Pages: 960
ISBN: 978-981-126-917-2 (hardcover)
ISBN: 978-981-127-015-4 (softcover)
Edited by internationally recognized authorities in the field, this expanded and updated new edition of the bestselling Handbook, containing many new articles, is aimed at the design and operation of modern particle accelerators. It is intended as a vade mecum for professional engineers and physicists engaged in these subjects. With a collection of more than 2000 equations, 300 illustrations and 500 graphs and tables, here one will find, in addition to common formulae of previous compilations, hard to find, specialized formulae, recipes and material data pooled from the lifetime experience of many of the world's most able practioners of the art and science of accelerators.
The seven chapters include both theoretical and practical matters as well as an extensive glossary of accelerator types. Chapters on beam dynamics and electromagnetic and nuclear interactions deal with linear and nonlinear single particle and collective effects including spin motion, beam-environment, beam-beam, beam-electron, beam-ion and intrabeam interactions. The impedance concept and related calculations are dealt with at length as are the instabilities due to the various interactions mentioned. A chapter on operational considerations including discussions on the assessment and correction of orbit and optics errors, realtime feedbacks, generation of short photon pulses, bunch compression, phase-space exchange, tuning of normal and superconducting linacs, energy recovery linacs, free electron lasers, cryogenic vacuum systems, steady state microbuching, cooling, space-charge compensation, brightness of light sources, collider luminosity optimization and collision schemes, machine learning, multiple frequency rf systems, FEL seeding, ultrafast electron diffraction, and Gamma Factory. Chapters on mechanical and electrical considerations present material data and important aspects of component design including heat transfer and refrigeration. Hardware systems for particle sources, feedback systems, confinement, including undulators, and acceleration (both normal and superconducting) receive detailed treatment in a sub-systems chapter, beam measurement and apparatus being treated therein as well.
Preface
Acknowledgments
Introduction
Beam Dynamics
Electromagnetic and Nuclear Interactions
Operational and Design Considerations
Mechanical Considerations
Electrical Considerations
Subsystems
Author Index
Subject Index
ISBN: 978-981-127-162-5 (hardcover)
This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of "Control of Partial Differential Equations". It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.
A Short Introduction to Carleman Estimates (Jeremi Darde and Sylvain Ervedoza)
Saturated Boundary Stabilization of Partial Differential Equations Using Control-Lyapunov Functions (Hugo Lhachemi and Christophe Prieur)
State Observation for Stochastic Partial Differential Equations (Qi Lu)
Uniqueness Theorems Under Kalman's Rank Condition and Asymptotic Synchronization for Second Order Dissipative Systems (Tatsien Li and Bopeng Rao)
Pages: 200
ISBN: 978-981-126-931-8 (hardcover)
The book gives a description of the principal models of quantum gravity which are based on a state sum for a piecewise linear (PL) spacetime manifold corresponding to a triangulation of a smooth spacetime manifold. There are detailed descriptions of Regge quantum gravity, spin-foam and spin-cube models, while the other models, like causal dynamical triangulations, are only briefly described, since the sum over triangulations is outside the scope of the book.
More details are given for the approach where the PL manifold is considered as a basic structure of spacetime, instead of being used as an auxiliary tool to define the gravitational path integral for a smooth manifold. One of the advantages of a PL spacetime is that it is straightforward to construct a finite gravitational path integral. Another advantage is that the problem of determination of the classical limit and calculation of the quantum corrections is solved by using the effective action method. Also, the smooth manifold limit becomes a smooth manifold approximation, since a smooth manifold can be approximated by a PL manifold which contains many simplicial cells.
Some physical effects of a QG theory on a PL spacetime are described, one of which is that the cosmological constant spectrum contains the observed value.
The book also contains a short exposition of higher gauge theory, which is an interesting way to generalize a gauge symmetry by using the concept of a 2-group, which is a categorical generalization of a group. This approach gives the spin-cube models.
Introduction
Classical Theories of Gravity on PL Manifolds
State-Sum Models of QG
Effective Actions for SS Models
Applications of PLQG
PLQG and Other QG Models
Appendices
Pages: 150
ISBN: 978-981-127-265-3 (hardcover)
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.
The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Preliminaries
Cofinally Complete Metric Spaces
Cofinal Completions
Cofinal Completeness vis-a-vis Hyperspaces
Stronger Cofinal Completeness
Pages: 160
ISBN: 978-981-126-853-3 (hardcover)
Calculi of temporal logic are widely used in modern computer science. The temporal organization of information flows in the different architectures of laptops, the Internet, or supercomputers would not be possible without appropriate temporal calculi. In the age of digitalization and High-Tech applications, people are often not aware that temporal logic is deeply rooted in the philosophy of modalities. A deep understanding of these roots opens avenues to the modern calculi of temporal logic which have emerged by extension of modal logic with temporal operators.
Computationally, temporal operators can be introduced in different formalisms with increasing complexity such as Basic Modal Logic (BML), Linear-Time Temporal Logic (LTL), Computation Tree Logic (CTL), and Full Computation Tree Logic (CTL*). Proof-theoretically, these formalisms of temporal logic can be interpreted by the sequent calculus of Gentzen, the tableau-based calculus, automata-based calculus, game-based calculus, and dialogue-based calculus with different advantages for different purposes, especially in computer science.
The book culminates in an outlook on trendsetting applications of temporal logics in future technologies such as artificial intelligence and quantum technology. However, it will not be sufficient, as in traditional temporal logic, to start from the everyday understanding of time. Since the 20th century, physics has fundamentally changed the modern understanding of time, which now also determines technology. In temporal logic, we are only just beginning to grasp these differences in proof theory which needs interdisciplinary cooperation of proof theory, computer science, physics, technology, and philosophy.
Philosophical Roots of Temporal Logic:
The Concept of Time
Towards Formal Systems of Temporal Logic
Computational Foundations of Temporal Logic:
Basic Modal Logic BML
Linear-Time Temporal Logic LTL
Computation Tree Logic CTL
Full Computation Tree Logic CTL*
Proof-Theoretical Foundations of Temporal Logic:
Gentzen-Calculus and Temporal Logic
Tableaux-based Calculus and Temporal Logic
Automata-based Calculus and Temporal Logic
Game-based Calculus and Temporal Logic
Gentzen-Calculus and Temporal Logic
Applications and Outlook of Temporal Logic:
Temporal Logic in Artificial Intelligence
Temporal Logic in Relativistic Physics
Temporal Logic in Quantum Computing
Societal Impact of Temporal Logic
Researchers and students of mathematical logic and foundations, theoretical computer science, and philosophy. The level is graduate with introductions on the undergraduate level. The book can be used for courses on temporal logic in mathematical logic as well as in computer science. It is also of general interest for the general reader in philosophy, social science (e.g., security issues), and history of science.