Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online

Download or read book Fundamental Aspects of Dislocation Theory written by John Arthur Simmons and published by . This book was released on 1970 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Theory and Stochastic Processes with Applications Second Edition written by Oliver Knill and published by World Scientific Publishing Company. This book was released on 2017-01-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).

Download or read book The Theoretical Foundation of Dendritic Function written by Wilfrid Rall and published by MIT Press. This book was released on 1995 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of fifteen previously published papers, some of them not widely available, have been carefully chosen and annotated by Rall's colleagues and other leading neuroscientists.

Download or read book Introduction to Elementary Particles written by David Jeffery Griffiths and published by HarperCollins Publishers. This book was released on 1987-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Quantum Theory written by Klaas Landsman and published by . This book was released on 2020-10-09 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Download or read book Quantum Theory Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Download or read book Quantum Information with Continuous Variables written by S.L. Braunstein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information may sound like science fiction but is, in fact, an active and extremely promising area of research, with a big dream: to build a quantum computer capable of solving problems that a classical computer could not even begin to handle. Research in quantum information science is now at an advanced enough stage for this dream to be credible and well-worth pursuing. It is, at the same time, too early to predict how quantum computers will be built, and what potential technologies will eventually strike gold in their ability to manipulate and process quantum information. One direction that has reaped many successes in quantum information processing relies on continuous variables. This area is bustling with theoretical and experimental achievements, from continuous-variable teleportation, to in-principle demonstrations of universal computation and efficient error correction. Now the time has come to compile some of the major results into one volume. In this book the leading researchers of the field present up-to-date developments of continuous-variable quantum information. This book is organized to suit many reader levels with introductions to every topic and in-depth discussions of theoretical and experimental results.

Download or read book Multiphysics Simulation by Design for Electrical Machines Power Electronics and Drives written by Marius Rosu and published by John Wiley & Sons. This book was released on 2017-12-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applied theory and advanced simulation techniques for electric machines and drives This book combines the knowledge of experts from both academia and the software industry to present theories of multiphysics simulation by design for electrical machines, power electronics, and drives. The comprehensive design approach described within supports new applications required by technologies sustaining high drive efficiency. The highlighted framework considers the electric machine at the heart of the entire electric drive. The book also emphasizes the simulation by design concept—a concept that frames the entire highlighted design methodology, which is described and illustrated by various advanced simulation technologies. Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives begins with the basics of electrical machine design and manufacturing tolerances. It also discusses fundamental aspects of the state of the art design process and includes examples from industrial practice. It explains FEM-based analysis techniques for electrical machine design—providing details on how it can be employed in ANSYS Maxwell software. In addition, the book covers advanced magnetic material modeling capabilities employed in numerical computation; thermal analysis; automated optimization for electric machines; and power electronics and drive systems. This valuable resource: Delivers the multi-physics know-how based on practical electric machine design methodologies Provides an extensive overview of electric machine design optimization and its integration with power electronics and drives Incorporates case studies from industrial practice and research and development projects Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives is an incredibly helpful book for design engineers, application and system engineers, and technical professionals. It will also benefit graduate engineering students with a strong interest in electric machines and drives.

Download or read book An Invitation to Morse Theory written by Liviu Nicolaescu and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.

Download or read book Interpolation Spaces written by J. Bergh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Lofstrom, writing a book on interpolation theory and he most generously put at Lofstrom's disposal an unfinished manu script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, LOfstrom prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boe1 Engebrand, Lena Mattsson and Birgit Hoglund for their expert typing of our manuscript.

Download or read book Introduction to Superstring Theory written by Elias Kiritsis and published by Cornell University Press. This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: String Theory, now almost 30 years of age, was partly forgotten but came back to the forefront of theoretical particle physics in 1984. In this book, based on lectures by the author at the K.U.Leuven and at the University of Padova, Elias Kiritsis takes the reader through the developments of the last 15 years: conformal field theory, the various superstrings and their spectra, compactifications, and the effective description of low energy degrees of freedom. It ends by showing a glimpse of the most recent developments, dualities of strings and higher dimensional objects, that influence both traditional field theory and present day mathematics. Readership: Theoretical physicists, and mathematicians with an interest in modern string theory. 1. Introduction 2. Historical perspective 3. Classical string theory 3.1. The point particle 3.2. Relativistic strings 3.3. Oscillator expansions 4. Quantization of the bosonic string 4.1. Covariant canonical quantization 4.2. Light-cone quantization 4.3. Spectrum of the bosonic string 4.4. Path integral quantization 4.5. Topologically non-trivial world-sheets 4.6. BRST primer 4.7. BRST in string theory and the physical spectrum 4.8. Interactions and loop amplitudes 5. Conformal field theory 5.1. Conformal transformations 5.2. Conformally invariant field theory 5.3. Radial quantization 5.4. Example: the free boson 5.5. The central charge 5.6. The free fermion 5.7. Mode expansions 5.8. The Hilbert space 5.9. Representations of the conformal algebra 5.10. Affine algebras 5.11. Free fermions and O(N) affine symmetry 5.12. N=1 superconformal symmetry 5.13. N=2 superconformal symmetry 5.14. N=4 superconformal symmetry 5.15. The CFT of ghosts 6. CFT on the torus 6.1. Compact scalars 6.2. Enhanced symmetry and the string Higgs effect 6.3. T-duality 6.4. Free fermions on the torus 6.5. Bosonization 6.6. Orbifolds 6.7. CFT on higher-genus Riemann surfaces 7. Scattering amplitudes and vertex operators of bosonic strings 8. Strings in background fields and low-energy effective actions 9. Superstrings and supersymmetry 9.1. Closed (type-II) superstrings 9.2. Massless R-R states 9.3. Type-I superstrings 9.4. Heterotic superstrings 9.5. Superstring vertex operators 9.6. Supersymmetric effective actions 10. Anomalies 11. Compactification and supersymmetry breaking 11.1. Toroidal compactifications 11.2. Compactification on non-trivial manifolds 11.3. World-sheet versus spacetime supersymmetry 11.4. Heterotic orbifold compactifications with N=2 supersymmetry 11.5. Spontaneous supersymmetry breaking 11.6. Heterotic N=1 theories and chirality in four dimensions 11.7. Orbifold compactifications of the type-II string 12. Loop corrections to effective couplings in string theory 12.1. Calculation of gauge thresholds 12.2. On-shell infrared regularization 12.3. Gravitational thresholds 12.4. Anomalous U(1)?s 12.5. N=1,2 examples of thresholds corrections 12.6. N=2 universality of thresholds 12.7. Unification 13. Non-perturbative string dualities: a foreword 13.1. Antisymmetric tensors and p-branes 13.2. BPS states and bounds 13.3. Heterotic/type-I duality in ten dimensions 13.4. Type-IIA versus M-theory 13.5. M-theory and the E8xE8 heterotic string 13.6. Self-duality of the type-IIB string 13.7. D-branes are the type-II R-R charged states 13.8. D-brane actions 13.9. Heterotic/type-II duality in six and four dimensions 14. Outlook Appendices A. Theta functions B. Toroidal lattice sums C. Toroidal Kaluza-Klein reduction D. N=1,2,4, D=4 supergravity coupled to matter E. BPS Multiplets and helicity supertrace formulae F. Modular forms G. Helicity string partition functions H. Electric-Magnetic duality in D=4 References ISBN10:9061868947 Imprint:Leuven University Press Language: English NUR * 925 Theoretische natuurkunde * Number of pages: v-316 * Width: 16 cm * Height: 24 cm * Elias Kiritsis, Author (all publications from this author/editor with Leuven University Press)

Download or read book Introduction to Optical Quantum Information Processing written by Pieter Kok and published by Cambridge University Press. This book was released on 2010-04-22 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.

Download or read book Basics of Bioinformatics written by Rui Jiang and published by Springer Science & Business Media. This book was released on 2013-11-26 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines 11 courses and 15 research topics in bioinformatics, based on curriculums and talks in a graduate summer school on bioinformatics that was held in Tsinghua University. The courses include: Basics for Bioinformatics, Basic Statistics for Bioinformatics, Topics in Computational Genomics, Statistical Methods in Bioinformatics, Algorithms in Computational Biology, Multivariate Statistical Methods in Bioinformatics Research, Association Analysis for Human Diseases: Methods and Examples, Data Mining and Knowledge Discovery Methods with Case Examples, Applied Bioinformatics Tools, Foundations for the Study of Structure and Function of Proteins, Computational Systems Biology Approaches for Deciphering Traditional Chinese Medicine, and Advanced Topics in Bioinformatics and Computational Biology. This book can serve as not only a primer for beginners in bioinformatics, but also a highly summarized yet systematic reference book for researchers in this field. Rui Jiang and Xuegong Zhang are both professors at the Department of Automation, Tsinghua University, China. Professor Michael Q. Zhang works at the Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA.

Download or read book Nonlinear Theory of Electroelastic and Magnetoelastic Interactions written by Luis Dorfmann and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified theory on nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classic theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize relevant theories of continuum mechanics, required to account for the deformability of material and present a constitutive framework for the nonlinear magneto-and electroelastic interactions in a highly deformable material. The equations contained in the book formulate and solve a variety of representative boundary-value problems for both nonlinear magnetoelasticity and electroelasticity.

Download or read book Quantum Information Meets Quantum Matter written by Bei Zeng and published by Springer. This book was released on 2019-03-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book approaches condensed matter physics from the perspective of quantum information science, focusing on systems with strong interaction and unconventional order for which the usual condensed matter methods like the Landau paradigm or the free fermion framework break down. Concepts and tools in quantum information science such as entanglement, quantum circuits, and the tensor network representation prove to be highly useful in studying such systems. The goal of this book is to introduce these techniques and show how they lead to a new systematic way of characterizing and classifying quantum phases in condensed matter systems. The first part of the book introduces some basic concepts in quantum information theory which are then used to study the central topic explained in Part II: local Hamiltonians and their ground states. Part III focuses on one of the major new phenomena in strongly interacting systems, the topological order, and shows how it can essentially be defined and characterized in terms of entanglement. Part IV shows that the key entanglement structure of topological states can be captured using the tensor network representation, which provides a powerful tool in the classification of quantum phases. Finally, Part V discusses the exciting prospect at the intersection of quantum information and condensed matter physics – the unification of information and matter. Intended for graduate students and researchers in condensed matter physics, quantum information science and related fields, the book is self-contained and no prior knowledge of these topics is assumed.