For the first time in book form, this comprehensive and systematic monograph presents the methods for the reversible synthesis of logic functions and circuits. This methodology offers designers the capability to solve major problems in system design now and in the future, such as the high rate of power consumption, and the emergence of quantum effects for highly dense ICs. The challenge addressed here is to design reliable systems that consume as little power as possible and in which the signals are processed and transmitted at very high speeds with very high signal integrity. Researchers in academia or industry and graduate students, who work in logic synthesis, computer design, computer-aided design tools, and low power VLSI circuit design, will find this book a valuable resource.

This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag). Moreover he played a decisive role in the foundation of these two series by helping to establish contacts between Birkhauser and the founder and present chief editor of this book series after his emigration from Moldavia in 1974. The volume is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to E. Meister. We hope that a great part of the numerous features of his life and work can be re-discovered from this book."

This book features selected papers from The Seventh International Conference on Research and Education in Mathematics that was held in Kuala Lumpur, Malaysia from 25 - 27th August 2015. With chapters devoted to the most recent discoveries in mathematics and statistics and serve as a platform for knowledge and information exchange between experts from academic and industrial sectors, it covers a wide range of topics, including numerical analysis, fluid mechanics, operation research, optimization, statistics and game theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists, and provides an excellent overview of the latest research in mathematical sciences.

Sophus Lie (1842-1899) is without doubt one of Norway's greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms Lie groups and Lie algebra are today part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug let us come close to both the person Sophus Lie and his time. We follow him through childhood at the vicarage in Nodfjordeid, his growing up in Moss, school and studying in Christiania, travelling in Europe and his contacts with the leading mathematicians of his time. The academic and scientific career brought Lie from Christiania to Leipzig as professor, before the attempt to call him back to Norway, when she stood on the threshhold to national sovereignty, was successful.

String Theory is our current best candidate for the unification of all fundamental forces, including gravity, in a consistent quantum framework. In this collection of lectures delivered at the Carg se Summer School "String Theory: from Gauge Interactions to Cosmology'', world leading experts provide an up-to-date survey of the latest developments in this topic, including the gauge/gravity correspondence, superstring cosmology and cosmic strings, topological string theory and matrix models, physics beyond the standard model and the landscape of vacua of string theory, conformal field theory and critical phenomena in statistical mechanics. Many more topics are also discussed in shorter contributions by School participants. Written with an emphasis on pedagogy, this volume will be a invaluable resource to students and experts alike.

2 Elementary systems on G-manifolds. 292 3 Two elementary systems: The(GxG)-manifold and its subma- fold splitting underdiag(GxG). 293 4 Examples of internal coordinates on(GxG). 297 5 Kronecker products and two-particle state decompositions on(Gx G). 298 6 Fusion of two elementary systems on(GxG). 300 7 Elementary systems on the Poincare-manifold. ' 301 7. 1 Mackey and covariant ?elds. 301 7. 2 From covariant to Mackey ?elds. 302 7. 3 Obstruction of Poincare-manifolds ' by covariant ?elds. 303 8 Relativistic position operators and coordinates. 305 8. 1 Position operators for relativistic Mackey ?elds. 305 8. 2 Position operators for ?elds with spin. 306 9 From Dirac ?elds to Bargmann-Wigner ?elds by fusion. 307 10 Elementary systems in interaction. 309 10. 1 Euclidean invariant interactions. 309 10. 2 Interacting Dirac spinor ?elds. 310 11 Scission of an elementary system. 311 12 Conclusion. 313 13 Appendix. 313 13. 1 A: Orthogonality and completeness of unitary represen- tions. 313 13. 2 B: Parameters, cosets and multiplication rules forSl(2,C). 313 13. 3 C: Observables in the relativistic 2-body system. 314 Propagation in crossed electric and magnetic ?elds 317 T. Kramer, C. Bracher 1 Introduction 317 2 Elastic scattering and quantum sources 318 2. 1 Connection to the propagator 319 2. 2 Currents generated by quantum sources 321 2. 3 Density of States 322 2. 4 Construction of the Green function 322 3 Matter waves in crossed electric and magnetic ?elds 324 3. 1 The quantum propagator 324 3.

The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green's and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

This book presents recent results in the following areas: spectral analysis of one-dimensional Schrodinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. Several developments treated appear for the first time in a book. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

This book is an outgrowth of ideas originating from 1. Kluvanek. Unfortunately, Professor Kluvanek did not live to contribute to the project of writing up in a systematic form, the circle of ideas to which the present work is devoted. It is more than likely that with his input, the approach and areas of emphasis of the resulting exposition would have been quite different from what we have here. Nevertheless, the stamp of Kluvanek's thought and philosophy (but not necessarily his approval) abounds throughout this book. Although the title gives no indication, integration theory in vector spaces is a cen tral topic of this work. However, the various notions of integration developed here are intimately connected with a specific application-the representation of evolutions by func tional integrals. The representation of a perturbation to the heat semigroup in terms of Wiener measure is known as the Feynman-Kac formula, but the term has a wider meaning in the present work. Traditionally, such representations have been used to obtain analytic information about perturbations to free evolutions as an alternative to arguments with a more operator-theoretic flavour. No applications of this type are given here. It is an un derlying assumption of the presentation of this material that representations of the nature of the Feynman-Kac formula are worth obtaining, and in the process of obtaining them, we may be led to new, possibly fertile mathematical structures-a view largely motivated by the pervasive use of path integrals in quantum physics."

This work is the first explicit examination of the key role that mathematics has played in the development of theoretical physics and will undoubtedly challenge the more conventional accounts of its historical development. Although mathematics has long been regarded as the "language" of physics, the connections between these independent disciplines have been far more complex and intimate than previous narratives have shown. The author convincingly demonstrates that practices, methods, and language shaped the development of the field, and are a key to understanding the mergence of the modern academic discipline. Mathematicians and physicists, as well as historians of both disciplines, will find this provocative work of great interest.

Every Thing Must Go aruges that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, they demonstrate how to build a metaphysics compatible with current fundamental phsyics ("ontic structural realism"), which, when combined with their metaphysics of the special sciences ("rainforet realism"), can be used to unify physics with the other sciences without reducing these sciences to physics intself. Taking science metaphysically seriously, Ladyman and Ross argue, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects.
Every Thing Must Go also assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the author's metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism vs. empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

This collection of essays presented to Carl Friedrich von Weizsäcker on the occasion of his 90th birthday addresses a wide readership interested in astronomy, physics, and the history and philosophy of science. The articles treat subjects such as the social responsibility of scientists, thermonuclear processes in stars and stellar neutrinos, turbulence and the emergence of planetary systems. Furthermore, considerable attention is paid to the unity of nature, the nature of time, and to information about, and interpretation of, the structure of quantum theory, all important philosophical problems of our times. The last section describes von Weizsäcker's ur-hypothesis and how it will theoretically permit the construction of particles and interactions from quantized bits of information.

This two-volume set containts parts I and II. Each volume is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions are split into two parts: ``Integrable Systems'' and ``Quantum Theories and Algebraic Geometry'', reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch."

A fascinating insight into the state-of-the-art in silicon microphotonics and on what we can expect in the near future. The book presents an overview of the current understanding of getting light from silicon. It concentrates mainly on low dimensional silicon structures, like quantum dots, wires and wells, but covers also alternative approaches like porous silicon and the doping of silicon with rare-earths. The emphasis is on the experimental and theoretical achievements concerning the optoelectronic properties of confined silicon structures obtained during recent years. Silicon based photonic crystals are in particular considered. An in depth discussion of the route towards a silicon laser is presented.

The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

The Advanced Study Institute on "Theoretical Aspects and New Developments in Magneto-Optics" was held at the University of Antwerpen (R.U.C.A.), from July 16 to July 28, 1979. The Institute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert (Belgium), A.S.L.K. (Belgium), Bell Telephone Mfg. CO. (Belgium), Esso Belgium, Generale Bankmaatschappij (Belgium), General Motors (Belgium), I.B.M. (Belgium), Kredietbank (Belgium), Metallurgie Hoboken-Over pelt (Belgium), National Science Foundation (U.S.A). A total of 60 lecturers and participants attended the Institute. Scope of the Institute The magneto-optic phenomena are due to the change of the polarizability of a substance as a result of the splitting of the quantized energy bands. Most of these phenomena were discovered during the second half of this century. The understanding of the magneto-optical effects of all kinds, however, was brought by the advent of quantum mechanics, and since then important progress has been made in many fields of experimental methods and techniques."

The word tribology was fIrst reported in a landmark report by P. Jost in 1966 (Lubrication (Tribology)--A Report on the Present Position and Industry's Needs, Department of Education and Science, HMSO, London). Tribology is the science and technology of two interacting surfaces in relative motion and of related subjects and practices. The popular equivalent is friction, wear and lubrication. The economic impact of the better understanding of tribology of two interacting surfaces in relative motion is known to be immense. Losses resulting from ignorance of tribology amount in the United States alone to about 6 percent of its GNP or about $200 billion dollars per year (1966), and approximately one-third of the world's energy resources in present' use, appear as friction in one form or another. A fundamental understanding of the tribology of the head-medium interface in magnetic recording is crucial to the future growth of the $100 billion per year information storage industry. In the emerging microelectromechanical systems (MEMS) industry, tribology is also recognized as a limiting technology. The advent of new scanning probe microscopy (SPM) techniques (starting with the invention of the scanning tunneling microscope in 1981) to measure surface topography, adhesion, friction, wear, lubricant-fIlm thickness, mechanical properties all on a micro to nanometer scale, and to image lubricant molecules and the availability of supercomputers to conduct atomic-scale simulations has led to the development of a new fIeld referred to as Microtribology, Nanotribology, or Molecular Tribology (see B. Bhushan, J. N. Israelachvili and U.

The fifth ERCOFfAC workshop 'Direct and Large-Eddy Simulation-5' (DLES-5) was held at the Munich University of Technology, August 27-29, 2003. It is part of a series of workshops that originated at the University of Surrey in 1994 with the intention to provide a forum for presentation and dis cussion of recent developments in the field of direct and large-eddy simula tion. Over the years the DLES-series has grown into a major international venue focussed on all aspects of DNS and LES, but also on hybrid methods like RANSILES coupling and detached-eddy simulation designed to provide reliable answers to technical flow problems at reasonable computational cost. DLES-5 was attended by 111 delegates from 15 countries. Its three-day pro gramme covered ten invited lectures and 63 original contributions partially pre sented in parallel sessions. The workshop was financially supported by the fol lowing companies, institutions and organizations: ANSYS Germany GmbH, AUDI AG, BMW Group, ERCOFfAC, FORTVER (Bavarian Research Asso ciation on Combustion), JM BURGERS CENTRE for Fluid Dynamics. Their help is gratefully acknowledged. The present Proceedings contain the written versions of nine invited lectures and fifty-nine selected and reviewed contributions which are organized in four parts: 1 Issues in LES modelling and numerics 2 Laminar-turbulent transition 3 Turbulent flows involving complex physical phenomena 4 Turbulent flows in complex geometries and in technical applications.

Since the invention of the laser, our fascination with the photon has led to one of the most dynamic and rapidly growing fields of technology. An explosion of new materials, devices, and applications makes it more important than ever to stay current with the latest advances. Surveying the field from fundamental concepts to state-of-the-art developments, Photonics: Principles and Practices builds a comprehensive understanding of the theoretical and practical aspects of photonics from the basics of light waves to fiber optics and lasers.

Providing self-contained coverage and using a consistent approach, the author leads you step-by-step through each topic. Each skillfully crafted chapter first explores the theoretical concepts of each topic and then demonstrates how these principles apply to real-world applications by guiding you through experimental cases illuminated with numerous illustrations. Coverage is divided into six broad sections, systematically working through light, optics, waves and diffraction, optical fibers, fiber optics testing, and laboratory safety. A complete glossary, useful appendices, and a thorough list of references round out the presentation. The text also includes a 16-page insert containing 28 full-color illustrations.

Containing several topics presented for the first time in book form, Photonics: Principles and Practices is simply the most modern, comprehensive, and hands-on text in the field.

He's back! The physicist returns with an entirely new compilation of questions and answers from his long-lived website where laypeople can ask questions about anything physics related. This book focuses on adjectives (practical, beautiful, surprising, cool, frivolous) instead of nouns like the first two books (atoms, photons, quanta, mechanics, relativity). The answers within Physics Is are responses to people looking for answers to fascinating (and often uninformed) questions. It covers topics such as sports, electromagnetism, gravitational theory, special relativity, superheroes, videogames, and science fiction. These books are designed for laypeople and rely heavily on concepts rather than formalism. That said, they keep the physics correct and don't water down, so expert physicists will find this book and its two companion titles fun reads. They may actually recognize similar questions posed to them by friends and family. As with the first two books, Physics Is ends with a chapter with questions from people who think that 'The physicist' is a psychic and from people who think they have the answers to life, the universe and everything.