This book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand–Naimark type theorems, a Vidav–Palmer type theorem, an unbounded representation theory, and miscellaneous applications. Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.
These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.
This book is devoted to the study of Tomita's observable algebras, their structure and applications. It begins by building the foundations of the theory of T*-algebras and CT*-algebras, presenting the major results and investigating the relationship between the operator and vector representations of a CT*-algebra. It is then shown via the representation theory of locally convex*-algebras that this theory includes Tomita–Takesaki theory as a special case; every observable algebra can be regarded as an operator algebra on a Pontryagin space with codimension 1. All of the results are proved in detail and the basic theory of operator algebras on Hilbert space is summarized in an appendix. The theory of CT*-algebras has connections with many other branches of functional analysis and with quantum mechanics. The aim of this book is to make Tomita’s theory available to a wider audience, with the hope that it will be used by operator algebraists and researchers in these related fields.
Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmüdgen [1990] and A. Inoue [1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).
This volume collects papers presented at the international workshop "Hadron-Nuclear Physics 09" held at Osaka, November 1619, 2009. The series of this workshop has provided opportunities to discuss common interests of hadron and nuclear physics. Hadrons and nuclei show up different layers of phenomena governed by the same dynamics dictated by the fundamental law of the strong interaction, Quantum Chromodynamics (QCD). The basic building blocks of matter, quarks and gluons, are confined in hadrons, generating their masses dynamically and breaking chiral symmetry spontaneously. The latter is the origin of the presence of the pion which governs the essential part of the nuclear interaction. Therefore, the common key words are chiral symmetry and pions. This volume contains reports of current achievements in hadron physics including exotic multiquark states, meson production reactions and non-linear dynamics of hadrons, and those in nuclear physics clustering phenomena, exotic neutron rich nuclei and the pions in nuclei. As related subjects, applications to astronuclear physics, including accelerator physics and laser physics are also discussed comprehensively.
Humanoid Robots: Modeling and Control provides systematic presentation of the models used in the analysis, design and control of humanoid robots. The book starts with a historical overview of the field, a summary of the current state of the art achievements and an outline of the related fields of research. It moves on to explain the theoretical foundations in terms of kinematic, kineto-static and dynamic relations. Further on, a detailed overview of biped balance control approaches is presented. Models and control algorithms for cooperative object manipulation with a multi-finger hand, a dual-arm and a multi-robot system are also discussed. One of the chapters is devoted to selected topics from the area of motion generation and control and their applications. The final chapter focuses on simulation environments, specifically on the step-by-step design of a simulator using the Matlab® environment and tools. This book will benefit readers with an advanced level of understanding of robotics, mechanics and control such as graduate students, academic and industrial researchers and professional engineers. Researchers in the related fields of multi-legged robots, biomechanics, physical therapy and physics-based computer animation of articulated figures can also benefit from the models and computational algorithms presented in the book. Provides a firm theoretical basis for modelling and control algorithm design Gives a systematic presentation of models and control algorithms Contains numerous implementation examples demonstrated with 43 video clips
Coal is more abundant than petroleum and natural gas. Further, coal is not localized but can be used by many more countries than petroleum. Therefore, if we can establish coal utilization technology, coal will bring about a great contribution to human life and society. On the other hand, shortage of petroleum and natural gas are anticipated in the second half of the 21st century. To compensate, the use of coal is expected to gradually increase during the 21st century. In the future, the development of the coal utilization technology will become more and more important to insure the supply of liquid fuels for transportation and carbon sources for the manufacture of chemicals and plastic materials.In order to develop such technologies, the elucidation of the structure of coal is a fundamental area of study. Further, more efficient coal utilization technology must be established to meet environmental legislation. One of the key technologies for this purpose is catalysis. This volume provides detail of the basic and practical aspects of the science and technology of coal utilization with and without catalysts. The actual structure of coal, the chemistry included in the reactivity of coal, the methods to elucidate the structure of coal and re-action mechanisms of coal conversion, the most important catalyst for converting coal to liquid and gas, the role of the catalysts in coal conversion, the problems in the process engineering, and how to meet environmental regulations are discussed in detail. The recent progress in studies on the structure and reactivity of coal made over the last century is summarized and reviewed with emphasis on both fundamental and applied aspects of the science and technology for coal processing in the presence and absence of catalysts. * This book highlights the issues faced in trying to discover more efficient coal utilization technology.* Provides detailed discussion on how to meet environmental regulations and legislation. * Fills the gap between both the scientific and practical sides of coal utilization with and without catalysts.
Starting with an introduction to the fundamental physics in chaotic instabilities in laser systems, this comprehensive and unified reference goes on to present the techniques and technology of synchronization of chaos in coupled lasers, as well as the many applications to lasers and optics, communications, security and information technology. Throughout, it presents the current state of knowledge, including encoding/decoding techniques, performance of chaotic communication systems, random number generation, and novel communication technologies.
This book covers an approach to conversational informatics which encompasses science and technology for understanding and augmenting conversation in the network age. A major challenge in engineering is to develop a technology for conveying not just messages but also underlying wisdom. Relevant theories and practices in cognitive linguistics and communication science, as well as techniques developed in computational linguistics and artificial intelligence, are discussed.
Ch. 1. Ingredients of the standard model. 1.1. Strong interaction - QCD. 1.2. Electroweak theory. 1.3. CKM mass matrix -- ch. 2. Symmetries and wave functions. 2.1. Why is symmetry important? 2.2. Symmetry current. 2.3. SU(2). 2.4. SU(3). 2.5. Multi-particle states. 2.6. Product-states. 2.7. Quark model wave functions -- ch. 3. Chiral symmetry. 3.1. Lorentz group and chiral fermions. 3.2. Chiral group. 3.3. Spontaneous breaking of chiral symmetry -- ch. 4. The sigma model. 4.1. Linear sigma model. 4.2. Non-linear sigma model. 4.3. Fermion field -- ch. 5. Chiral bag model. 5.1. The MIT bag model. 5.2. The little bag model. 5.3. The Skyrme model. 5.4. The chiral bag model. 5.5. Chiral casimir effects. 5.6. The edgehog solution -- ch. 6. Nucleon properties. 6.1. Semiclassical method. 6.2. Isospin rotation of the hedgehog solution. 6.3. Axial properties. 6.4. Non-rigid quantization of the skyrmion. 6.5. Electromagnetic properties. 6.6. Chiral bag with vector mesons -- ch. 7. Large-Nc baryons. 7.1. Introduction. 7.2. General counting rules. 7.3. Counting rules for solitons. 7.4. Large-Nc algebra for baryons. 7.5. Finite Nc. 7.6. Other representations and gA -- ch. 8. Excited baryons. 8.1. Systematics in baryon masses. 8.2. Quarks in a deformed oscillator potential. 8.3. Electromagnetic transitions.
Extensive studies of high-Tc cuprate superconductors have stimualted investigations into various transition-metal oxides. Mott transitions in particular provide fascinating problems and new concepts in condensed matter physics. This book is a collection of overviews by well-known, active researchers in this field. It deals with the latest developments, with particular emphasis on the theoretical, spectroscopic, and transport aspects.
New products and new business development require innovative, creative marketing solutions in order to successfully differentiate them from competing products in the marketplace. This important book explores and elucidates the essence of creativity, with an emphasis on how to proceed with R&D activities strategically and how to connect them with successful products, services and commercialization. Using interesting, real case studies such as ?Healthy Tea?? developed by Japan Coca-Cola, Inc., the recommendation engine ?Teach Me Electronic Appliances?, and the development of various robots, the book uncovers the secret of successful marketing and shows how to develop and deploy new products and services on a sustainable basis. It will therefore appeal to both business practitioners as well as researchers and students interested in innovation and marketing issues.
The World of Nano-Biomechanics, Second Edition, focuses on the remarkable progress in the application of force spectroscopy to molecular and cellular biology that has occurred since the book's first edition in 2008. The initial excitement of seeing and touching a single molecule of protein/DNA is now culminating in the development of various ways to manipulate molecules and cells almost at our fingertips, enabling live cell operations. Topics include the development of molecular biosensors, mechanical diagnosis, cellular-level wound healing, and a look into the advances that have been made in our understanding of the significance of mechanical rigidity/flexibility of protein/DNA structure for the manifestation of biological activities. The book begins with a summary of the results of basic mechanics to help readers who are unfamiliar with engineering mechanics. Then, representative results obtained on biological macromolecules and structures, such as proteins, DNA, RNA, polysaccharides, lipid membranes, subcellular organelles, and live cells are discussed. New to this second edition are recent developments in three important applications, i.e., advanced AFM-data analysis, high-resolution mechanical biosensing, and the use of cell mechanics for medical diagnosis. - Explains the basic physical concepts and mathematics of elementary mechanics needed to understand and perform experimental work on small-scale biological samples - Presents recent developments of force-based biosensing - Includes novel applications of nano-biomechanics to the medical field
This book presents the most recent description of rubber reinforcement, focusing on the network-like structure formation of nanofiller in the rubber matrix under the presence of bound rubber. The resultant filler network is visualized by electron tomography applied to rubber. In the case of natural rubber, the self-reinforcement effect is uniquely functioning, and new template crystallization is suggested. Here, the crystallites are also believed to arrange themselves in a network-like manner. These results are of great use, particularly for engineers, in designing rubber reinforcement.
These notes are devoted to a systematic study of developing the Tomita-Takesaki theory for von Neumann algebras in unbounded operator algebras called O*-algebras and to its applications to quantum physics. The notions of standard generalized vectors and standard weights for an O*-algebra are introduced and they lead to a Tomita-Takesaki theory of modular automorphisms. The Tomita-Takesaki theory in O*-algebras is applied to quantum moment problem, quantum statistical mechanics and the Wightman quantum field theory. This will be of interest to graduate students and researchers in the field of (unbounded) operator algebras and mathematical physics.
This book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand–Naimark type theorems, a Vidav–Palmer type theorem, an unbounded representation theory, and miscellaneous applications. Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.
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