Typical Singularities of Differential 1-forms and Pfaffian Equations
Typical Singularities of Differential 1-forms and Pfaffian Equations

Author: Mikhail Zhitomirskiĭ

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 194

ISBN-13: 9780821897423

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Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskii presents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.

Real and Complex Singularities
Real and Complex Singularities

Author: James William Bruce

Publisher: CRC Press

Published: 1999-08-26

Total Pages: 292

ISBN-13: 9781584881421

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The boundaries of singularity theory are broad and vague, connecting the most important applications of mathematics and science with more abstract areas. Optics, robotics, computer vision, Hamiltonian mechanics, bifurcation theory and differential equations are among the variety of topics that benefit from developments in the theory. With singularity theory encompassing more and more applications, Real and Complex Singularities provides insight into the future of this expanding field. Comprising refereed contributions to the Fifth Workshop on Real and Complex Singularities, this volume addresses three important areas related to the broad subject of singularities. The first section deals with questions within singularity theory itself, representing the topics currently being investigated. The second explores applications of singularity theory to differential geometry, robotics, and computer vision. The final section consists of applications to bifurcation theory and dynamical systems. With over two-hundred tables that provide quick access to data, this volume is a complete overview of the most current topics and applications of singularity theory. Real and Complex Singularities creates the opportunity for you to stay up-to-date with recent advances and discover promising directions for future research in the field.

IUTAM Symposium on Simulation and Identification of Organized Structures in Flows
IUTAM Symposium on Simulation and Identification of Organized Structures in Flows

Author: J.N. Sørensen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 512

ISBN-13: 9401146012

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This volume contains reviewed papers from the 1997 IUTAM Symposium, presenting the latest results from leading scientists within the field of detection and simulation of organized flow structures. It describes various aspects of complex, organized flow motion, including topics from decomposition techniques to topological concepts.

Systems: Theory and Practice
Systems: Theory and Practice

Author: Rudolf Albrecht

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 320

ISBN-13: 3709164516

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There is hardly a science that is without the notion of "system". We have systems in mathematics, formal systems in logic, systems in physics, electrical and mechanical engineering, architectural-, operating-, infonnation-, programming systems in computer science, management-and PJoduction systems in industrial applications, economical-, ecological-, biological systems, and many more. In many of these disciplines formal tools for system specification, construction, verification, have been developed as well as mathematical concepts for system modeling and system simulation. Thus it is quite natural to expect that systems theory as an interdisciplinary and well established science offering general concepts and methods for a wide variety of applications is a subject in its own right in academic education. However, as can be seen from the literature and from the curricula of university studies -at least in Central Europe-, it is subordinated and either seen as part of mathematics with the risk that mathematicians, who may not be familiar with applications, define it in their own way, or it is treated separately within each application field focusing on only those aspects which are thought to be needed in the particular application. This often results in uneconomical re-inventing and re-naming of concepts and methods within one field, while the same concepts and methods are already well introduced and practiced in other fields. The fundamentals on general systems theory were developed several decades ago. We note the pioneering work of M. A. Arbib, R. E. Kalman, G. 1. Klir, M. D.

Linear and Quasi-linear Equations of Parabolic Type
Linear and Quasi-linear Equations of Parabolic Type

Author: Olʹga A. Ladyženskaja

Publisher: American Mathematical Soc.

Published: 1988

Total Pages: 74

ISBN-13: 9780821815731

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Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

Ordinary Differential Equations with Constant Coefficient
Ordinary Differential Equations with Constant Coefficient

Author: Serge_ Konstantinovich Godunov

Publisher: American Mathematical Soc.

Published: 1997-08-19

Total Pages: 298

ISBN-13: 9780821897799

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This book presents the theory of ordinary differential equations with constant coefficients. The exposition is based on ideas developing the Gelfand-Shilov theorem on the polynomial representation of a matrix exponential. Boundary value problems for ordinary equations, Green matrices, Green functions, the Lopatinskii condition, and Lyapunov stability are considered. This volume can be used for practical study of ordinary differential equations using computers. In particular, algorithms and computational procedures, including the orthogonal sweep method, are described. The book also deals with stationary optimal control systems described by systems of ordinary differential equations with constant coefficients. The notions of controllability, observability, and stabilizability are analyzed, and some questions on the matrix Lure-Riccati equations are studied.

Equivalence, Invariants and Symmetry
Equivalence, Invariants and Symmetry

Author: Peter J. Olver

Publisher: Cambridge University Press

Published: 1995-06-30

Total Pages: 546

ISBN-13: 9780521478113

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Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Modular Forms and Hecke Operators
Modular Forms and Hecke Operators

Author: A. N. Andrianov

Publisher: American Mathematical Soc.

Published: 2016-01-29

Total Pages: 346

ISBN-13: 1470418681

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he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.