Guri Marchuk's Books

Adjoint Equations and Analysis of Complex Systems

By: Guri I. Marchuk

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Adjoint Equations and Analysis of Complex Systems

By: Guri I. Marchuk

New statements of problems arose recently demanding thorough ana lysis. Notice, first of all, the statements of problems using adjoint equations which gradually became part of our life. Adjoint equations are capable to bring fresh ideas to various problems of new technology based on linear and nonlinear processes. They became part of golden fund of science through quantum mechanics, theory of nuclear reactors, optimal control, and finally helped in solving many problems on the basis of perturbation method and sensitivity theory. To emphasize the important role of adjoint problems in science one should mention four-dimensional analysis problem and solution of inverse problems. This range of problems includes first of all problems of global climate changes on our planet, state of environment and protection of environ ment against pollution, preservation of the biosphere in conditions of vigorous growth of population, intensive development of industry, and many others. All this required complex study of large systems: interac tion between the atmosphere and oceans and continents in the theory of climate, cenoses in the biosphere affected by pollution of natural and anthropogenic origin. Problems of local and global perturbations and models sensitivity to input data join into common complex system.

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Page Count

475

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401706212

ISBN 13

9789401706216

Mathematical Modelling of Immune Response in Infectious Diseases

By: Guri I. Marchuk

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Mathematical Modelling of Immune Response in Infectious Diseases

By: Guri I. Marchuk

Beginning his work on the monograph to be published in English, this author tried to present more or less general notions of the possibilities of mathematics in the new and rapidly developing science of infectious immunology, describing the processes of an organism's defence against antigen invasions. The results presented in this monograph are based on the construc tion and application of closed models of immune response to infections which makes it possible to approach problems of optimizing the treat ment of chronic and hypertoxic forms of diseases. The author, being a mathematician, had creative long-Iasting con tacts with immunologists, geneticist, biologists, and clinicians. As far back as 1976 it resulted in the organization of a special seminar in the Computing Center of Siberian Branch of the USSR Academy of Sci ences on mathematical models in immunology. The seminar attracted the attention of a wide circle of leading specialists in various fields of science. All these made it possible to approach, from a more or less united stand point, the construction of models of immune response, the mathematical description of the models, and interpretation of results.

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Page Count

356

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401587981

ISBN 13

9789401587983

Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

By: Guri I. Marchuk,Valeri I. Agoshkov,Victor P. Shutyaev

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Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

By: Guri I. Marchuk,Valeri I. Agoshkov,Victor P. Shutyaev

Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses: Principles for constructing adjoint operators in nonlinear problems Properties of adjoint operators and solvability conditions for adjoint equations Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation Known results on adjoint equations and perturbation algorithms in nonlinear problems This groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.

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Page Count

288

Publisher

CRC Press

Published Date

ISBN 10

1351468804

ISBN 13

9781351468800

Disease Dynamics

By: Alexander Asachenkov,Guri Marchuk,Ronald Mohler,Serge Zuev

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Disease Dynamics

By: Alexander Asachenkov,Guri Marchuk,Ronald Mohler,Serge Zuev

This text discusses mathematical modelling, analysis and control of the immune system and disease dynamics. The purpose of the book is the practical application of mathematics to immunology and medicine in order to establish a basis for more effective treatment, to provide a tutorial systematic description of how the immune system controls diseases and to present several significant examples such as malignant tumour dynamics and control, and viral hepatitis.

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