C Corduneanu

Functional Equations with Causal Operators

ISBN: 0-415-27186-X
Pub Date: 01 APR 2002
Type: Hardback Book
Extent: 256 pages (Dimensions 246X174 mm)

Functional Equations with Causal Operators presents the connection between the equations with causal operators and classical types of functional equations that mathematicians will encounter in the literature. It provides basic theorems of existence and uniqueness of the solution and properties of solutions or families of solutions. This volume describes in detail the fundamentals of linear equations, stability theory and several applications and examples.

The book is intended to provide basic theory of functional equations (including functional differential equations) with causal operators. These equations encompass most types of equations which are used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument and integro-differential equations of the Volterra type.

Contents:
1. Introduction 2. Auxilliary Concepts 3. Existence Theory for Functional Equations With Causal Operators 4. Linear Quasilinear Equations with Causal Operators 5. Stability Theory 6. Neutral Functional Equations 7. Miscellanea (Applications and Generalizations)

Series Information: Stability and Control: Theory, Methods and Applications, Volume 16

edited by John C Taylor (University of Cambridge)

GAUGE THEORIES IN THE TWENTIETH_CENTURY

By the end of the 1970s, it was clear that all the known forces of nature (including, in a sense, gravity) were examples of gauge theories, characterized by invariance under symmetry transformations chosen independently at each position and each time. These ideas culminated with the finding of the W and Z gauge bosons (and perhaps also the Higgs boson). This important book brings together the key papers in the history of gauge theories, including the discoveries of: the role of gauge transformations in the quantum theory of electrically charged particles in the 1920s; nonabelian gauge groups in the 1950s; vacuum symmetry-breaking in the 1960s; asymptotic freedom in the 1970s. A short introduction explains the significance of the papers, and the connections between them.

Contents:

Gauge Invariance in Electromagnetism
Non-Abelian Gauge Theories
Gravity as a Gauge Theory
Gauge Invariance and Superconductivity
Spontaneous Symmetry Breaking and Particle Physics
Gauge-Fixing in Non-Abelian Gauge Theories
Gauge Identities and Unitarity
Asymptotic Freedom
Monopoles and Vortex Lines
Non-Pertubative Approaches
Instantons and Vacuum Structure
Three-Dimensional Gauge Fields and Topological Actions
Gauge Theories and Mathematics

Readership: Graduate students, researchers and lecturers in mathematical, theoretical, quantum and high energy physics, as well ashistorians of science.

404pp Pub. date: Oct 2001
ISBN 1-86094-281-4
ISBN 1-86094-282-2(pbk)

M Frias (University of Buenos Aires, Argentina)

FORK ALGEBRAS IN ALGEBRA, LOGIC AND COMPUTER SCIENCE

Fork algebras are a formalism based on the relational calculus, with interesting algebraic and metalogical properties. Their representability is especially appealing in computer science, since it allows a closer relationship between their language and models. This book gives a careful account of the results and presents some applications of Fork algebras in computer science, particularly in system specification and program construction. Many applications of Fork algebras in formal methods are foreseen, and the book covers all the essentials in order to provide the reader with a better understanding.

Contents:

Introduction and Motivations
Algebras of Relations and Relation Algebras
Proper and Abstract Fork Algebras
Finite Axiomatizability and Independence
Algebraizing First-Order Logic
Algebraization of Non-Classical Logics
A Calculus for Program Construction

Readership: Graduate students and researchers using relational methods in computer science.

220pp (approx.) Pub. date: Scheduled Spring 2002
ISBN 981-02-4876-8

edited by Edward Kapuscik & Andrzej Horzela
(H Niewodniczanski Institute of Nuclear Physics, Poland)

QUANTUM THEORY AND SYMMETRIES
Proceedings of the 2nd International Symposium Krakow, Poland 18 - 21 July 2001

This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.

Contents:

Plenary Sessions:
The Interacting Fock Space of Haldane's Exclusion Statistics (L Accardi & M Nhani)
Complex Hamiltonians Having Real Spectra (C M Bender)
Quantum Field Theory as Dynamical System (H-J Borchers)
Generalized Symmetries and Time (M Heller)
Beta-lattices for Aperiodic Order (J-P Gazeau)
Gauss Law and Global Charge for QCD on the Lattice (J Kijowski & G Rudolph)
Quantum Entanglement and Symmetries (M Kus)
From Noncommutative Space-time to Quantum Relativistic Symmetries with Fundamental Mass Parameter (J Lukierski)
Quantum Theory on the Torus with Magnetic Field (H Narnhofer)
Nonlocal Reflection by Photonic Barriers (G Nimtz & A Haibel)
Tomographic Map in Framework of Star-Product Quantization (O V Man'ko et al.)
Algorithmic Cooling and Scalable Quantum Computers: Ways to Improve the Space-Time Requirements of the Algorithm (T Mor & Y Weinstein)
Lightfront Formalism versus Holography & Chiral Scanning (B Schroer)
Broken Symmetries (W Thirring)
Parallel Sessions:
Quantum Optics, Coherent States and Winger Functions
Quantum Groups and Noncommutative Geometry
Quantum Computing and Control
Gauge, Field and String Theories
Integrable Systems
Symmetries in Molecular Physics
Discrete Periodic and Aperiodic Systems
Associated Workshop:
Extensions of Quantum Theory, Lie Theory and its Applications in Physics

Readership: Researchers, lecturers and graduate students in theoretical, mathematical and quantum physics.

450pp (approx.) Pub. date: Scheduled Spring 2002
ISBN 981-02-4887-3

Helein, Frederic

Harmonic Maps, Conservation Laws and Moving Frames

This accessible introduction to harmonic map theory and its analytical aspects, covers recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.

SERIES NAME: Cambridge Tracts in Mathematics vol.150

SUBJECT: Mathematics - analysis, probability

March 2002
288 Pages

Hardback
0-521-81160-0