Mathematical / Computational / Theoretical physics Books
Springer Fachmedien Wiesbaden Übungsbuch Physik für Studierende der
Book SynopsisDieses Übungsbuch enthält zahlreiche Aufgaben zum Inhalt einer Einführungsvorlesung Physik. Mithilfe von ausführlichen Lösungen und Erklärungen lernen und üben Studierende die Anwendung physikalischer Rechenmethoden und die hierfür erforderliche Mathematik. Vor allem in Kombination mit dem Lehrbuch Physik für Studierende der Biowissenschaften, Chemie und Medizin bildet es eine ideale Basis für die Klausurvorbereitung und weiterführende Vorlesungen.Der erste Teil des Buches bietet Übungsserien mit Aufgaben, die entsprechend dem Inhalt typischer Physikvorlesungen strukturiert sind und dabei Themen von der klassischen Mechanik bis hin zur Atom- und Quantenphysik abdecken. Jede Übungsserie besteht aus einem Verständnisteil und einem Übungsteil, der durch anwendungsorientierte Aufgaben aus Biowissenschaften, Chemie und Medizin ergänzt wird.Das Gelernte kann dann anhand des zweiten Teils überprüft werden, der aus verschiedenen Testserien besteht: Hier sind gemischte Aufgaben aus den jeweiligen Inhalten der zwei Semester enthalten, wie sie auch in Physikklausuren zu finden sind.Table of ContentsMathematische Grundlagen.- Klassische Mechanik.- Zustandsformen der Materie.- Thermodynamik.- Schwingungen.- Wellen.- Optik.- Klassische Elektrodynamik.- Atom- und Quantenphysik.- Testserien Physik I.- Testserien Physik II.
£28.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Mathematics for Physicists and Engineers: Fundamentals and Interactive Study Guide
Book SynopsisThis textbook takes physics and engineering undergraduates through the mathematics they need in the first years of study. It offers an accessible approach which is characterized by the combination of the textbook with a detailed study guide. This study guide, supplied as freely accessible downloads for each chapter, divides the whole learning task into small units. You will read and study a limited section of the textbook and then return to the study guide afterwards. Learning results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. The degree of difficulty slowly rises, which will let you gain confidence and experience your own progress, thus fostering motivation. The sequence of studies can be individualized according to performance and can be regarded as a full tutorial course. This combination of a textbook with a detailed study guide is a powerful means to meet the rising importance of learning outside of lectures at home and will be of great benefit, especially to students learning remotely. Table of Contents
£67.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Solid State Theory, Volume 1: Basics: Phonons and
Book SynopsisThe textbooks “Solid State Theory" give an introduction to the methods, contents and results of modern solid state physics in two volumes. This first volume has the basic courses in theoretical physics as prerequisites, i.e. knowledge of classical mechanics, electrodynamics and, in particular, quantum mechanics and statistical physics is assumed. The formalism of second quantization (occupation number representation), which is needed for the treatment of many-body effects, is introduced and used in the book. The content of the first volume deals with the classical areas of solid state physics (phonons and electrons in the periodic potential, Bloch theorem, Hartree-Fock approximation, density functional theory, electron-phonon interaction). The first volume is already suitable for Bachelor students who want to go beyond the basic courses in theoretical physics and get already familiar with an application area of theoretical physics, e.g. for an elective subject "Theoretical (Solid State) Physics" or as a basis for a Bachelor thesis. Every solid-state physicist working experimentally should also be familiar with the theoretical methods covered in the first volume. The content of the first volume can therefore also be the basis for a module "Solid State Physics" in the Master program in Physics or, together with the content of the 2nd volume, for a module "Theoretical Solid State Physics" or "Advanced Theoretical Physics". The following second volume covers application areas such as superconductivity and magnetism to areas that are current research topics (e.g. quantum Hall effect, high-temperature superconductivity, low-dimensional structures).Table of Contents
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Solid State Theory, Volume 2: Applications:
Book SynopsisThe present volume 2 covers advanced topics in theoretical solid state physics and thus ties in directly with the fundamentals. Solids in external fields or more generally in non-equilibrium and deviations from the ideal 3-dimensional crystal structure (surfaces, impurities, low-dimensional structures, quantum dots, etc.) are treated. The consideration of collective phenomena such as superconductivity and magnetism complete the presentation. The reader is assumed to have the contents of Volume 1 (electrons and phonons in ideal crystals, Bloch theorem, population number representation or 2nd quantization, electron-electron and electron-phonon interaction) as well as the basic knowledge of general theoretical physics (mechanics, electrodynamics, quantum mechanics, and statistical physics) usually available after a bachelor's degree in physics. Volume 2 is thus ideally suited for students in the master's program in physics who wish to specialize in (experimental or theoretical) solid-state physics. Addressing current topics (e.g., Kondo effect, fractional quantum Hall effect, 2-dimensional crystals such as graphene, giant magnetoresistance effect, and others) provides an optimal transition to modern research.The new edition has been completely revised, expanded with numerous exercises and existing redesigned, with the associated solutions now included in the book.Table of ContentsElectronic transport in solids.- Optical (or dielectric) properties of solids.- Deviations from the ideal, three-dimensional crystal structure.- Solids in the external magnetic field.- Superconductivity.- Collective magnetism.- Solutions to the exercise problems.
£49.99
Springer Fachmedien Wiesbaden Einführung in die Theoretische Physik: Klassische
Book SynopsisDieses Lehrbuch bietet Studierenden der ersten Semester eine Einführung in die Theoretische Physik sowie die dazu erforderlichen mathematischen Werkzeuge. Parallel zu den Inhalten der Klassischen Mechanik lernen Sie die nötige Mathematik gleich mit – und auch die Denkweise in der Theoretischen Physik kennen. Unter sorgfältiger Berücksichtigung des Wissensstands von Studienanfängern wird eine ausführliche, schrittweise Darstellung von allen Herleitungen und Beispielen geboten. Dabei werden Ihnen nicht nur die analytischen Lösungsverfahren gezeigt, sondern Sie erhalten auch einen Einblick in die große Bedeutung von computergestützten, numerischen Verfahren. Das Buch beginnt mit den Leitbegriffen des Zustands und der Bewegungsgleichung, worauf aufbauend die Struktur der Newton‘schen Mechanik in leicht nachvollziehbarer Art und Weise vermittelt wird. Als dazugehörige mathematische Themen werden komplexe Zahlen, Vektoren und Matrizen, Taylor-Reihen, gewöhnliche Differenzialgleichungen, Fourier-Reihen, partielle Ableitungen und Elemente der Vektoranalysis behandelt. Ebenso finden Sie in diesem Buch eine Untersuchung elementarer Erhaltungssätze als auch deren Anwendung auf physikalische Fragestellungen wie z.B. die Begründung der Kepler‘schen Gesetze.Table of ContentsVorwort.- 1 Grundkonzepte.- 2 Beschreibung der Bewegung von Massenpunkten.- 3 Dynamische Gesetze für einen Massenpunkt.- 4 Gewöhnliche Differenzialgleichungen.- 5 Fourier-Reihen.- 6 Nichtlineare Dynamik.- 7 Systeme mit mehr als einem Teilchen.- 8 Partielle Ableitungen.- 9 Energie.- 10 Zweiteilchenproblem mit Gravitationskraft.- 11 Drehbewegungen.- 12 Spezielle Relativitätstheorie - 13 Anhänge: A Computerprogramm zu Kap. 1.- B Computerprogramm zu Kap. 6.- Index.
£26.59
Springer Fachmedien Wiesbaden Komplexe Strukturen: Entropie und Information
Book SynopsisDie Erforschung komplexer Strukturen ist gegenwärtig eines der interessantesten wissenschaftlichen Themen. Dieses Buch behandelt Möglichkeiten der Beschreibung und quantitativen Charakterisierung komplexer Strukturen mit Hilfe verschiedener Entropie- und Informationsmaße. Nach einer allgemein verständlichen Einführung der Grundbegriffe werden die für eine quantitative Analyse erforderlichen Konzepte ausführlich behandelt und an zahlreichen Beispielen, wie Zeitreihen, Biosequenzen, literarischen Texten und Musikstücken, veranschaulicht.Table of ContentsKomplexität und Entropie - Selbstorganisation und Information - Informationstheoretische Maße - Dynamisch generierte Strukturen - Entropie und Komplexität natürlicher Sequenzen - Quantitative Ästhetik
£44.99
Springer Fachmedien Wiesbaden Elemente der theoretischen Physik: Band 1,
Book SynopsisDas Buch vermittelt die Grundlagen und wichtigsten Konzepte der Theoretischen Mechanik und Speziellen Relativitätstheorie, soweit sie in Lehramts- und Bachelorstudiengängen benötigt werden. Dabei handelt es sich nicht um eine im Sinne des Master- oder des früheren Diplomstudiums "möglichst umfassend" gehaltene Darstellung, sondern um eine - im Vergleich zu anderen Lehrbuchwerken zur Theoretischen Physik schlank gehaltene - Darlegung der theoretischen Grundpfeiler der modernen Physik.Table of ContentsKlassische Mechanik - Spezielle Relativitätstheorie - Lösungen und Lösungstipps zu den Aufgaben - Mathematischer Anhang - Einheiten und Konstanten
£28.49
Springer Verlag Note di fisica statistica
Book SynopsisIl testo si configura come un' introduzione alla fisica statistica rivolto in primo luogo a quei corsi di studio in ingegneria che più hanno a che fare con le proprietà fisiche dei materiali, ed ha lo scopo di fornire le basi microscopiche del comportamento termodinamico di cui si fa uso sia in molti corsi tradizionali, quali quelli di termofluidica d'interesse per l'ingegneria chimica e nucleare, che in corsi rivolti ad applicazioni avanzate nella scienza dei materiali e nelle nanotecnologie. Particolare attenzione viene quindi dedicata all'impiego di metodi di fisica statistica nella scienza dei materiali, approfondendo tematiche relative alle vibrazioni nei solidi, ai processi di nucleazione liquido/vapore, alla struttura dello stato fluido e vetroso, ai plasmi, ai materiali magnetici, al gas di Fermi e alla superfluidità. Per il suo carattere generale, e per l'accento posto sui fondamenti della meccanica quantistica, il volume si presta comunque a costituire anche un testo introduttivo alla meccanica statistica per studenti dei corsi di laurea in fisica.Trade ReviewFrom the reviews:“The book covers the main typical arguments of a course on statistical physics and thermodynamics in the Italian university system. … the author intends to transmit to the readers: the subject of statistical physics is not only useful, but is also far to be boring and can reveal an intrinsic beauty. Also, the style of writing the different chapters reveals the intention of the author to give a pleasant environment for the study of the subject.” (Francesco Salvarani, Zentralblatt MATH, Vol. 1241, 2012)
£49.49
Birkhauser Verlag AG Numerical methods for atomic quantum gases
Book SynopsisThe achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.
£17.09
Birkhauser Verlag AG Highlights in the quantum theory of condensed
Book SynopsisThe birth of condensed matter physics in Italy is linked to a small number of very distinguished scientists. Mario Tosi, Professor of Physics of Matter at the Scuola Normale Superiore, is unquestionably among the leading figures, a true founder of the theoretical activity in the country and a true catalyst of novel research directions internationally. This volume collects the proceedings of a symposium held at Scuola Normale Superiore di Pisa, designed to show Mario Tosi's broad, deep influence in very diverse areas of the quantum theory of condensed matter. The topics covered in the volume represent the breadth of his interests and the highlights in the quantum theory of condensed matter: liquids, electronic states in complex structures, quantum degenerate gases, many-body physics.
£18.04
Birkhauser Verlag AG On the work of Givental relative to mirror
Book SynopsisThese are the informal notes of two seminars held at the Università di Roma “La Sapienza”, and at the Scuola Normale Superiore in Pisa in spring and autumn 1997. We discuss in detail the content of the parts of a paper by Givental dealing with mirror symmetry for projective complete intersections.
£10.99
Birkhauser Verlag AG Spectral properties of Schroedinger operators and
Book SynopsisThese are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. We propose to discuss here certain spectral properties of Schrödinger operators H=-D+V(x) (D the Laplacian and V a potential) which have application to scattering theory. We consider an operator H with potential V of class SR. We show that the positive point spectrum of H is a discrete set in R+. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly. This property is shown to hold also for generalized eigenfunctions. We then establish the limiting absorbing principle, which is a basic tool in our study.
£10.16
Birkhauser Verlag AG Symmetry in physics
Book SynopsisThese notes contain lectures on the theory of group representations and its applications to the physics of atoms, molecules and crystals, given at Purdue University, Scuola Normale Superiore (Pisa, Italy) and Universidad Técnica Federico Santa Maria (Valparaiso, Chile) on and off over a period of over 25 years. The topics selected reflect my special interests and their scope is limited by the time available to the students. The style is somewhat concise and will require careful attention on the part of the reader.
£11.99
Birkhauser Verlag AG An introduction to computational physics: Part I:
Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. Grid methods are the tool of the trade for the solution of ordinary and partial differential equations and consequently they represent a “must” for anyone dealing with computational science. With grid methods, a major distinction is made between methods which do not require matrix algebra and those which do.
£11.99
Birkhauser Verlag AG An introduction to computational physics: Part
Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. The second part deals with various types of particle methods, both deterministic and stochastic, used in modern applications of computer simulations in physics and related disciplines.
£11.99
Birkhauser Verlag AG Lectures on nonlinear physics
Book SynopsisThe main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. I try to present the material of the lectures (delivered at SNS Pisa in April -- June 1999) in such a way that the students do not need to use additional literature during the first reading. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; the use of the multiple time scale expansion method to solve problems of nonlinear oscillations; description of nonlinear wave steepening and shock wave formation using the Lagrange variables; solution of nonlinear elliptic equations considering the Liouville equation; soliton solutions of the Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.
£11.99
Birkhauser Verlag AG Ground state properties and excitation spectrum
Book SynopsisElectron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.
£14.98
Birkhauser Verlag AG Quantum Gases in Quasi-One-Dimensional Arrays
Book SynopsisThe experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. This thesis presents an overview of theoretical and experimental facts on ultra-cold atomic gases. A Green's function scheme is examined, and the book also applies a novel spin-density-functional approach to the study of Fermi gases inside one-dimensional optical lattices.Table of ContentsPreface.- 1. Reviews on Ultra-cold quantum gases.- 2. Theory of matter transport in quasi-1D arrays.- 3. Density-functional theory of 1D Fermi gases.- 4. Ultra-cold attractive fermions in 1D optical lattices.
£14.99
Birkhauser Verlag AG Asymptotics in Dynamics, Geometry and PDEs;
Book SynopsisThese are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
£26.99
Birkhauser Verlag AG Resurgence, Physics and Numbers
Book SynopsisThis book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues. Table of ContentsAsymptotics, ambiguities and resurgence.- Nonlinear eigenvalue problems.- Feynman diagrams and their algebraic lattices.- Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas.- The resurgent approach to topological string theory.- WKB and resurgence in the Mathieu equation.- Renormalised conical zeta values.- Combinatorics of Poincaré's and Schröder's equations.
£21.84
Springer Unbounded Self-adjoint Operators on Hilbert Space
Book SynopsisThe book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extensionTrade ReviewFrom the reviews:“The book is devoted to the exposition of the theory of unbounded operators in the Hilbert space. … book starts with a standard introduction to the theory of closed and closable operators, with an explanation of the important difference between self-adjoint and symmetric operators. … Among the advantages of the book is the inclusion of a nice and voluminous selection of exercises. … the book can be used for teaching a graduate course in spectral theory to students in analysis and to physicists … .” (G. V. Rozenblum, Mathematical Reviews, January, 2013)“I recommend the book as a reference for readers interested in the general theory of unbounded self-adjoint operators in Hilbert space. It is a valuable reference for numerous topics, including closed and adjoint operators, the general spectral theorem for self-adjoint operators, groups and semigroups of operators, semibounded and sectorial forms and their associated operators, and self-adjoint extensions of symmetric operators. … A special feature of the book is the inclusion of numerous examples based on multiplication operators and first and second order differential operators.” (Anton Zettl, SIAM Review, Vol. 55 (3), 2013)“The book can be used for teaching a graduate course in spectral theory to students and is also suitable for self-study. The book consists of six parts, each of which is subdivided into several chapters, each chapter ending with a section containing exercises. … The book concludes with appendices devoted to basic topics in analysis and the theory of bounded operators.” (Michael Perelmuter, Zentralblatt MATH, Vol. 1257, 2013)Table of ContentsI Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral Integrals.- 5 Spectral Decomposition of Selfadjoint and Normal Operators.- III Special Topics.- 6 One-Parameter Groups and Semigroups of Operators.- 7 Miscellaneous.- IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators.- 8 Perturbations of Selfadjoint Operators.- 9 Trace Class Perturbations of Spectra of Selfadjoint Operators.- V Forms and Operators.- 10 Semibounded Forms and Selfadjoint Operators.- 11 Sectorial Forms and m-Sectorial Operators.- 12 Discrete Spectrum of Selfadjoint Operators.- VI Selfadjoint Extention Theory of Symmetric Operators.- 13 Selfajoint Extensions: Cayley Transform and Krein Transform.- 14 Selfadjoint Extensions: Boundary Triplets.- 15 Sturm-Liouville Operators.- One-Dimensional Moment Problem.
£54.99
Atlantis Press (Zeger Karssen) Lectures on the Mathematics of Quantum Mechanics
Book SynopsisThe first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.Trade Review“QM has also been the source of many interesting mathematical problems and developments to which only very few books devote careful attention and discussion. One of the praiseworthy merits of Dell'Antonio's book is to present a comprehensive and updates account of such important mathematical results. … For these reasons the book qualifies as a must for the education of mathematical physics graduate students and clearly provides very useful information also for theoretical physicists as well for mathematicians.” (Franco Strocchi, zbMATH 1357.81001, 2017)“This is a huge book on the mathematical foundations of quantum theory, including both non-relativistic quantum mechanics (QM) and quantum field theories (QFT). … the specialized reader will find in the book a very nice reference for checking concepts and ways of proceedings in these domains. It is a remarkable book.” (Décio Krause, Mathematical Reviews, May, 2016)Table of ContentsElements of the history of Quantum Mechanics I.- Elements of the history of Quantum Mechanics II.- Axioms, states, observables, measurement, difficulties.- Entanglement, decoherence, Bell’s inequalities, alternative theories.- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity andgenerators.- Operators on Hilbert spaces I; Basic elements.- Quadratic forms.- Properties of free motion, Anholonomy,Geometric phase.- Elements of C ∗-algebras, GNS representation,automorphisms and dynamical systems.- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form.- Semigroups and dissipations. Markov approximation.- Quantum dynamical semigroups I.- Positivity preserving contraction semigroups on C ∗-algebras.- Conditional expectations.- Complete Dissipations.- Weyl system, Weyl algebra, lifting symplectic maps.- Magnetic Weyl algebra.- A Theorem of Segal.- Representations of Bargmann, Segal, Fock.- Second quantization.- Other quantizations (deformation, geometric).
£89.99
Atlantis Press (Zeger Karssen) Lyapunov Exponents of Linear Cocycles:
Book SynopsisThe aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.Trade Review“The effort of the authors to make this text self-contained and to make the exposition very clear and delightful was successful, making this monograph an excellent contribution for both graduate student and anyone interested in the continuity of Lyapunov Exponents.” (Paulo Varandas, Mathematical Reviews, June, 2018)Table of ContentsIntroduction.- Estimates on Grassmann Manifolds.- Abstract Continuity of Lyapunov Exponents.- The Oseledets Filtration and Decomposition.- Large Deviations for Random Cocycles.- Large Deviations for Quasi-Periodic Cocycles.- Further Related Problems.
£63.90
Springer Verlag, Singapore Entropy, Divergence, and Majorization in
Book SynopsisRich information-theoretic structure in out-of-equilibrium thermodynamics exists in both the classical and quantum regimes, leading to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories such as matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it.The book focuses on both purely information-theoretic concepts and their physical implications. From the mathematical point of view, rigorous proofs of fundamental properties of entropies, divergences, and majorization are presented in a self-contained manner. From the physics perspective, modern formulations of thermodynamics are discussed, with a focus on stochastic thermodynamics and resource theory of thermodynamics. In particular, resource theory is a recently developed field as a branch of quantum information theory to quantify “useful resources” and has an intrinsic connection to various fundamental ideas of mathematics and information theory. This book serves as a concise introduction to important ingredients of the information-theoretic formulation of thermodynamics. Trade Review“The book has three appendices on quantum divergences and their monotonicity, hypothesis testing and asymptotic equipartition properties. A large number of references are cited at the end of the book. The book presents wealth of theoretical information on quantum information theory. … The book may be used as a reference for the researchers in quantum information theory.” (K. N. Shukla, zbMATH 1505.80001, 2023)Table of Contents1Introduction.- 2Classical entropy and divergence.- 3Classical majorization.- 4Classical thermodynamics.- 5Quantum entropy and divergence.- 6Quantum majorization.- 7Approximate and asymptotic majorization and divergence.- 8Quantum thermodynamics.- AGeneral quantum divergences and their monotonicity.- BHypothesis testing.- CClassical asymptotic equipartition properties.- References.
£47.49
Springer Verlag, Singapore Differential Equations and Applications: ICABS
Book SynopsisThis book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system.Table of Contents1. Virtual Element Method for Singularly Perturbed Reaction-Diffusion Problems on Polygonal Domains: J.L. Gracia and D. Irisarri.- 2. Global Uniform Convergence for Weakly Coupled System of Singularly Perturbed Convection Diffusion Problems: S. Chandra Sekhara Rao, Varsha Srivastava, and Abhay Kumar Chaturvedi.- 3. A Parameter Uniform Fitted Mesh Method for a Weakly Coupled System of Three Partially Singularly Perturbed Convection-Diffusion Equations: Valarmathi Sigamani, Saravana Sankar Kalaiselvan, John J H Miller.- 4. Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type: Parthiban Saminathan and Franklin Victor.- 5. A First-Order Convergent Parameter Uniform Numerical Method for a Singularly Perturbed Second-Order Delay-Differential Equation of Reaction-Diffusion Type with a Discontinuous Source Term: Manikandan Mariappan, John J H Miller, Valarmathi Sigamani.- 6. Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems: R. Mahendran and V. Subburayan.- 7. A Parameter Uniform Essentially First-Order Convergence of a Fitted Mesh Method for a Class of Parabolic Singularly Perturbed Robin Problem for a System of Reaction-Diffusion Equations: R. Ishwariya, Valarmathi Sigamani, John J H Miller.- 8. Finite Difference Method and Analysis for First-Order Hyperbolic Delay Differential Equations: S. Karthick and V. Subburayan.- 9. Fitted Mesh Methods for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations: Saravana Sankar Kalaiselvan, Valarmathi Sigamani, John J H Miller.- 10. Numerical Analysis of a Finite Difference Method for a Linear System of Singularly Perturbed Parabolic Delay Differential Reaction-Diffusion Equations with Discontinuous Source Terms: Parthiban Saminathan and Franklin Victor.
£97.49
Springer Verlag, Singapore Fractional Derivative Modeling in Mechanics and
Book SynopsisThis textbook highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes in details the research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also includes latest findings, such as variable order derivative, distributed order derivative and its applications. Different from other textbooks in this subject, the book avoids lengthy mathematical demonstrations, and presents the theories in close connection to the applications in an easily readable manner. This textbook is intended for students, researchers and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.Table of ContentsPreface Chapter 1 Introduction 1.1 History of fractional calculus 1.2 Geometric and physical interpretation of fractional derivative equation 1.3 Application in science and engineering Chapter 2 Mathematical foundation of fractional calculus 2.1 Definition of fractional calculus 2.2 Properties of fractional calculus 2.3 Fourier and Laplace transform of the fractional calculus 2.4 Analytical solution of fractional-order equations 2.5 Questions and discussions Chapter 3 Fractal and fractional calculus 3.1 Fractal introduction and application 3.2 The relationship between fractional calculus and fractal Chapter 4 Fractional diffusion model 4.1 The fractional derivative anomalous diffusion equation 4.2 Statistical model of the acceleration distribution of turbulence particle 4.3 Lévy stable distributions 4.4 Stretched Gaussian distribution 4.5 Tsallis distribution 4.6 Ito formula 4.7 Random walk model Chapter 5 Typical applications of fractional differential equations 5.1 Power-law phenomena and non-gradient constitutive relation 5.2 Fractional Langevin equation 5.3 The complex damped vibration 5.4 Viscoelastic and rheological models 5.5 The power law frequency dependent acoustic dissipation 5.6 The fractional variational principle of mechanics 5.7 Fractional Schrödinger equation 5.8 Other application fields 5.9 Some applications of fractional calculus in biomechanics 5.10 Some applications of fractional calculus in the modeling of drug release process Chapter 6 Numerical methods for fractional differential equations 6.1 Time fractional differential equations 6.2 Space fractional differential equations 6.3 Open issues of numerical methods for FDEs Chapter 7 Current development and perspectives of fractional calculus 7.1 Summary and Discussion 7.2 Perspectives Appendix I Special Functions Appendix II Related electronic resources of fractional dynamics
£41.24
Springer Verlag, Singapore The Special Theory of Relativity: A Mathematical Approach
Book SynopsisThis textbook expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics, and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.Table of ContentsPre-Relativity and Galilean Transformations.- Michelson-Morley Experiment and Velocity of Light.- Lorentz Transformations.- Mathematical Properties of Lorentz Transformations.- More mathematical Properties of Lorentz Transformations.- Geometrical Interpretation of spacetime.- Relativistic Velocity and Acceleration.- Four Dimensional World.- Mass in Relativity.- Relativistic Dynamics.- Photon in Relativity.- Relativistic Lagrangian and Hamiltonian.- Electrodynamics in Relativity.- Electromagnetic waves.- Relativistic Mechanics of Continua.
£999.99
Springer Verlag, Singapore Optical Waveguide Theory: Mathematical Models,
Book SynopsisThis book addresses the most advanced to-date mathematical approach and numerical methods in electromagnetic field theory and wave propagation. It presents the application of developed methods and techniques to the analysis of waves in various guiding structures —shielded and open metal-dielectric waveguides of arbitrary cross-section, planar and circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media and layered media with absorption. It also looks into spectral properties of wave propagation for the waveguide families being considered, and the relevant mathematical techniques such as spectral theory of non-self-adjoint operator-valued functions are described, including rigorous proofs of the existence of various types of waves. Further, numerical methods constructed on the basis of the presented mathematical approach and the results of numerical modeling for various structures are also described in depth. The book is beneficial to a broad spectrum of readers ranging from pure and applied mathematicians in electromagnetic field theory to researchers and engineers who are familiar with mathematics. Further, it is also useful as a supplementary text for upper-level undergraduate students interested in learning more advanced topics of mathematical methods in electromagnetics.Table of ContentsChapter 1.IntroductionThe purpose of this chapter is to provide a survey of our book by placing what we have to say in a historical context. Chapter 2. Some concepts and definitions of the set theory, function theory, and operator theoryThe purpose of this chapter is to present an overview of the mathematical apparatus used in this book, to give theorems and proofs used in the subsequent book chapters. The presentation focuses in particular on the necessary elements of the spectral theory of nonselfadjoint operator-valued functions. Chapter 3. Shielded regular waveguides of arbitrary cross-sectionThis chapter is devoted to the analysis of the wave propagation in shielded waveguides of arbitrary cross-section filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. Spectral properties of the problems of wave propagation for the considered waveguide family are investigated. Definitions of various types of waves are formulated, the existence and distribution of the wave spectra are studied. Chapter 4. Planar waveguidesThis chapter addresses waves in plane waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. Spectral properties of the problems of wave propagation for this family of waveguides are investigated in detail. Chapter 5. Waveguides of circular cross-sectionThis chapter is devoted to the analysis of wave propagation in circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. The notions, results and methods developed in Chapter 3 are applied and concretized for this family of waveguides. The existence of real and complex normal waves and analysis of the distribution of the wave spectra are backed by a variety of numerical results. Chapter 6. Open regular waveguides of arbitrary cross-sectionIn this chapter, open waveguides of arbitrary cross-section are considered; the material filling consists of inhomogeneous dielectrics, metamaterials, chiral and anisotropic media, and media with absorption. The problems on normal waves are formulated with the conditions at infinity that enable one to take into account all types of waves, including complex and leaky. Spectral properties of the problems of wave propagation in open waveguides are investigated using the specially developed extensions of the spectral theory and particularly the operator-pencil approach. Chapter 7. Conclusion
£113.99
Springer Verlag, Singapore Physical Kinetics: Classical and Quantum Problems
Book SynopsisThis book includes problems based on the material in the course of physical kinetics for the students of general and applied physics. It contains 60 problems with detailed solutions. The comments to the problems reflect the connection with the problems and methods of modern physical kinetics. A brief introduction gives the necessary information for solving and understanding the problems. The book is proposed for students and postgraduates studying the theoretical physics. The book is used as a supplement to the textbooks published on physical kinetics. The purpose of the book is to help students in training the practical skills and mastering the basic elements of physical kinetics. To understand the subject matter, it is sufficient to know the traditional courses of theoretical physics.Table of Contents1. Brief reminders 1.1. The Boltzmann transport equation 1.2. The generalized susceptibility and the linear response 1.3. The fluctuation-dissipation theorem 1.4. The Onsager reciprocal relations 1.5. The Lindblad master equation 2. Problems 2.1. The Langevin equation and the fluctuation-dissipation theorem 2.2. The Boltzmann transport equation in the τ-approximation: the thermoelectric effects in conductors 2.3. Galvanomagnetic effects in metals 2.4. Kinetic phenomena in a metal and normal Fermi liquid 2.5. Electron-phonon scattering in a metal: the transport coefficients 2.6. The electron scattering with magnetic impurities: the Kondo effect 2.7. Weak localization effects in a metal with impurities 2.8. Ballistic electron transport in the mesoscopic systems 2.9. The rarified Bose and Fermi gases 2.10. The hopping Mott conductivity and the Coulomb gap 2.11. Kinetics of phonons and thermal conductivity in dielectrics 2.12. The hydrodynamics of normal and superfluid liquids: sound oscillations and energy dissipation 2.13. Kapitza resistance and kinetic phenomena at the superfluidsolid helium interface 2.14. Collisionless plasma: the permittivity and the longitudinal and transverse oscillations 2.15. Kinetics of first-order phase transitions: melting and solidification 2.16. Macroscopic quantum tunneling 2.17. Macroscopic quantum nucleation 2.18. Open quantum systems: the Lindblad equation 2.19. Elements of diagrammatic Keldysh technique for non-equilibrium systems 3. Solutions of Problems 3.1. The Langevin equation and the fluctuation-dissipation theorem 3.2. The Boltzmann transport equation in the _-approximation: the thermoelectric effects in conductors 3.3. Galvanomagnetic effects in metals 3.4. Kinetic phenomena in a metal and normal Fermi liquid 3.5. Electron-phonon scattering in a metal: the transport coefficients 3.6. The electron scattering with magnetic impurities: the Kondo effect 3.7. Weak localization effects in a metal with impurities 3.8. Ballistic electron transport in the mesoscopic systems 3.9. The rarified Bose and Fermi gases 3.10. The hopping Mott conductivity and the Coulomb gap 3.11. Kinetics of phonons and thermal conductivity in dielectrics 3.12. The hydrodynamics of normal and superfluid liquids: sound oscillations and energy dissipation 3.13. Kapitza resistance and kinetic phenomena at the superfluidsolid helium interface 3.14. Collisionless plasma: permittivity and the longitudinal and transverse oscillations 3.15. Kinetics of first-order phase transitions: melting and solidification 3.16. Macroscopic quantum tunneling 3.17. Macroscopic quantum nucleation 3.18. Open quantum systems: the Lindblad equation 3.19. Elements of diagrammatic Keldysh technique for non-equilibrium systems Bibliography Index
£66.49
Springer Verlag, Singapore Non-Bloch Band Theory of Non-Hermitian Systems
Book SynopsisThis book constructs a non-Bloch band theory and studies physics described by non-Hermitian Hamiltonian in terms of the theory proposed here.In non-Hermitian crystals, the author introduces the non-Bloch band theory which produces an energy spectrum in the limit of a large system size. The energy spectrum is then calculated from a generalized Brillouin zone for a complex Bloch wave number. While a generalized Brillouin zone becomes a unit circle on a complex plane in Hermitian systems, it becomes a circle with cusps in non-Hermitian systems. Such unique features of the generalized Brillouin zone realize remarkable phenomena peculiar in non-Hermitian systems. Further the author reveals rich aspects of non-Hermitian physics in terms of the non-Bloch band theory. First, a topological invariant defined by a generalized Brillouin zone implies the appearance of topological edge states. Second, a topological semimetal phase with exceptional points appears, The topological semimetal phase is unique to non-Hermitian systems because it is caused by the deformation of the generalized Brillouin zone by changes of system parameters. Third, the author reveals a certain relationship between the non-Bloch waves and non-Hermitian topology.Table of ContentsIntroduction.- Hermitian Systems and Non-Hermitian Systems.- Non-Hermitian Open Chain and Periodic Chain.- Non-Bloch Band Theory of Non-Hermitian Systems and Bulk-Edge Correspondence.- Topological Semimetal Phase With Exceptional Points in One-Dimensional Non-Hermitian Systems.- Non-Bloch Band Theory in Bosonic Bogoliubov-de Gennes Systems.- Summary and Outlook.
£123.49
Springer Verlag, Singapore Lie Theory and Its Applications in Physics:
Book SynopsisThis volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021.Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field.The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras.This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.Table of ContentsPlenary Talks: T. Kobayashi, Multiplicity in Restricting Minimal Representations.- Yang-Hui He, From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook.- I. Todorov, Octonionic Clifford Algebra for the Internal Space of the Standard Model.- P. Vitale, The Jacobi Sigma Model.- P. Aschieri, Levi-Civita Connections on Braided Algebras.- N. Bobev, Notes on AdS4 Holography and Higher-Derivative Supergravity.- T. Brzezinski, Homothetic Rota-Baxter Systems and Dyckm-Algebras.- M. Henkel, Quantum Dynamics Far from Equilibrium: a Case Study in the Spherical Model.- Hankyung Ko and V. Mazorchuk, On First Extensions in S -Subcategories of O.- Robert de Mello Koch and Sanjaye Ramgoolam, Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories.- G. Manolakos, G. Patellis and G. Zoupanos, Reducing the N = 1, 10D E8 Gauge Theory over a Modified Flag Manifold.- String Theories, (Super-)Gravity, Cosmology: Andre Alves Lima, Galen M. Sotkov and Marian Stanishkov, Ramond States of the D1-D5 CFT Away from the Free Orbifold Point.- L. Anguelova, Primordial Black Hole Generation in a Two-field Inflationary Model.- D. Staicova, Late Time Cosmic Acceleration with Uncorrelated Baryon Acoustic Oscillations.- L. Ravera, On the Hidden Symmetries of D = 11 Supergravity.- F. Nieri, Defects at the Intersection: the Supergroup Side.- T. Masuda, A New S-matrix Formula and Extension of the State Space in Open String Field Theory.- E. Boffo, Dual Dilaton with R and Q Fluxes.- Representation Theory: E. Poletaeva, On 1-Dimensional Modules over the Super-Yangian of the Superalgebra Q(1).- N. I. Stoilova and Joris Van der Jeugt, A Klein Operator for Paraparticles.- G. Sengor and C. Skordis, Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter.- S. Aoki, Janos Balog, T. Onogi, and S. Yokoyama, Bulk Reconstruction from a Scalar CFT at the Boundary by the Smearing with the Flow Equation.- Y. Wang and Chih-Hao Fu, Building Momentum Kernel from Shapovalov Form.- Ilia Smilga, Action of w0 on VL for Orthogonal and Exceptional Groups.- Ood Shabtai, Pairs of Spectral Projections of Spin Operators.- Integrable Systems: Jean-Emile Bourgine, Algebraic Engineering and Integrable Hierarchies.- Cestm ˇ ´ır Burd´ık and O. Navratil, Nested Bethe Ansatz for RTT–Algebra An.- O. Vaneeva, O. Magda and A. Zhalij, Lie Reductions and Exact Solutions of Generalized Kawahara Equations.- Y. Nasuda, Several Exactly Solvable Quantum Mechanical Systems and the SWKB Quantization Condition.- A. Pribytok, Automorphic Symmetries and AdSn Integrable Deformations.- Applications to Quantum Theory: M. Kirchbach, T. Popov, and J.-A. Vallejo, The Conformal-Symmetry–Color-Neutrality Connection in Strong Interaction.- I. Salom and N. Manojlovic, sℓ(2) Gaudin Model with General Boundary Terms.- T. Barron and A. Kazachek, Entanglement of Mixed States in Kahler Quantization.- J. Alnefjord, A. Lifson, C. Reuschle, and M. Sjodahl, The Chirality-Flow Formalism for Standard Model Calculations.- F. Kuipers, Spacetime Stochasticity and Second Order Geometry.- Special Mathematical Results: P. Moylan, Velocity Reciprocity in Flat and Curved Space-Time.- S. Stoimenov and M. Henkel, Meta-Schrodinger Transformations.- Hulya Arg ¨ uz¨, The Quantum Mirror to the Quartic del Pezzo Surface.- A. Ganchev, Bidirectional Processes - in Category Theory, Physics, Engineering.- Gauge Theories and Applications: Richard S. Garavuso, Nonholomorphic Superpotentials in Heterotic Landau-Ginzburg Models.- F. Feruglio, Automorphic Forms and Fermion Masses.- T. Ishibashi, Wilson Lines and Their Laurent Positivity.- Maro Cvitan, Predrag Dominis Prester, Stefano Gregorio Giaccari, Mateo Paulisiˇ c´, and Ivan Vukovic´, Gauging Higher-Spin-Like Symmetries Using the Moyal Product.- N. Ikeda and S. Sasaki, Integration of Double Field Theory Algebroids and Pre-rackoid in Doubled Geometry.- H. Mori, S. Sasaki, K. Shiozawa, Doubled Aspects of Algebroids and Gauge Symmetry in Double Field Theory.- C. Anghel and D. Cheptea, Lie Algebroids and Weight Systems.- Structures on Lie Groups and Lie Algebras: K. Arashi, Visible Actions of Certain Affine Transformation Groups of a Siegel Domain of the Second Kind.- A. Brus, Jiˇr´ı Hrivnak´ and L. Motlochova´, Quantum Particle on Lattices in Weyl Alcoves.- A. Latorre and L. Ugarte, Abelian J-Invariant Ideals on Nilpotent Lie Algebras.- Alexis Langlois-Remillard, The Dihedral Dunkl–Dirac Symmetry Algebra with Negative Clifford Signature.- Tekin Karadag˘, Lie Structure on Hopf Algebra Cohomology.- Esther Garcıa, Miguel Gomez Lozano, and Ruben Munoz Alcazar, Filtration Associated to an Abelian Inner Ideal and the Speciality of the Subquotient of a Lie Algebra.- Esther Garc´ıa, Miguel Gomez Lozano, and Guillermo Vera de Salas, Nilpotent Inner Derivations in Prime Superalgebras.
£159.99
Springer Verlag, Singapore Nonlinear Waves: From Dissipative Solitons to
Book SynopsisThis book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.Table of Contents
£123.49
Springer Verlag, Singapore Synergies in Analysis, Discrete Mathematics, Soft
Book SynopsisThis book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23–27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).Table of ContentsPART I ANALYSIS AND MODELLINGThe Second- and Third-order Hermitian Toeplitz Determinants for Some Subclasses of Analytic Functions Associated with Exponential Function,P.Gurusamy, R. Jayasankar and S. SivasubramanianSome Results on a Starlike Class with Respect to $(j, m) $-symmetric FunctionsK. Renuka Devi, S. Sivasubramanian, Hamid Shamsan and S. LathaExperimental Evaluation of Four Intermediate Filters to Improve the Motion Field EstimationVanel Lazcano and Claudio Isa-MohorOn the $s^{th}$ Derivative of a PolynomialBarchand Chanam and Kshetrimayum KrishnadasOn the Problem of Pricing a Double Barrier Option in a Modified Black–Scholes Environment G. Venkiteswaran and S. UdayabaskaranCaputo Sequential Fractional Differential Equations with ApplicationsAghalaya S. Vatsala and Govinda PageniPART II DISCRETE MATHEMATICS AND APPLICATIONSHerscovici’s Conjecture on Product of Some Complete Bipartite GraphsA. Lourdusamy and S. Saratha NellainayakiOn Fault-Tolerant Metric Dimension of Heptagonal Circular Ladder and Its Related GraphsSunny Kumar Sharma and Vijay Kumar BhatBKS Fuzzy Inference Employing h-ImplicationsSayantan Mandal and Balasubramaniam Jayaram Note on Distributivity of Different String Operations over Language SetsUjjwal Kumar Mishra, Kalpana Mahalingam and Rama RaghavanA Generalization of Chi-binding FunctionsM. A. Shalu and T. P. SandhyaA Short Proof of Ore’s f-factor Theorem using FlowsSriraman Sridharan and Patrick VilamajoPART III FUZZY SETS AND SOFT COMPUTINGA Decision-making Problem Involving Soft Fuzzy Number Valued Information System: Energy Efficient Light Emitting Diode BlubsFelbin C. Kennedy, Masilla Moses Kennedy, Arul Roselet Meryline S. andJayachandiran M.Role of Single-valued Linear Octagonal Neutrosophic Numbers in Multi-attribute Decision-making ProblemsSubasri S., Arul Roselet Meryline S. and Felbin C. Kennedy
£82.49
Springer Verlag, Singapore Einstein Constraints and Ricci Flow: A
Book SynopsisThis book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike. Table of ContentsIntroduction.- Geometric preliminaries.- Ricci flow background.- Ricci flow conjugation of initial data sets.- Concluding remarks.
£94.99
Springer-Verlag GmbH Proceedings of the 2nd International Conference on Sustainability and Emerging Technologies for Smart Manufacturing
£246.39
Springer Transverse Instability of Solitary Waves
Book SynopsisChapter 1 Introduction.- Chapter 2 Literature Review.- Chapter 3 Multisymplectic Wave Equations and Dirac Operators.- Chapter 4 Solitary Wave Solutions and Their Properties.- Chapter 5 Linearisation about Solitary Waves.- Chapter 6 Spectral Stability and the Evans Function.- Chapter 7 Derivatives of the Evans Function.- Chapter 8 Summary of Hypotheses Used.- Chapter 9 Example: Nonlinear Wave Equation in 2 + 1.- Chapter 10 Concluding Remarks.
£107.99
Springer Fractional Derivatives for Physicists and
Book Synopsis
£134.99
Springer Mathematical Foundations for PostQuantum Cryptography
Book Synopsis1. Algebraic Geometry.- 2. Number Theory.- 3. Theory of Computation.- 4. Quantum Computation.- 5. Quantum Field Theory.- 6. Mathematical Physics.- 7. Representation Theory.- 8. Lattice Theory.- 9. Multivariate Polynomial Theory.- 10. Data Encryption.- 11. Digital Signature.- 12. Searchable Encryption.- 13. Obfuscation.- 14. Privacy Protection.- 15. Copyright Protection.- 16. ID-based Encryption.
£42.74
Springer Verlag, Singapore Space–Time Conservation Element and Solution
Book SynopsisThis open access book introduces the fundamentals of the space–time conservation element and solution element (CESE) method, which is a novel numerical approach for solving equations of physical conservation laws. It highlights the recent progress to establish various improved CESE schemes and its engineering applications. With attractive accuracy, efficiency, and robustness, the CESE method is particularly suitable for solving time-dependent nonlinear hyperbolic systems involving dynamical evolutions of waves and discontinuities. Therefore, it has been applied to a wide spectrum of problems, e.g., aerodynamics, aeroacoustics, magnetohydrodynamics, multi-material flows, and detonations. This book contains algorithm analysis, numerical examples, as well as demonstration codes. This book is intended for graduate students and researchers who are interested in the fields such as computational fluid dynamics (CFD), mechanical engineering, and numerical computation.Table of ContentsIntroduction.- Non-dissipative Core Scheme of CESE Method.- CESE Schemes with Numerical Dissipation.- Multi-Dimensional CESE Schemes on Cartesian Meshes.- CESE Schemes on Unstructured Meshes.- High-Order CESE Schemes.- Numerical Features of CESE Schemes.- Application: Hypersonic Aerodynamics.- Application: Compressible Multi-Fluid.- Other Applications.- Summary.
£31.86
Springer Verlag, Singapore Macdonald Polynomials: Commuting Family of q-Difference Operators and Their Joint Eigenfunctions
Book SynopsisThis book is a volume of the Springer Briefs in Mathematical Physics and serves as an introductory textbook on the theory of Macdonald polynomials. It is based on a series of online lectures given by the author at the Royal Institute of Technology (KTH), Stockholm, in February and March 2021. Macdonald polynomials are a class of symmetric orthogonal polynomials in many variables. They include important classes of special functions such as Schur functions and Hall–Littlewood polynomials and play important roles in various fields of mathematics and mathematical physics. After an overview of Schur functions, the author introduces Macdonald polynomials (of type A, in the GLn version) as eigenfunctions of a q-difference operator, called the Macdonald–Ruijsenaars operator, in the ring of symmetric polynomials. Starting from this definition, various remarkable properties of Macdonald polynomials are explained, such as orthogonality, evaluation formulas, and self-duality, with emphasis on the roles of commuting q-difference operators. The author also explains how Macdonald polynomials are formulated in the framework of affine Hecke algebras and q-Dunkl operators.Table of ContentsOverview of Macdonald polynomials.- Preliminaries on symmetric functions.- Schur functions.- Macdonald polynomials: Definition and examples.- Orthogonality and higher order q-difference operators.- Self-duality, Pieri formula and Cauchy formulas.- Littlewood–Richardson coefficients and branching coefficients.- Affine Hecke algebra and q-Dunkl operators (overview).
£29.99
Springer Topological Phases in Condensed Matter Physics
Book SynopsisSymmetry and Topology.- Topology in One Dimensional (1D) tight binding Models.- Quantum Hall Eect.- Graphene: A Hobby Horse for studying Topology.- Anomalous Quantum Hall and Spin Hall eects in Graphene.- Fractional Quantum Hall Eect: Role of Coulomb Interactions.- Topology Beyond Fermionic Systems.- Appendix.- Postscript.
£999.99
Taylor & Francis Ltd A First Course In Chaotic Dynamical Systems
a huge range and FREE tracked UK delivery on ALL orders.
£80.74
Taylor & Francis Ltd Linear Algebra An InquiryBased Approach Textbooks in Mathematics
a huge range and FREE tracked UK delivery on ALL orders.
£80.74
Taylor & Francis Ltd Spectral Methods Using Multivariate Polynomials On The Unit Ball Chapman HallCRC Monographs and Research Notes in Mathematics
a huge range and FREE tracked UK delivery on ALL orders.
£147.25
Taylor & Francis Ltd The Method of Moments in Electromagnetics
a huge range and FREE tracked UK delivery on ALL orders.
£175.75
Taylor & Francis Ltd Coupled Systems Theory Models and Applications in Engineering 22 Chapman HallCRC Numerical Analysis and Scientific Computing Series
a huge range and FREE tracked UK delivery on ALL orders.
£58.89
Taylor & Francis Ltd Mimetic Discretization Methods
a huge range and FREE tracked UK delivery on ALL orders.
£58.89
Taylor & Francis Ltd The Divergence Theorem and Sets of Finite Perimeter
a huge range and FREE tracked UK delivery on ALL orders.
£58.89
