M.A. Akivis's Books

Projective Differential Geometry of Submanifolds

By: M.A. Akivis,V.V. Goldberg

Write a review Read reviews Take a Quiz Solve Book Puzzle

Projective Differential Geometry of Submanifolds

By: M.A. Akivis,V.V. Goldberg

In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations.Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

375

Publisher

Elsevier

Published Date

ISBN 10

0080887163

ISBN 13

9780080887166

Elie Cartan (1869-1951)

By: M. A. Akivis,B. A. Rosenfeld

Write a review Read reviews Take a Quiz Solve Book Puzzle

Elie Cartan (1869-1951)

By: M. A. Akivis,B. A. Rosenfeld

This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

334

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853554

ISBN 13

9780821853559

An Introduction to Linear Algebra and Tensors

By: M. A. Akivis,V. V. Goldberg

Write a review Read reviews Take a Quiz Solve Book Puzzle

An Introduction to Linear Algebra and Tensors

By: M. A. Akivis,V. V. Goldberg

Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

196

Publisher

Courier Corporation

Published Date

ISBN 10

0486148785

ISBN 13

9780486148786

Theory of Games and Statistical Decisions

By: David A. Blackwell,M. A. Girshick

Write a review Read reviews Take a Quiz Solve Book Puzzle

Theory of Games and Statistical Decisions

By: David A. Blackwell,M. A. Girshick

Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

388

Publisher

Courier Corporation

Published Date

ISBN 10

0486150895

ISBN 13

9780486150895

Seismic Waves and Rays in Elastic Media

By: M.A. Slawinski

Write a review Read reviews Take a Quiz Solve Book Puzzle

Seismic Waves and Rays in Elastic Media

By: M.A. Slawinski

This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves.The book is divided into three parts: Elastic continua, Waves and rays, and Variational formulation of rays. In Part I, continuum mechanics are used to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such material. In Part II, these equations are used to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, the high-frequency approximation is used and establishes the concept of a ray. In Part III, it is shown that in elastic continua a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary travel time.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

425

Publisher

Elsevier

Published Date

ISBN 10

0080540899

ISBN 13

9780080540894

Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

Write a review Read reviews Take a Quiz Solve Book Puzzle

Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes. Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.

Average ratings

N/A