Optimal Control and Geometry: Integrable Systems

Author: Velimir Jurdjevic

Publisher: Cambridge University Press

ISBN: 1107113881

Category: Mathematics

Page: 400

View: 2664

DOWNLOAD NOW »

The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems. These Hamiltonians provide an original and unified account of the existing theory of integrable systems. The book particularly explains much of the mystery surrounding the Kepler problem, the Jacobi problem and the Kovalevskaya Top. It also reveals the ubiquitous presence of elastic curves in integrable systems up to the soliton solutions of the non-linear Schroedinger's equation. Containing a useful blend of theory and applications, this is an indispensable guide for graduates and researchers in many fields, from mathematical physics to space control.
Release

Geometry and Complexity Theory

Author: J. M. Landsberg

Publisher: Cambridge University Press

ISBN: 1107199239

Category: Computers

Page: 339

View: 3251

DOWNLOAD NOW »

This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.
Release

Formal Geometry and Bordism Operations

Author: Eric Peterson

Publisher: Cambridge University Press

ISBN: 1108428037

Category: Mathematics

Page: 418

View: 9656

DOWNLOAD NOW »

Delivers a broad, conceptual introduction to chromatic homotopy theory, focusing on contact with arithmetic and algebraic geometry.
Release

Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 2534

DOWNLOAD NOW »

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.
Release