2008, Approx. 300 p. 10 illus., Hardcover
ISBN: 978-3-540-74863-2
Due: March 2008
About this book
In this book the exceptional role of Leonhard Euler (1707 ? 1783) in the history of science will be analyzed and emphasized, especially demonstrated for his fundamental contributions to physics. Although Euler is famous as the leading mathematician of the 18th century his contributions to physics are as important and rich of new methods and solutions. There are many books devoted to Euler as mathematician, but not as physicist. This book will fill the gap.
Euler's contributions to mechanics are rooted in his program published in two volumes entitled Mechanics or the science of motion analytically demonstrated very early in 1736. The importance of Euler’s theory results from the simultaneous development and application of mathematical and physical methods. It is of particular interest to study how Euler made immediate use of his mathematics for mechanics and coordinated his progress in mathematics with his progress in physics. Euler’s work represents a rare example of a simultaneous and harmonic composition of results of different origin and nature which have been joined into a unique marvellous result. Euler’s mechanics is not only a model for a consistently formulated theory, but allows for generalizations of Euler's principles.
Though his pioneering work on mechanics had an essential influence in the 18th century, its impact on the 19th century was obscured by the overwhelming success of his mathematical writings. Euler anticipated Mach’s later criticism of absolute motion and Einstein’s assumption on the invariance of the equation of motion in inertial systems. It will be demonstrated that even problems in contemporary physics may be advantageously reconsidered and reformulated in terms of Euler’s early unified approach.
Table of contents
The Predecessors. Descartes, Newton and Leibniz.- Newton and Leibniz on time, space and forces.- Newton and Leibniz on the foundation of the calculus.- Euler's program for mechanics.- The foundation of the calculus.- Euler's early relativisitc theory.- Euler's Wirksamkeit and Helmholtz's treatment of the energy law and beyond.- Euler's mechanics and Schrodinger's quantum mechanics.
Series: Modern Birkhauser Classics
Originally published as a hardcover edition in the series: Systems & Control: Foundations & Applications
1st ed. 1992. 2nd, corr. printing 1995. Reprint, 2008, XII, 260 p., Softcover
ISBN: 978-0-8176-4732-2
A Birkhauser book
About this textbook
Covers a remarkable number of topics in a concise manner
Includes material on the realization of both linear and nonlinear systems, impulsive control, and positive linear systems: subjects not usually covered in an introductory-level book
Excellent book for introducing a mathematician to control theory
Ideal for a novel one-semester course covering both linear and nonlinear systems
Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus.
In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems.
The book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory.
Table of contents
Preface.- Introduction.- Part I. Elements of classical control theory.- Controllability and observability.- Stability and stabilizability.- Realization theory.- Systems with constraints.- Part II. Nonlinear control systems.- Controllability and observability of nonlinear systems.- Stability and stabilizability.- Realization theory.- Part III. Optimal control.- Dynamic programming.- Dynamic programming for impulse control.- The maximum principle.- The existence of optimal strategies.- Part IV. Infinite dimensional linear systems.- Linear control systems.- Controllability.- Stability and stabilizability.- Linear regulators in Hilbert spaces.- Appendix.- Metric spaces.- Banach spaces.- Hilbert spaces.- Bochner's integral.- Spaces of continuous functions.- Spaces of measurable functions.- References.- Notations.- Index
Series: Lecture Notes in Mathematics , Vol. 1928
2008, XIV, 378 p. 34 illus., Softcover
ISBN: 978-3-540-75858-7
About this book
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology.
Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Table of contents
Series: Publications of the Scuola Normale Superiore
Subseries: Lecture Notes (Scuola Normale Superiore) , Vol. 6
2008, Approx. 150 p., Softcover
ISBN: 978-88-7642-313-0
About this textbook
This volume collects lecture notes from courses delivered in the past years at the Scuola Normale Superiore in Pisa, and also at the Trento and Funchal Universities. It presents an introductory course on differential stochastic equations and Malliavin calculus. The lectures are addressed to readers familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Ito's formula. The second part deals with the differential stochastic equations and their connection with parabolic problems. The book gives several applications, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von-Neumann theorems.
Table of contents
1. Gaussian measures in Hilbert spaces.- 2. L2 and Sobolev spaces w.r.t. a Gaussian measure.- 3. Brownian Motion.- 4. Markov property of the Brownian motion.- 5. The Ito integral.- 6. The Ito formula.- 7. Stochastic differential equations.- 8. Transition evolution operators.- 9. Formulae of Feynman?Kac and Girsanov.- 10. One dimensional Malliavin calculus.- 11. Malliavin calculus in more dimensions.- 12. Asymptotic behaviour of the transition semigroup.
Series: The IMA Volumes in Mathematics and its Applications , Vol. 147
2008, Approx. 220 p., Hardcover
ISBN: 978-0-387-75145-0
Due: December 2007
About this book
This book is drawn from the recent literature on the asymptotic behavior of random permanents and random matchings. In particular, the authors present an elegant connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the so-called U-statistics -- objects of fundamental importance in the non-parametric statistical inference.
This book is self-contained and accessible to any mathematics, statistics or engineering graduate student who has taken basic introductory courses in probability theory and mathematical statistics.
Dr.Grzegorz A. Rempala is a Professor of Statistics in the Department of Mathematics at the University of Louisville in Louisville, KY. Dr. Jacek Wesolowski is a Professor of Mathematics and Associate Dean for Research at the Faculty of Mathematics and Information Science, Warsaw University of Technology in Warsaw, Poland.
The volume is a result of the authors’ collaborative effort initiated at the IMA during the Institute's 2003/04 annual program on "Probability and Statistics in Complex Systems: Genomics, Networks, and Finance Engineering".
Table of contents
Basic Concepts.- Properties of P-statistics.- Asymptotics for Random Permanents.- Weak Convergence of Permanent Processes.- Weak Convergence of P-statistics.- Permanent Designs and Related Topics.- Products of Partial Sums and Wishart Determinants.