations are based on open sources and photographs of the author. Drawings from Leonardo's codices are based on digitized manuscripts available in the public domain.

The publication is addressed to students, graduate students and art experts, as well as to a wide range of readers interested in theory and history of art, artistic culture of Renaissance Italy.

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 Septuagint, being the fi rst written biblical translation, was also the early testimony of understanding of the sacred text. It was not inferior by age to the scrolls of Qumran and earlier than the New Testament books, as well as than the written form of aramaic targums. The whole literature of Judaeo-Hellenism is associated with it. For the early Greek Christian communities it was the fi rst form of Scriptura Sacra. Opposition of angels and demons, idea of creation of the Universe «ex nihilo» were perceived by the European thought through the Septuagint. The study of this textual witness now seems to be more and more important and, from other side, more and more complicated, due to the scale and the depth of sources, and also due to the crisis of understanding.

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