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Lie Groups : An Approach through Invariants and Representations
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.
Lie Algebras and Applications
This book, designed for advanced graduate students and post-graduate researchers, provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, a concise exposition is given of the basic concepts of Lie algebras, their representations and their invariants. The second part contains a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Lewis Fry Richardson : His Intellectual Legacy and Influence in the Social Sciences
A pioneer in meteorology and peace research and remains a towering presence in both fields. This edited volume reviews his work and assesses its influence in the social sciences, notably his work on arms races and their consequences, mathematical models, the size distribution of wars, and geographical features of conflict
Level Crossing Methods in Stochastic Models
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems faster, more easily, and more intuitively.
Leonhard Euler
Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstei .This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.
Lectures on Quantum Gravity
A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.
Lectures in Supercomputational Neurosciences : Dynamics in Complex Brain Networks
The present volume is an introduction, largely from the physicists' perspective, to the subject matter with in-depth contributions by system neuroscientists. A conceptual model for complex networks of neurons is introduced that incorporates many important features of the real brain, such as various types of neurons, various brain areas, inhibitory and excitatory coupling and the plasticity of the network. The computational implementation on supercomputers, which is introduced and discussed in detail in this book, will enable the readers to modify and adapt the algortihm for their own research.
Lectures in Supercomputational Neurosciences : Dynamics in Complex Brain Networks
The present volume is an introduction, largely from the physicists' perspective, to the subject matter with in-depth contributions by system neuroscientists. A conceptual model for complex networks of neurons is introduced that incorporates many important features of the real brain, such as various types of neurons, various brain areas, inhibitory and excitatory coupling and the plasticity of the network. The computational implementation on supercomputers, which is introduced and discussed in detail in this book, will enable the readers to modify and adapt the algortihm for their own research.
Learning through Community : Exploring Participatory Practices
A collection of case studies that explore the learning that people do through community engagement. Developed within a network of Canadian researchers and their community partners, it explores learning that is organized by the learners themselves, collectively, rather than as individuals. Reflecting the contributors’ political priorities, the volume begins with groups that are highly marginalized in our society: immigrant women, sex trade workers, senior citizens, garment workers, women doing community economic development, and people who identify with disability and anti-poverty movements.
Learning from clusters : A critical assessment from an economic-geographical perspective
Edited volumes run the danger of being a hotchpotch of contributions on a wide variety of topics. Here, we have explicitly focused on a central theme in contemporary economic geography and regional science, namely the relationship between learning, innovation and clustering. Internationally renowned scientists made both theoretical and empirical contributions to this volume. We think this book constitutes a broad palette of contemporary thinking and research on the relationship between spatial concentration and innovation and hope it will play a significant role in future debates on this issue.
Learning About Particles - 50 Privileged Years
Embedded in an autobiographic framework, this book retraces vividly and in some depth the golden years of particle physics as witnessed by one of the scientists who made seminal contributions to the understanding of what is now known as the Standard Model of particle physics. Well beyond a survey of interest to historians of sciences and researchers in the field, this book is a must for all students and young researchers who have learned about the theoretical and experimental facts that make up the standard model through modern textbooks only. It will provide the interested reader with a first hand account and deeper understanding of the multilayered and sinuous development that finally led to the present architecture of this theory.
Learners in a Changing Learning Landscape: Reflections from a Dialogue on New Roles and Expectations
Today's learners face constant change. Adaptive learner expertise is key to their survival on a learning journey that lasts a lifetime. This requires new thinking of all actors in the learning environment. The fundamental process through which this book was created is an extended in-depth dialogue among researchers, lifelong learners, educators, and thinkers.
Leakage in Nanometer CMOS Technologies
It is essential for circuit and system designers to understand the components of leakage, sensitivity of leakage to different design parameters, and leakage mitigation techniques in nanometer technologies. This book provides an in-depth treatment of these issues for researchers and product designers.
Lead-Free Electronic Solders : A Special Issue of the Journal of Materials Science : Materials in Electronics
In the last few decades the effect of lead contamination on human health has received significant attention. Based on such concerns, elimination of lead from ceramic glaze, paint, plumbing etc. has been legislated and implemented. However, until recently, solders used in electronics, based on suitability and knowledge-base developed over a long period of time, remained lead-based. Successive rapid advances in microelectronic devices in recent decades make them obsolete within a very short period after their introduction resulting in significant quantities of electronic wastes in landfills. Leaching of toxic lead from such electronic wastes can result in contamination of the human food chain causing serious health hazards. As a consequence, several European and Pacific Rim countries have passed legislations warranting elimination of lead from electronic solders by fast approaching deadlines. Global economic pressures brought on by such legislations have resulted in a flurry of research activities to find suitable lead-free substitutes for the traditional leaded electronic solders.
Laws of Nature
The book is concerned with the laws of nature and in particular with the laws of physics. The authors discuss three important questions: First, whether the observed regularities are based on strict "laws of nature" that hold rigorously and without any exception. Second, what we call a "law of nature" is studied by comparing this concept with invariance principles, causality principles, teleological principles and means of predicting future events. Finally, on the basis of these investigations the authors treat the ambitious and intricate third question, why the laws of nature hold. Are there rational reasons for this largely unexplained phenomenon? This book addresses students as well as researchers. It will be an excellent reference for those interested in the philosophical foundations of the natural sciences.
Lattice Hadron Physics
This series of lectures draws upon the developments made in recent years in implementing chirality on the lattice via the overlap formalism. These developments exploit chiral effective field theory in order to extrapolate lattice results to physical quark masses, new forms of improving operators to remove lattice artefacts, analytical studies of finite volume effects in hadronic observables, and state-of-the-art lattice calculations of excited resonances. This volume is designed to assist those outside the field who want quickly to becoming literate in these topics. So it is intended for graduate students and experienced researchers in other areas of hadronic physics to provide the background through which they can appreciate, if not become active in, contemporary lattice gauge theory and its applications to hadronic phenomena.
Lattice : Multivariate Data Visualization with R
R is rapidly growing in popularity as the environment of choice for data analysis and graphics both in academia and industry. Lattice brings the proven design of Trellis graphics (originally developed for S by William S. Cleveland and colleagues at Bell Labs) to R, considerably expanding its capabilities in the process. Lattice is a powerful and elegant high level data visualization system that is sufficient for most everyday graphics needs, yet flexible enough to be easily extended to handle demands of cutting edge research. Written by the author of the lattice system, this book describes it in considerable depth, beginning with the essentials and systematically delving into specific low levels details as necessary. No prior experience with lattice is required to read the book, although basic familiarity with R is assumed.
Laser Resonators and Beam Propagation : Fundamentals, Advanced Concepts, Applications
Optical Resonators provides a detailed discussion of the properties of optical resonators for lasers from basic theory to recent research. In addition to describing the fundamental theories of resonators such as geometrical optics, diffraction, and polarisation the characteristics of all important resonator schemes and their calculation are presented. Experimental examples, practical problems and a collection of measurement techniques support the comprehensive treatment of the subject. Optical Resonators is the only book currently available that provides a comprehensive overview of the the subject. Combined with the structure of the text and the autonomous nature of the chapters this work will be as suitable for those new to the field as it will be invaluable to specialists conducting research. This second edition has been enlarged by new sections on Q-switching and resonators with internal phase/amplitude control. In addition, the whole book has been brought up-to-date.
Large-Scale Nonlinear Optimization
Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research.The chapters of the book including theoretical analysis, algorithmic development, implementation issues and applications.
