Part of Cambridge Tracts in Mathematics
Originally published in 1932 as number twenty=seven in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account of the theory of modular invariants as embodied in the work of Dickson, Glenn and Hazlett. Appendices are included. This book will be of value to anyone with an interest in modular invariants and the history of mathematics.
Product details
Publication planned for: March 2015
format: Paperback
isbn: 9781107493766
length: 94 pages
dimensions: 216 x 140 x 6 mm
weight: 0.13kg
Preface
Part I:
1. A new notation
2. Galois fields and Fermat's theorem
3. Transformations in the Galois fields
4. Types of concomitants
5. Systems and finiteness
6. Symbolical notation
7. Generators of linear transformations
8. Weight and isobarbism
9. Congruent concomitants
10. Relation between congruent and algebraic covariants
11. Formal covariants
13. Dickson's theorem
14. Formal invariants of linear form
15. The use of symbolical operators
16. Annihilators of formal invariants
17. Dickson's method for formal covariants
18. Symbolical representation of pseudo-isobaric formal covariants
19. Classes
20. Characteristic invariants
21. Syzygies
22. Residual covariants
23. Miss Sanderson's theorem
24. A method of finding characteristic invariants
25. Smallest full systems
26. Residual invariants of linear forms
27. Residual invariants of quadratic forms
28. Cubic and higher forms
29. Relative unimportance of residual covariants
30. Non-formal residual covariants
Part II:
31. Rings and fields
32. Expansions
33. Isomorphism
34. Finite expansions
35. Transcendental and algebraic expansions
36. Rational basis theorem of E. Noether
37. The fields Ky+/-f
38. Expansions of the first and second sorts
39. The theorem on divisor chains
40. R-modules
41. A theorem of Artin and of van der Waerden
42. The finiteness criterion of E. Noether
43. Application of E. Noether's theorem to modular covariants
Appendix I
Appendix II
Appendix III
Index.
Publication planned for: June 2015
format: Hardback
isbn: 9781107035409
This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.
1. Introduction
Part I. Theory:
2. Stability, limit sets and stability regions
3. Energy function theory
4. Stability regions of continuous dynamical systems
5. Stability regions of attracting sets of complex nonlinear dynamical systems
6. Quasi-stability regions of continuous dynamical systems ? theory
7. Stability regions of constrained dynamical systems
8. Relevant stability boundary of continuous dynamical systems
9. Stability regions of discrete dynamical systems
Part II. Estimation:
10. Estimating stability regions of continuous dynamical systems
11. Estimating stability regions of complex continuous dynamical systems
12. Estimating stability regions of discrete dynamical systems
13. A constructive methodology to estimate stability regions of nonlinear dynamical systems
14. Estimation of relevant stability regions
15. Critical evaluation of numerical methods for approximating stability boundaries
Part III. Advanced Topics:
16. Stability regions of two-time scale continuous dynamical systems
17. Stability regions for a class of non-hyperbolic dynamical systems ? theory and estimation
18. Optimal estimation of stability regions for a class of large-scale nonlinear dynamic systems
19. Bifurcations of stability regions
Part IV. Applications:
20. Application of stability regions to direct stability analysis of large-scale electric power systems
21. Stability-region-based methods for multiple optimal solutions of nonlinear programming
22. Perspectives and future directions.
EMS Textbooks in Mathematics
ISBN 978-3-03719-151-4
February 2015, 197 pages, hardcover, 16.5 x 23.5 cm.
Spectral theory is a diverse area of mathematics that derives its motivations, goals and impetus from several sources. In particular, the spectral theory of the Laplacian on a compact Riemannian manifold is a central object in differential geometry. From a physical point a view, the Laplacian on a compact Riemannian manifold is a fundamental linear operator which describes numerous propagation phenomena: heat propagation, wave propagation, quantum dynamics, etc. Moreover, the spectrum of the Laplacian contains vast information about the geometry of the manifold.
This book gives a self-containded introduction to spectral geometry on compact Riemannian manifolds. Starting with an overview of spectral theory on Hilbert spaces, the book proceeds to a description of the basic notions in Riemannian geometry. Then its makes its way to topics of main interests in spectral geometry. The topics presented include direct and inverse problems. Direct problems are concerned with computing or finding properties on the eigenvalues while the main issue in inverse problems is gknowing the spectrum of the Laplacian, can we determine the geometry of the manifold?h
Addressed to students or young researchers, the present book is a first introduction in spectral theory applied to geometry. For readers interested in pursuing the subject further, this book will provide a basis for understanding principles, concepts and developments of spectral geometry.
Surveys in Differential Geometry,Volume 19 (2014)
To Be Published: 10 April 2015
2015 Hardcover (ISBN 9781571463036)
310 pages
This volume of Surveys in Differential Geometry is dedicated to the three most eminent contributors to the subject of regularity and existence of nonlinear partial differential equations, which has played such an important role in geometry. These are Richard Hamilton, Leon Simon, and Karen Uhlenbeck.
Presented topics include: analysis related to minimal submanifolds, Yang-Mills theory, Kahler metrics, Monge-Ampere equations, curve flows, and general relativity.
This volume is part of the Surveys in Differential Geometry book series.
March 2015, c2016
Wiley introduces a new offering in dynamic systems?Dynamic Systems: Modeling,
Simulation, and Control by Craig Kluever. This text highlights essential
topics such as analysis, design, and control of physical engineering systems,
often composed of interacting mechanical, electrical and fluid subsystem
components.
Dynamic Systems: Modeling, Simulation, and Control is intended for an introductory course in dynamic systems and control, and written for mechanical engineering and other engineering curricula. Major topics covered in this text include mathematical modeling, system-response analysis, and an introduction to feedback control systems.
Dynamic Systems integrates an early introduction to numerical simulation using MATLABRfs Simulink for integrated systems. SimulinkR and MATLABR tutorials for both software programs will also be provided. The authorfs text also has a strong emphasis on real-world case studies. Derived from top-tier engineering from the AMSE Journal of Dynamic Systems, Measurement, and Control, case studies are leveraged to demonstrate fundamental concepts as well as the analysis of complex engineering systems. In addition, Dynamic Systems delivers a wide variety of end of chapter problems, including conceptual problems, MATLABR problems, and Engineering Application problems.
Preface vii
1 INTRODUCTION TO DYNAMIC SYSTEMS AND CONTROL 1
1.1 Introduction 1
1.2 Classification of Dynamic Systems pp
1.3 Modeling Dynamic Systems pp
and more
*
ISBN: 978-3-527-41330-0
264 pages
April 2015
A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems.
Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications.
With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.
Preface XI
1 Introduction to the Theory of Oscillations 1
1.1 General Features of the Theory of Oscillations 1
1.2 Dynamical Systems 2
1.2.1 Types of Trajectories 3
1.2.2 Dynamical Systems with Continuous Time 3
1.2.3 Dynamical Systems with Discrete Time 4
1.2.4 Dissipative Dynamical Systems 5
and more