Mathematical / Computational / Theoretical physics Books
MP-AMM American Mathematical Hyperbolic Dynamics Fluctuations and Large
Book SynopsisThe papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas.Table of Contents Hyperbolic dynamics, fluctuations and large deviations by D. Dolgopyat, Y. Pesin, M. Pollicott, and L. Stoyanov Large deviations and thermodynamical formalism: The almost Borel structure of diffeomorphisms with some hyperbolicity by J. Buzzi Lectures on large deviations in probability and dynamical systems by Y. Kifer Thermodynamic formalism for countable Markov shifts by O. M. Sarig Limit theorems for dynamical systems: Limit theorems for horocycle flows by G. Forni Limit theorems in dynamical systems using the spectral method by S. Gouezel Kinetic limits of dynamical systems by J. Marklof Additional topics: Limit theorems for toral translations by D. Dolgopyat and B. Fayad Spectral gap properties and limit theorems for some random walks and dynamical systems by Y. Guivarc'h The martingale approach after Varadhan and Dolgopyat by J. De Simoi and C. Liverani
£110.70
MP-AMM American Mathematical Singular Perturbation in the Physical Sciences
Book SynopsisThis book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small centre manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included.Trade ReviewIn all, this book is a valuable completion to the literature on singular perturbations. It might be the first reference to read but also a good auxiliary in understanding more specialized books or papers."—Vladimir Răsvan, Zentralblatt MATH"This is a lucid textbook written in an easy style. The book will be useful to researchers and graduate students in various areas of mathematics, mechanics, and physics."—V.A. Sobolev, Mathematical ReviewsTable of Contents What is a singular perturbation? Asymptotic expansions Matched asymptotic expansions Matched asymptotic expansions in PDE Prandtl boundary layer theory Modulated oscillations Modulation theory by transforming variables Nonlinear resonance Bibliography Index
£108.00
MP-AMM American Mathematical Random Growth Models
Book SynopsisBased on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held in 2017. The articles give an introduction to the most-studied models; first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation.Table of Contents M. Damron, Random growth models: Shape and convergence rate J. Hanson, Infinite geodesics, asymptotic directions, and Busemann functions in first-passage percolation P. Sosoe, Fluctuations in first-passage percolation F. Rassoul-Agha, Busemann functions, geodesics, and the competition interface for directed last-passage percolation T. Seppalainen, The corner growth model with exponential weights I. Corwin, Exactly solving the KPZ equation Index.
£101.70
MP-AMM American Mathematical Classification and Identification of Lie Algebras
Book SynopsisServes as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible.Table of Contents Title page Contents Preface Acknowledgments Part 1. General theory Introduction and motivation Basic concepts Invariants of the coadjoint representation of a Lie algebra Part 2. Recognition of a Lie algebra given by its structure constants Identification of Lie algebras through the use of invariants Decomposition into a direct sum Levi decomposition. Identification of the radical and Levi factor The nilradical of a Lie algebra Part 3. Nilpotent, solvable and Levi decomposable Lie algebras Nilpotent Lie algebras Solvable Lie algebras and their nilradicals Solvable Lie algebras with abelian nilradicals Solvable Lie algebras with Heisenberg nilradical Solvable Lie algebras with Borel nilradicals Solvable Lie algebras with filiform and quasifiliform nilradicals Levi decomposable algebras Part 4. Low-dimensional Lie algebras Structure of the lists of low-dimensional Lie algebras Lie algebras up to dimension 3 Four-dimensional Lie algebras Five-dimensional Lie algebras Six-dimensional Lie algebras Bibliography Index
£103.50
MP-AMM American Mathematical Nonlinear Dispersive Waves and Fluids
Book SynopsisAddresses the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.Table of Contents N. Basharat, Y. Hu, and S. Zheng, Blowup rate for mass critical rotational nonlinear Schrodinger equations D. Cao, T. Mengesha, and T. Phan, Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients R. Denlinger, Virial estimates for hard spheres Y. Du, G. Chen, and J. Liu, The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited, I: The critical generalized KdV equation L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited, II: The supercritical Zakharov-Kuznetsov equation C. Flores, S. Oh, and D. Smith, Stabilization of dispersion-generalized Benjamin-Ono D. Garrisi and V. Georgiev, Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one S. Gustafson and D. Roxanas, Below-threshold solutions of a focusing energy-critical heat equation in $\mathbb{R}^4$ D. Li and X. Zhang, A regularity upgrade of pressure S. Miao, On large future-global-in-time solutions to energy-supercritical nonlinear wave equation J. Murphy, The nonlinear Schrodinger equation with an inverse-square potential Y. Shao and C. Wang, The harmonic map heat flow on conic manifolds K. Yamazaki, On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian J. Zhang, S. Zheng, and S. Zhu, Orbital stability of standing waves for fractional Hartree equation with unbounded potentials.
£103.50
MP-AMM American Mathematical Mathematical Theory of Scattering Resonances
Book SynopsisFocuses on the simplest case of scattering by compactly supported potentials, and provides pointers to modern literature where more general cases are studied. The book also presents an approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.Trade ReviewThis is an up to date account of modern mathematical scattering theory with an emphasis on the deep interplay between the location of the scattering poles or resonances, and the underlying dynamics and geometry. The masterful exposition reflects the authors' significant roles in shaping this very active field. A must read for researchers and students working in scattering theory or related areas." - Peter Sarnak, Institute for Advanced Study"This is a very broad treatise of the modern theory of scattering resonances, beautifully written with a wealth of important mathematical results as well as applications, motivations and numerical and experimental illustrations. For experts, it will be a basic reference and for non-experts and graduate students an appealing and quite accessible introduction to a fascinating field with multiple connections to other branches of mathematics and to physics." - Johannes Sjostrand, Universite de Bourgogne"Resonance is the Queen of the realm of waves. No other book addresses this realm so completely and compellingly, oscillating effortlessly between illustration, example, and rigorous mathematical discourse. Mathematicians will find a wonderful array of physical phenomena given a solid intuitive and mathematical foundation, linked to deep theorems. Physicists and engineers will be inspired to consider new realms and phenomena. Chapters travel between motivation, light mathematics, and deeper mathematics, passing the baton from one to the other and back in a way that these authors are uniquely qualified to do." - Eric J. Heller, Harvard UniversityTable of Contents Introduction Potential scattering: Scattering resonances in dimension one Scattering resonances in odd dimensions Geometric scattering: Black box scattering in $\mathbb{R}^n$ Scattering on hyperbolic manifolds Resonances in the semiclassical limit: Resonance-free regions Resonances and trapping Appendices: Notation Spectral theory Fredholm theory Complex analysis Semiclassical analysis Bibliography Index.
£112.10
American Mathematical Society Vertex Operator Algebras Number Theory and
Book SynopsisExplores active research on vertex operator algebras and vector-valued modular forms and offers original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these, and open problems from some of the leaders in these areas.Table of Contents P. Bantay, Orbifold deconstruction: A computational approach. K. Barron, N. Vander Werf, and J. Yang, The level one Zhu algebra for the Virasoro vertex operator algebra. L. Candelori, J. Fogliasso, C. Marks, and S. Moses, Period relations for Riemann surfaces with many automorphisms. A. Ros Camacho, On the Landau-Ginzburg/conformal field theory correspondence. J. F. R. Duncan, From the monster to Thompson to O'Nan. C. Franc and S. Rayan, Nonabelian Hodge theory and vector valued modular forms; R. L. Griess, Jr., Research topics in finite groups and vertex algebras. C. H. Lam, Automorphism group of an orbifold vertex operator algebra associated with the Leech lattice. L. Long, Some numeric hypergeometric supercongruences. K. Nagatomo, G. Mason, and Y. Sakai, Vertex operator algebras with central charge 8 and 16. K. Nagatomo, Y. Kurokawa, and Y. Sakai, Pseudo-characters of the symplectic fermions and modular linear differential equations. G. Mason, Five not-so-easy pieces: Open problems with vertex rings. M. Miyamoto, Vertex operator algebras and modular invariance..
£110.20
MP-AMM American Mathematical Asymptotics of Random Matrices and Related Model
Book SynopsisDescribes a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations. The author shows how these equations are derived, and how to obtain the concentration of measure estimates required to study these equations asymptotically.Table of Contents Introduction The example of the GUE Wigner random matrices Beta-ensembles Discrete beta-ensembles Continuous beta-models: The several cut case Several matrix-ensembles Universality for beta-models Bibliography Index
£45.90
MP-AMM American Mathematical The YangMills Heat Equation with Finite Action in
Book Synopsis
£67.50
MP-AMM American Mathematical Partial Compactification of Monopoles and Metric
Book SynopsisView the abstract.
£68.40
American Mathematical Society Curvature of Space and Time with an Introduction
Book SynopsisIntroduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein field equations.Table of Contents Introduction to Riemannian geometry Differential calculus with tensors Curvature General relativity Introduction to geometry analysis Bibliography Index
£54.15
American Mathematical Society On Pseudoconformal BlowUp Solutions to the
Book SynopsisView the abstract.
£67.45
MP-AMM American Mathematical Spiral Waves Linear and Nonlinear Theory
Book Synopsis
£68.40
American Mathematical Society The Mathematical Analysis of the Incompressible
Book SynopsisProvides graduate students with exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.Table of Contents Ideal incompressible fluids: The Euler equations Existence of solutions and continuation criteria for Euler Incompressible viscous fluids: The Navier-Stokes equations Leray-Hopf weak solutions of Navier-Stokes Mild solutions of Navier-Stokes A survey of some advanced topics Appendix Bibliography Index
£67.50
MP-AMM American Mathematical Dynamics Near the Subcritical Transition of the
Book SynopsisThe second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re.
£67.50
American Mathematical Society From Representation Theory to Mathematical Physics and Back
£104.40
MP-AMM American Mathematical Recovery Methodologies Regularization and
Book SynopsisIntroduces the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. By avoiding extreme technicalities and elaborate proof techniques, this is an accessible resource for students and researchers.Table of Contents Introductory remarks: Constituents of the univariate antenna problem Regularization tools: Functional and Fourier analytic auxiliaries Regularization methodologies: Matricial methodologies of resolution Compact operator methodologies of resolution Example realizations light: Univariate differentiation Reconstruction and regularization methods Regularization examples: Regularization methodologies in geotechnology Sampling tools: Lattice point and special function theoretic auxiliaries Sampling methodologies: Sampling over continuously connected pointsets Sampling over discretely given pointsets Polyharmonic finite bandwidth sampling Polyharmonic infinite bandwidth sampling Polymetaharmonic finite bandwidth sampling Polymetaharmonic infinite bandwidth sampling Sampling examples: Sampling methodologies in technology Concluding remarks: Recovery as interconnecting whole List of symbols Bibliography Index
£103.50
Springer Spinors in Hilbert Space
Book Synopsis1. Hilbert Space.- 2. Spinors.- Finite Number of Dimensions.- 3. Rotations in n Dimensions.- 4. Null Vectors and Null Planes.- 5. The Independence Theorem.- 6. Specification of a Null Plane without Its Coordinates.- 7. Matrix Notation.- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation.- 9. Complex Rotations.- 10. The Noncommutative Algebra.- 11. Rotation Operators.- 12. Fixation of the Coefficients of Rotation Operators.- 13. The Ambiguity of Sign.- 14. Kets and Bras.- 15. Simple Kets.- Even Number of Dimensions.- 16. The Ket Matrix.- 17. The Two-Ket-Matrix Theorem.- 18. The Connection between Two Ket Matrices.- 19. The Representation of Kets.- 20. The Representative of a Simple Ket. General.- 21. The Representative of a Simple Ket. Special Cases.- 22. Fixation of the Coefficients of Simple Kets.- 23. The Scalar Product Formula.- Infinite Number of Dimensions.- 24. The Need for Bounded Matrices.- 25. The Infinite Ket Matrix.- 26. Passage from One Ket Matrix to Another.Table of Contents1. Hilbert Space.- 2. Spinors.- Finite Number of Dimensions.- 3. Rotations in n Dimensions.- 4. Null Vectors and Null Planes.- 5. The Independence Theorem.- 6. Specification of a Null Plane without Its Coordinates.- 7. Matrix Notation.- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation.- 9. Complex Rotations.- 10. The Noncommutative Algebra.- 11. Rotation Operators.- 12. Fixation of the Coefficients of Rotation Operators.- 13. The Ambiguity of Sign.- 14. Kets and Bras.- 15. Simple Kets.- Even Number of Dimensions.- 16. The Ket Matrix.- 17. The Two-Ket-Matrix Theorem.- 18. The Connection between Two Ket Matrices.- 19. The Representation of Kets.- 20. The Representative of a Simple Ket. General.- 21. The Representative of a Simple Ket. Special Cases.- 22. Fixation of the Coefficients of Simple Kets.- 23. The Scalar Product Formula.- Infinite Number of Dimensions.- 24. The Need for Bounded Matrices.- 25. The Infinite Ket Matrix.- 26. Passage from One Ket Matrix to Another.- 27. The Various Kinds of Ket Matrices.- 28. Failure of the Associative Law.- 29. The Fundamental Commutators.- 30. Boson Variables.- 31. Boson Emission and Absorption Operators.- 32. Infinite Determinants.- 33. Validity of the Scalar Product Formula.- 34. The Energy of a Boson.- 35. Physical Application.
£94.99
Birkhauser Boston Infinite Dimensional Lie Algebras An Introduction Progress in Mathematics 44
Table of Contents1. Basic definitions.- 2. The invariant bilinear form and the generalized Casimir operator.- 3. Integrable representations and the Weyl group of a Kac-Moody algebra.- 4. Some properties of generalized Cartan matrices.- 5. Real and imaginary roots.- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group.- 7. Affine Lie algebras: the realization (case k = 1).- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms.- 9. Highest weight modules over the Lie algebra g(A).- 10. Integrable highest weight modules: the character formula.- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem.- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities.- 13. Affine Lie algebras, theta functions and modular forms.- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations.- Index of notations and definitions.- References.
£85.49
Springer-Verlag New York Inc. Computational Inelasticity
Book SynopsisThis book goes back a long way. There is a tradition of research and teaching in inelasticity at Stanford that goes back at least to Wilhelm Flugge and Erastus Lee. I joined the faculty in 1980, and shortly thereafter the Chairman of the Applied Mechanics Division, George Herrmann, asked me to present a course in plasticity. I decided to develop a new two-quarter sequence entitled Theoretical and C- putational Plasticity which combined the basic theory I had learned as a graduate student at the University of California at Berkeley from David Bogy, James Kelly, Jacob Lubliner, and Paul Naghdi with new computational techniques from the ?nite-element literature and my personal research. I taught the course a couple of times and developed a set of notes that I passed on to Juan Simo when he joined thefacultyin1985. IwasChairmanatthattimeandIaskedJuantofurtherdevelop the course into a full year covering inelasticity from a more comprehensive p- spective. Juan embarked on this path creatingTrade Review"This book is well written, is easy to follow, and contains much useful material for researchers and graduate students in various branches of engineering and applied mathematics." Newsletter of the EMS, Issue 42, December 2001Table of ContentsMotivation. One-Dimensional Plasticity and Viscoplasticity.- Classical Rate-Independent Plasticity and Viscoplasticity.- Integration Algorithms for Plasticity and Viscoplasticity.- Discrete Variational Formulation and Finite-Element Implementation.- Nonsmooth Multisurface Plasticity and Viscoplasticity.- Numerical Analysis of General Return Mapping Algorithms.- Nonlinear Continuum Mechanics and Phenomenological Plasticity Models.- Objective Integration Algorithms for Rate Formulations of Elastoplasticity.- Phenomenological Plasticity Models Based on the Notion of an Intermediate Stress-Free Configuration.- Viscoelasticity.
£71.55
Taylor & Francis Inc Analytic Hyperbolic Geometry in N Dimensions
Book SynopsisThe concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation language of Einstein described in this book plays a universal computational role, which extends far beyond the domain of special relativity. This book will encourage researchers to use the author's novel techniques to formulate their own results. The book provides new mathematical tools, such as hyperbolic simplexes, for the study of hyperbolic geometry Trade Review"Anyone who is concerned with hyperbolic geometry should use this wonderful and comprehensive book as a helpful compendium."—Zentralblatt MATH 1312Table of ContentsList of Figures. Preface. Author’s Biography. Introduction. Einstein Gyrogroups and Gyrovector Spaces. Einstein Gyrogroups. Problems. Einstein Gyrovector Spaces. Problems. Relativistic Mass Meets Hyperbolic Geometry. Problems. Mathematical Tools for Hyperbolic Geometry. Barycentric and Gyrobarycentric Coordinates. Problems. Gyroparallelograms and Gyroparallelotopes. Problems. Gyrotrigonometry. Problems. Hyperbolic Triangles and Circles. Gyrotriangles and Gyrocircles. Problems. Gyrocircle Theorems. Problems. Hyperbolic Simplices, Hyperplanes and Hyperspheres in N Dimensions. Gyrosimplices. Problems. Gyrosimplex Gyrovolume. Problems. Hyperbolic Ellipses and Hyperbolas. Gyroellipses and Gyrohyperbolas. Problems. VI Thomas Precession. Thomas Precession. Problems. Bibliography. Index.
£175.75
Springer-Verlag New York Inc. Paradoxes in the Theory of Relativity
Book SynopsisThat Einstein''s insight was profound goes without saying. A strildng indication of its depth is the abundance of unexpected riches that others have found in his work - riches reserved for those daring to give serious attention to implications that at first sight seem unphysical. A famous instance is that of the de Broglie waves. If, in ac cordance with Fermat''s principle, a photon followed the path of least time, de Broglie felt that the photon should have some phys ical means of exploring alternative paths to determine which of them would in fact require the least time. For this and other rea sons, he assumed that the photon had a nonvanishing rest mass, and, in accordance with Einstein''s E = h v, he endowed the photon with a spread-out pulsation of the form A Sin(27TEt/h) in the photon''s rest frame. According to the theory of relativity such a pulsation, every where simultaTable of ContentsI. The Name and Content of the Theory of Relativity.- II. Einstein’s Postulates and the Lorentz Transformations.- III. Paradoxes in Kinematics.- IV. Paradoxes in Relativistic Dynamics.- V. Are Velocities Higher than the Velocity of Light Possible?.- VI. Negative and Imaginary Proper Masses.- Literature Cited.
£40.49
Taylor & Francis Inc Introduction to Mathematical Modeling
Book SynopsisIntroduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes.Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.Table of ContentsThe Process of Mathematical Modeling. Modeling with ODEs. Systems of ODES. Stability. Bifurcations. Modeling with PDES. Modeling of Fluid flow. Geophysical Modeling. Nonlinear PDEs. Variational Principles.
£82.64
Taylor & Francis Inc Numerical Methods in Computational Mechanics
Book SynopsisThis book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanics. It reviews the basic concepts in linear algebra and advanced matrix theory, before covering solution of systems of equations, symmetric eigenvalue solution methods, and direct integration of discrete dynamic equations of motion, illustrated with numerical examples. This book suits a graduate course in mechanics based disciplines, and will help software developers in computational mechanics. Increased understanding of the underlying numerical methods will also help practicing engineers to use the computational mechanics software more effectively.Trade Review"This book is a collection of the most relevant numerical methods used in computational mechanics. It is a clear and rigorous presentation of algorithms corresponding to numerical methods for solving systems of linear and nonlinear algebraic equations, for finding eigenvalues and eigenvectors of matrices, and for integration of dynamic equations of motion. This hands-on presentation will certainly be welcomed by users of computational mechanics software interested in gaining a better understanding of the implemented algorithms as well as developers of software. In addition, the book could be used as a textbook for a graduate level course in computational mechanics." — Corina S. Drapaca, Pennsylvania State University, USA"This book is a collection of the most relevant numerical methods used in computational mechanics. It is a clear and rigorous presentation of algorithms corresponding to numerical methods for solving systems of linear and nonlinear algebraic equations, for finding eigenvalues and eigenvectors of matrices, and for integration of dynamic equations of motion. This hands-on presentation will certainly be welcomed by users of computational mechanics software interested in gaining a better understanding of the implemented algorithms as well as developers of software. In addition, the book could be used as a textbook for a graduate level course in computational mechanics." — Corina S. Drapaca, Pennsylvania State University, USATable of ContentsReview of Matrix Analysis. Review of Methods of Analysis In Structural Mechanics. Solution of System of Linear Equations. Iterative Solution Methods for System of Linear Equations. Conjugate Gradient Methods. Solution Methods for System of Nonlinear Equations. Eigenvalue Solution Methods. Direct Integration of Dynamic Equation of Motion. The Generalized Difference Method.
£80.74
Taylor & Francis Inc Spectral and Scattering Theory for Second Order
Book SynopsisThe book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.Table of ContentsSecond Order Elliptic Differential Operators in L2(Ω). Spectrum of the Operator L. Growth Estimates of the Generalized Eigenfunctions. Principle of Limiting Asorptions and Absolute Continuity. Examples. Spectral Representations and Scattering for Short-range perturbations. Spectral Representations and Scattering for "Long-range" perturbations. One Dimensional Schrodinger operator. Uniform Resolvent Estimates. Smoothing and Strichartz estimates. Several Topics for Evolution Equations.
£147.25
Nova Science Publishers Inc Mathematical & Physical Aspects of Experimental
Book Synopsis
£195.19
Nova Science Publishers Inc Perturbation Theory: Advances in Research and
Book SynopsisPerturbation Theory: Advances in Research and Applications begins with a deliberation on the development of a formalism of the Exchange perturbation theory (EPT) that accounts for the general identity principle of electrons that belong to different atomic centres. The possible applications of the theory concerning scattering and collision problems are discussed, and the authors apply the TDEPT to the description of the positron scattering on a Lithium atom as an example. Next, spin fluctuations in metallic multiband systems are discussed, including how to calculate the effect of itinerant spin excitations on the electronic properties and formulate a theory of spin fluctuation-induced superconductivity. The function of spin-orbit coupling is emphasized. Following this, the authors review how, governed by chiral symmetry, the long- and intermediate-range parts of the $NN$ potential unfold order by order, proceeding up to sixth order where convergence is achieved. Perturbative and nonperturbative approaches to nuclear amplitude are discussed, including the implications for renormalization. Continuing, this book presents proof of the good convergence properties of the new expansions on mathematical models that simulate the physical polarization function for light quarks and its derivative (the Adler function), in various prescriptions of renormalization-group summation. An overview of the calculation of one-loop corrections to the baryon axial vector current in the large-Nc heavy baryon chiral perturbation theory is offered, where Nc is the number of color charges. The matrix elements of the space components of the renormalization of the baryon axial vector current between SU(6) symmetric states yield the values of the axial vector couplings.
£163.19
Welcome Rain Publishers,US Classical Mathematics: A Concise History of
Book SynopsisA panoramic view of the development of the enduring principles and concepts of modern mathematics.
£8.99
Taylor & Francis Inc Operator Algebras, Mathematical Physics, and Low
Book SynopsisThis volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.Table of ContentsNON-COMMUTATIVE SPHERES and NUMERICAL QUANTUM MECHANICS; Matricial and Ultramatricial Topology; Remarks on the Three-Manifold Invariants ? p; The Crossed Product of the Irrational Rotation Algebra by the Flip; Quadratic and Exchange Algebras, and Modified Yang-Baxter Relations for the Selfdual Yang-Mills System and the WZNW Model; Regular Actions of Hopf Algebras on the C*-Algebra Generated by a Hilbert Space; Operator Algebras, Group Actions and Abstract Duals; A Classification of Certain Simple C*-Algebras; On Two Quantized Tensor Products 1; Geometry of Differential Equations and Projective Representations of the witt Algebra; Spin Model on Knot Projections; Towards Extracting Physical Predictions from Alain Connes' Version of the Standard Model (The New Grand Unification?); A Commutator Inequality; Duals of Compact Groups Realized by Semigroups of Non-Unital Endomorphisms of C *-Algebras; A New Index for Continuous Semigroups of *-Endomorphisms of B(H); Topological Orbit Equivalence; Toeplitz C *-Alegras on Pseudoconvex Domains with Transverse Symmetries; Normal Subgroups of the Automorphism Group of a Factor; Subfactors and Invariants of 3-Manifolds
£142.50
International Press of Boston Inc Superstring Theory
Book SynopsisThis work presents lectures from the important String Theory International Conference held in 2002 in Hangzhou, China. These include talks given by several mathematicians of particular prominence in the field, among them Stephen Hawking and Edward Witten. Interest in string theory is driven largely by the hope that it will evolve to be the ultimate 'Theory of Everything'. Work on string theory has led to advances in many branches of mathematics. This rapidly developing subject is one of the mainstream topics of mathematics in the 21st century. The current volume presents lectures from the important String Theory International Conference held in 2002 in Hangzhou, China. These include talks given by several mathematicians of particular prominence in the field, among them Stephen Hawking and Edward Witten.
£46.00
Taylor & Francis Inc Integral Theorems for Functions and Differential
Book SynopsisThe theory of holomorphic functions of several complex variables emerged from the attempt to generalize the theory in one variable to the multidimensional situation. Research in this area has led to the discovery of many sophisticated facts, structures, ideas, relations, and applications. This deepening of knowledge, however, has also revealed more and more paradoxical differences between the structures of the two theories. The authors of this Research Note were driven by the quest to construct a theory in several complex variables that has the same structure as the one-variable theory. That is, they sought a reproducing kernel for the whole class that is universal and from same class. Integral Theorems for Functions and Differential Forms in Cm documents their success. Their highly original approach allowed them to obtain new results and refine some well-known results from the classical theory of several complex variables. The 'hyperholomorphic" theory they developed proved to be a kind of direct sum of function theories for two Dirac-type operators of Clifford analysis considered in the same domain.In addition to new results and methods, this work presents a first-look at a brand new setting, based upon the natural language of differential forms, for complex analysis. Integral Theorems for Functions and Differential Forms in Cm reveals a deep link between the fields of several complex variables theory and Clifford analysis. It will have a strong influence on researchers in both areas, and undoubtedly will change the general viewpoint on the methods and ideas of several complex variables theory.Trade Review"…the book will be interesting to specialists in complex analysis and its applications".- Mathematical Reviews, 2003a"This well-written book is a valuable contribution to the broad field of interactions between complex analysis and partial differential equations...Moreover, the book can be used for individual studies, because fundamental concepts and important theorems are explained in detail."-Mathematical Reviews, Issue 94aTable of ContentsIntroduction. Differential Forms. Differential Forms with Co-Efficients in 2x2 Matrices. Hyperholomorphic Functions and Differential Forms in Cm. Cauchy's Theorem. Morera's Theorem. Cauchy's Integral Representation. Hyperholomorphic D-problem. Complex Hodge-Dolbeault System. Relations with Clifford Analysis.
£161.50
Taylor & Francis Inc An Introduction to Semiflows
Book SynopsisThis book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be extended naturally and applied to study the asymptotic behavior of the solutions of DEEs. The authors concentrate on three types of absorbing sets: attractors, exponential attractors, and inertial manifolds. They present the fundamental properties of these sets, and then proceed to show the existence of some of these sets for a number of dynamical systems generated by well-known physical models. In particular, they consider in full detail two particular PDEEs: a semilinear version of the heat equation and a corresponding version of the dissipative wave equation. These examples illustrate the most important features of the theory of semiflows and provide a sort of template that can be applied to the analysis of other models.The material builds in a careful, gradual progression, developing the background needed by newcomers to the field, and culminating in a more detailed presentation of the main topics than found in most sources. The authors' approach to and treatment of the subject builds the foundation for more advanced references and research on global attractors, exponential attractors, and inertial manifolds.Table of ContentsDynamical Processes. Attractors of Semiflows. Attractors for Semilinear Evolution Equations. Exponential Attractors. Inertial Manifolds. Examples. A Non-Existence Result for Inertial Manifolds. Appendix: Selected Results from Analysis. Bibliography. Index. Nomenclature
£161.50
Taylor & Francis Inc Effective Computational Methods for Wave
Book SynopsisDue to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology.Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.Table of ContentsPreface. Nonlinear Dispersive Waves: Numerical Simulations of Singular Solutions of Nonlinear Schrödinger Equations. Numerical Solution of the Nonlinear Helmholtz Equation. Theory and Numerical Analysis of Boussinesq Systems: A Review. The Helmholtz Equation and its Paraxial Approximations in Underwater Acoustics: Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide. Parabolic Equation Techniques in Underwater Acoustics. Numerical Solution of the Parabolic Equation in Range-Dependent Waveguides. Exact Boundary Conditions for Acoustic PE Modeling over an N2-Linear Half-Space. Numerical Methods for Elastic Wave Propagation. Introduction and Orientation. The Mathematical Model for Elastic Wave Propagation. Finite Element Methods with Continuous Displacement. Finite Element Methods with Discontinuous Displacement. Fictitious Domains Methods for Wave Diffraction. Space Time Mesh Refinement Methods. Numerical Methods for Treating Unbounded Media. Waves in Compressible Flows. High-Order Accurate Space Discretization Methods for Computational Fluid Dynamics. Governing Equations. High-Order Finite-Difference Schemes. ENO and WENO Schemes. The Discontinuous Galerkin (DG) Method. Index.
£161.50
Taylor & Francis Inc Dynamics of Third-Order Rational Difference
Book SynopsisExtending and generalizing the results of rational equations,Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.Table of ContentsPreface. Introduction. Preliminaries. Equations with Bounded Solutions. Existence of Unbounded Solutions. Period Trichotomies. Known Results for Each of the 225 Special Cases. Appendices. Bibliography. Index.
£161.50
Watchmaker Publishing The Science of Mechanics: A Critical and Historical Account of Its Development
£23.97
Society for Industrial and Applied Mathematics (SIAM) The Defocusing Nonlinear Schrödinger Equation
Book Synopsis
£90.95
Society for Industrial & Applied Mathematics,U.S. Tensor Analysis: Spectral Theory and Special
Book SynopsisTensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory – some of which are nontrivial – have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors.Tensor Analysis is unique in that it is the first book on the spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors, which is covered in a chapter.Table of Contents List of Figures. List of Algorithms. Preface. Chapter 1: Introduction. Chapter 2: Eigenvalues of Tensors. Chapter 3: Nonnegative Tensors. Chapter 4: Spectral Hypergraph Theory via Tensors. Chapter 5: Positive Semidefinite Tensors. Chapter 6: Completely Positive Tensors and Copositive Tensors. Bibliography. Index.
£76.50
Morgan & Claypool Publishers Modelling Physics with Microsoft Excel
Book SynopsisThis book demonstrates some of the ways in which Microsoft Excel® may be used to solve numerical problems in the field of physics. But why use Excel in the first place? Certainly, Excel is never going to out-perform the wonderful symbolic algebra tools that we have today – Mathematica, Mathcad, Maple, MATLAB, etc. However, from a pedagogical stance, Excel has the advantage of not being a ‘black box’ approach to problem solving. The user must do a lot more work than just call up a function. The intermediate steps in a calculation are displayed on the worksheet. Another advantage is the somewhat less steep learning curve. This book shows Excel in action in various areas within physics. Some Visual Basic for Applications (VBA) has been introduced, the purpose here is to show how the power of Excel can be greatly extended and hopefully to whet the appetite of a few readers to get familiar with the power of VBA. Those with programming experience in any other language should be able to follow the code.
£33.20
Nova Science Publishers Inc Particle of Life: Mathematical Abstraction or
Book SynopsisThe book presents a mathematical answer to the ancient philosophical question "How mind is related to matter". It proves that in the mathematical world, the bridge from matter to mind requires extension and modification of quantum physics. The proposed dynamical model that captures behaviour of living things is based upon the extension of the First Principles of classical physics to include the phenomenological behaviour of living systems, i.e. to develop a new mathematical formalism within the framework of classical dynamics that would allow one to capture the specific properties of natural or artificial living systems. The proposed mathematical formalism is quantum-inspired. It is based upon coupling the classical dynamical system representing the motor dynamics with the corresponding Liouville equation describing the evolution of initial uncertainties in terms of the probability density and representing the mental dynamics. Along with the main objective, the book addresses fundamental departures from classical views on some unsolved problems in quantum mechanics. By moving from the Schrödinger to the Madelung equation, it demonstrates that randomness in quantum mechanics has the same mathematical origin as that in turbulence and chaos. It illuminates the origin of entanglement and interference of probabilities. These results are reinforced by similar properties of L-particle that are based upon a modification of the Madelung equation. Therefore, the model of L-particle fits well into the mathematical formalism of modern physics, and that rouses a belief that L-particle is not only a mathematical abstraction, but a reality as well.
£92.99
Nova Science Publishers Inc China's Evolving IT Capabilities: Cloud
Book Synopsis
£139.49
Nova Science Publishers Inc Space Time Geometry & Quantum Events
Book SynopsisIt is well-known that the fundamental problem in contemporary theoretical physics is the "pacific coexistence" between General Relativity and Quantum Mechanics. The scenarios of the explorable relationships between classical space-time and quantum land are various: the geometrodynamic one (by a proper extension of geometry), the stochastic fractal one (defining a middle land mediated by QFT-like hypotheses), the emergent one (from a physical viewpoint, by the collective behaviours of discrete entities, which mathematically means that the geometry derives from an algebraic structure of events).This anthology includes some of the most significant voices on the problem of the possible relations between the space-time dynamics and the quantum networks of events.
£159.74
Nova Science Publishers Inc Proposed Cloud Computing Business Framework
Book SynopsisThis book gives an overview of Cloud Computing (CC) and presents a literature review explaining the development of CC. Selected frameworks are discussed, including those suitable for this research. Technical and organisational challenges for CC are also identified. This book focuses on organisational challenges and recommendations to address organisational challenges. To help organisations achieve good Cloud design, deployment and services, there is a need for the proposal and development of a framework, the Cloud Computing Business Framework (CCBF), which explains how three research questions are connected together. The CCBF is a conceptual and an architectural framework to be validated through modelling, simulation, experiments and hybrid case studies. The architecture of the CCBF is presented to explain how different key areas can relate to each other and fit into the framework. Results of case studies, simulations, modelling and experiments are used to validate CCBF and are discussed in details which collaborators find results of CCBF useful for their Cloud adoption. Selected results have been published including four journals and one book chapter. Finally, future work plans are proposed and followed-up steps are explained.
£170.39
Nova Science Publishers Inc Brownian Motion: Elements, Dynamics &
Book SynopsisThe fields of study in which random fluctuations arise and cannot be ignored are as disparate and numerous as there are synonyms for the word "noise." In the nearly two centuries following the discovery of what has come to be known as Brownian motion, named in homage to botanist Robert Brown, scientists, engineers, financial analysts, mathematicians, and literary authors have posited theories, created models, and composed literary works which have accounted for environmental noise. This volume offers a glimpse into the ways in which Brownian motion has crept into a myriad of fields of study through fifteen distinct chapters written by mathematicians, physicists, and other scholars. The intent is to especially highlight the vastness of scholarly work that explains various facets of Nature made possible by one scientist''s curiosity sparked by observing sporadic movement of specks of pollen under a microscope in a 19th century laboratory.
£230.39
Murphy & Moore Publishing A Modern Approach to Mathematical Physics
Book Synopsis
£112.27
States Academic Press Mathematical Methods for Physics
Book Synopsis
£105.99
Morgan & Claypool Publishers Adventures with Lissajous Figures
Book Synopsis
£23.75
Morgan & Claypool Publishers Logic for Physicists
Book Synopsis
£23.75
Morgan & Claypool Publishers Theory of Electromagnetic Pulses
Book Synopsis
£23.75
