Mathematical / Computational / Theoretical physics Books

Book SynopsisThis new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.Trade ReviewFrom the reviews: "We find here a book where the theory is developed with rigours in parallel with a strong physical intuition. Comparison with experiments and simulations are always proposed and carefully analysed. The book contains at the end a very rich and complete bibliography ... I warmly encourage everyone interested in boundary-layer theory to have this book in his bookcase." Physicalia "... I do recommend the book highly, especially for its long historical perspective, including all the diagrams comparing theory and experiment that remind us that engineering is practical ..." SIAM ReviewsTable of ContentsPart I. Fundamentals of Viscous Flows.- 1. Some Features of Viscous Flows.- 2. Fundamentals of Boundary–Layer Theory.- 3. Field Equations for Flows of Newtonian Fluids.- 4. General Properties of the Equations of Motion.- 5. Exact Solutions of the Navier–Stokes Equations.- Part II. Laminar Boundary Layers.- 6 Boundary–Layer Equations in Plane Flow; Plate Boundary Layer.- 7 General Properties and Exact Solutions of the Boundary–Layer Equations for Plane Flows.- 8 Approximate Methods for Solving the Boundary–Layer Equations for Steady Plane Flows.- 9 Thermal Boundary Layers Without Coupling of the Velocity Field to the Temperature Field.- 10 Thermal Boundary Layers with Coupling of the Velocity Field to the Temperature Field.- 11. Boundary–Layer Control (Suction/Blowing).- 12. Axisymmetric and Three–Dimensional Boundary Layers.- 13. Unsteady Boundary Layers.- 14. Extensions to the Prandtl Boundary–Layer Theory.- Part III. Laminar–Turbulent Transition.- 15. Onset of Turbulence (Stability Theory).- Part IV. Turbulent Boundary Layers.- 16. Fundamentals of Turbulent Flows.- 17. Internal Flows.- 18. Turbulent Boundary Layers Without Coupling of the Velocity Field to the Temperature Field.- 19. Turbulent Boundary Layers with Coupling of the Velocity Field to the Temperature Field.- 20. Axisymmetric and Three–Dimensional Turbulent Boundary Layers.- 21. Unsteady Turbulent Boundary Layers.- 22. Turbulent Free Shear Flows.- Part V. Numerical Methods in Boundary–Layer Theory.- 23. Numerical Integration of the Boundary–Layer Equations.

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Book SynopsisAs a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.Table of ContentsRemarks on Mathematial Physics.- 1 Introduction.- 2 Dynamical Systems.- 3 Ordinary Differential Equations.- 4 Linear Dynamics.- 5 Classification of Linear Flows.- 6 Hamiltonian Equations and Symplectic Group.- 7 Stability Theory.- 8 Variational Principles.- 9 Ergodic Theory.- 10 Symplectic Geometry.- 11 Motion in a Potential.- 12 Scattering Theory.- 13 Integrable Systems and Symmetries.- 14 Rigid and Non-Rigid Bodies.- 15 Perturbation Theory.- 16 Relativistic Mechanics.- 17 Symplectic Topology.- A Topological Spaces and Manifolds.- B Differential Forms.- C Convexity and Legendre Transform.- D Fixed Point Theorems, and Results about Inverse Images.- E Group Theory.- F Bundles, Connection, Curvature.- G Morse Theory.- H Solutions of the Exercises.- Bibiography.- Index of Proper Names.- Table of Symbols.- Image Credits.- Index.

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Book SynopsisThis second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.Trade Review“This is a thorough and easy-to-follow text for a beginning course in real analysis … . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. … Will be popular with students because of the detailed explanations and the worked examples.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)Table of Contents1 Some General Mathematical Concepts and Notation: 1.1 Logical Symbolism.- 1.2 Sets and Elementary Operations on them.- 1.3 Functions.- 1.4 Supplementary Material.- 2 The Real Numbers: 2.1 Axioms and Properties of Real Numbers.- 2.2 Classes of Real Numbers and Computations.- 2.3 Basic Lemmas on Completeness.- 2.4 Countable and Uncountable Sets.- 3 Limits: 3.1 The Limit of a Sequence.- 3.2 The Limit of a Function.- 4 Continuous Functions: 4.1 Basic Definitions and Examples.- 4.2 Properties of Continuous Functions.- 5 Differential Calculus: 5.1 Differentiable Functions.- 5.2 The Basic Rules of Differentiation.- 5.3 The Basic Theorems of Differential Calculus.- 5.4 Differential Calculus Used to Study Functions.- 5.5 Complex Numbers and Elementary Functions.- 5.6 Examples of Differential Calculus in Natural Science.- 5.7 Primitives.- 6 Integration: 6.1 Definition of the Integral.- 6.2 Linearity, Additivity and Monotonicity of the Integral.- 6.3 The Integral and the Derivative.- 6.4 Some Applications of Integration.- 6.5 Improper Integrals.- 7 Functions of Several Variables: 7.1 The Space Rm and its Subsets.- 7.2 Limits and Continuity of Functions of Several Variables.- 8 Differential Calculus in Several Variables: 8.1 The Linear Structure on Rm.- 8.2 The Differential of a Function of Several Variables.- 8.3 The Basic Laws of Differentiation.- 8.4 Real-valued Functions of Several Variables.- 8.5 The Implicit Function Theorem.- 8.6 Some Corollaries of the Implicit Function Theorem.- 8.7 Surfaces in Rn and Constrained Extrema.- Some Problems from the Midterm Examinations: 1. Introduction to Analysis (Numbers, Functions, Limits).- 2. One-variable Differential Calculus.- 3. Integration. Introduction to Several Variables.- 4. Differential Calculus of Several Variables.- Examination Topics: 1. First Semester: 1.1. Introduction and One-variable Differential Calculus.- 2. Second Semester: 2.1. Integration. Multivariable Differential Calculus.- Appendices: A Mathematical Analysis (Introductory Lecture).- B Numerical Methods for Solving Equations (An Introduction).- C The Legendre Transform (First Discussion).- D The Euler–Maclaurin Formula.- E Riemann–Stieltjes Integral, Delta Function, and Generalized Functions.- F The Implicit Function Theorem (An Alternative Presentation).- References.- Subject Index.- Name Index.

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Book SynopsisThis book is about supergravity, which combines the principles of general relativity and local gauge invariance with the idea of supersymmetries between bosonic and fermionic degrees of freedom. The authors give a thorough and pedagogical introduction to the subject suitable for beginning graduate or advanced undergraduate students in theoretical high energy physics or mathematical physics. Interested researchers working in these or related areas are also addressed. The level of the presentation assumes a working knowledge of general relativity and basic notions of differential geometry as well as some familiarity with global supersymmetry in relativistic field theories. Bypassing curved superspace and other more technical approaches, the book starts from the simple idea of supersymmetry as a local gauge symmetry and derives the mathematical and physical properties of supergravity in a direct and “minimalistic” way, using a combination of explicit computations and geometrical reasoning. Key topics include spinors in curved spacetime, pure supergravity with and without a cosmological constant, matter couplings in global and local supersymmetry, phenomenological and cosmological implications, extended supergravity, gauged supergravity and supergravity in higher spacetime dimensions.Table of ContentsIntroduction.- From Global to Local SUSY.- Gravity and spinors.- D=4 N=1 SUGRA.- Matter couplings in global SUSY.- Matter couplings in SUGRA.- SUGRA phenomenology.- Extended supergravities.- Gauged supergravity.- SUGRA in any dimension.

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Book SynopsisThis book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.Trade Review"The presentation provides significant insight into a large part of the current issues of interest in the physics of Bose systems and especially into the "kitchen" of several relevant mathematical techniques. As such, it is highly recommended to both advanced researchers and students preparing to work in this field." (Mathematical Reviews)Table of ContentsThe Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincaré Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for Trapped Bosons.- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases.- One-Dimensional Behavior of Dilute Bose Gases in Traps.- Two-Dimensional Behavior in Disc-Shaped Traps.- The Charged Bose Gas, the One- and Two-Component Cases.- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model.

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Book Synopsis"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century." --Bulletin of Symbolic Logic (Review of first edition)Trade ReviewFrom the book reviews:“The book is a thorough, deep, fascinating work. It is not only recommended, it is compulsory for anyone interested in the history of mathematical ideas.” (László I. Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 75 (1-2), 2009)Table of ContentsThe Emergence of Sets within Mathematics.- Institutional and Intellectual Contexts in German Mathematics, 1800–1870.- A New Fundamental Notion: Riemann’s Manifolds.- Dedekind and the Set-theoretical Approach to Algebra.- The Real Number System.- Origins of the Theory of Point-Sets.- Entering the Labyrinth-Toward Abstract Set Theory.- The Notion of Cardinality and the Continuum Hypothesis.- Sets and Maps as a Foundation for Mathematics.- The Transfinite Ordinals and Cantor’s Mature Theory.- In Search of an Axiom System.- Diffusion, Crisis, and Bifurcation: 1890 to 1914.- Logic and Type Theory in the Interwar Period.- Consolidation of Axiomatic Set Theory.

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Book SynopsisThis book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.Trade ReviewFrom the reviews: “It is worth pointing out that the book is mainly a text about commutative hypercomplex numbers and some of their applications to a 2-dimensional Minkowski spacetime. … This book should be interesting to anybody who is interested in applications of hypercomplex numbers … . In conclusion, I recommend this book to anyone who wants to learn about hypercomplex numbers.” (Emanuel Gallo, Mathematical Reviews, Issue 2010 d)Table of ContentsThe Mathematics of Minkowski Space-Time: 1 N-Dimensional Hypercomplex Numbers and the associated Geometries.- Commutative Hypercomplex Number Systems.- The General Two-Dimensional System.- Linear Transformations and Geometries.- The Geometries Associated with Hypercomplex Numbers.- Conclusions.- 2 Trigonometry in the Minkowski Plane.- Geometrical Representation of Hyperbolic Numbers.- Basics of Hyperbolic Trigonometry.- Geometry in Pseudo-Euclidean Cartesian Plane.- Trigonometry in the Pseudo-Euclidean Plane.- Theorems on Equilateral Hyperbolas in the Pseudo-Euclidean Plane.- Some Examples of Triangle Solutions in the Minkowski Plane.- Conclusions.- 3 Uniform and Accelerated Motions in the Minkowski Space-Time (Twin Paradox).- Inertial Motions.- Inertial and Uniformly Accelerated Motions.- Non-uniformly Accelerated Motions.- Conclusions.- 4 General Two-Dimensional Hypercomplex Numbers.-Geometrical Representation.- Geometry and Trigonometry in Two-Dimensional Algebras.- Some Properties of Fundamental Conic Section.- Numerical Examples.- 5 Functions of a Hyperbolic Variable.- Some Remarks on Functions of a Complex Variable.- Functions of Hypercomplex Variables.- The Functions of a Hyperbolic Variable.- The Elementary Functions of a Canonical Hyperbolic Variable.- H-Conformal Mappings.- Commutative Hypercomplex Systems with Three Unities.- 6 Hyperbolic Variables on Lorentz Surfaces.- Introduction.- Gauss: Conformal Mapping of Surfaces.- Extension of Gauss Theorem: Conformal Mapping of Lorentz Surfaces.- Beltrami: Complex Variables on a Surface.- Beltrami’s Integration of Geodesic Equations.- Extension of Beltrami’s Equation to Non-Definite Differential Forms.- 7 Constant Curvature Lorentz Surfaces.- Introduction.- Constant Curvature RiemannSurfaces.- Constant Curvature Lorentz Surfaces.- Geodesics and Geodesic Distances on Riemann and Lorentz Surfaces.- Conclusions.- 8 Generalization of Two-Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle).- Physical Meaning of Transformations by Hyperbolic Functions.- Physical Interpretation of Geodesics on Riemann and Lorentz Surfaces with Positive Constant Curvature.- Einstein’s Way to General Relativity.- Conclusions.- II An Introduction to Commutative Hypercomplex Numbers.- 9 Commutative Segre’s Quaternions.- Introduction.- Hypercomplex Systems with Four Units.- Historical Introduction of Segre’s Quaternion.- Algebraic Properties of Commutative Quaternions.- Functions of a Quaternion Variable.- Mapping by Means of Quaternion Functions.- Elementary Functions of the Quaternions.- Elliptic-Hyperbolic Quaternions.- Elliptic-Parabolic Generalized Segre’s Quaternions.- 10 Constant Curvature Segre’s Quaternion Spaces.- Introduction.- Quaternion differential geometry and geodesic equations.- Orthogonality in Segre’s Quaternion Space.- Constant Curvature Quaternion Spaces.- Geodesic Equations in Quaternion Space.- Beltrami’s Integration Method for Quaternion Spaces.- Beltrami’s Integration Method for Quaternion Spaces.- Conclusions.- 11 A Matrix Formalization for Commutative Hypercomplex Systems.- Mathematical Operations.- Properties of the Characteristic Matrix M.- Functions of Hypercomplex Variable.- Functions of a Two-Dimensional Hypercomplex Variable.- Derivatives of a Hypercomplex Function.- Characteristic Differential Equation.- A Equivalence Between the Formalizations of Hypercomplex Numbers.

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Book SynopsisOne studying the motion of fluids relative to particulate systems is soon impressed by the dichotomy which exists between books covering theoretical and practical aspects. Classical hydrodynamics is largely concerned with perfect fluids which unfortunately exert no forces on the particles past which they move. Practical approaches to subjects like fluidization, sedimentation, and flow through porous media abound in much useful but uncorrelated empirical information. The present book represents an attempt to bridge this gap by providing at least the beginnings of a rational approach to fluid­ particle dynamics, based on first principles. From the pedagogic viewpoint it seems worthwhile to show that the Navier-Stokes equations, which form the basis of all systematic texts, can be employed for useful practical applications beyond the elementary problems of laminar flow in pipes and Stokes law for the motion of a single particle. Although a suspension may often be viewed as a continuum for practical purposes, it really consists of a discrete collection of particles immersed in an essentially continuous fluid. Consideration of the actual detailed boundary­ value problems posed by this viewpoint may serve to call attention to the limitation of idealizations which apply to the overall transport properties of a mixture of fluid and solid particles.Table of Contents1. Introduction.- 1–1 Definition and purpose, 1. 1–2 Historical review, 8. 1–3 Application in science and technology, 13..- 2. The Behavior of Fluids in Slow Motion.- 2–1 The equations of change for a viscous fluid, 23. 2–2 Mechanical energy dissipation in a viscous fluid, 29. 2–3 Force and couple acting on a body moving in a viscous fluid, 30. 2–4 Exact solutions of the equations of motion for a viscous fluid, 31. 2–5 Laminar flow in ducts, 33. 2–6 Simplifications of the Navier-Stokes equations, especially for slow motion, 40. 2–7 Paradoxes in the solution of the creeping motion equations, 47. 2–8 Molecular effects in fluid dynamics, 49. 2–9 Non-newtonian flow, 51. 2–10 Unsteady creeping flows, 52..- 3. Some General Solutions and Theorems Pertaining to the Creeping Motion Equations.- 3–1 Introduction, 58. 3–2 Spherical coordinates, 62. 3–3 Cylindrical coordinates, 71. 3–4 Integral representations, 79. 3–5 Generalized reciprocal theorem, 85. 3–6 Energy dissipation, 88..- 4. Axisymmetrical Flow.- 4–1 Introduction, 96. 4–2 Stream function, 96. 4–3 Relation between stream function and local velocity, 98. 4–4 Stream function in various coordinate systems, 99. 4–5 Intrinsic coordinates, 100. 4–6 Properties of the stream function, 102. 4–7 Dynamic equation satisfied by the stream function, 103. 4–8 Uniform flow, 106. 4–9 Point source or sink, 106. 4–10 Source and sink of equal strength, 107. 4–11 Finite line source, 108. 4–12 Point force, 110. 4–13 Boundary conditions satisfied by the stream function, 111. 4–14 Drag on a body, 113. 4–15 Pressure, 116. 4–16 Separable coordinate systems, 117. 4–17 Translation of a sphere, 119. 4–18 Flow past a sphere, 123. 4–19 Terminal settling velocity, 124. 4–20 Slip at the surface of a sphere, 125. 4–21 Fluid sphere, 127. 4–22 Concentric spheres, 130. 4–23 General solution in spherical coordinates, 133. 4–24 Flow through a conical diffuser, 138. 4–25 Flow past an approximate sphere, 141. 4–26 Oblate spheroid, 145. 4–27 Circular disk, 149. 4–28 Flow in a venturi tube, 150. 4–29 Flow through a circular aperture, 153. 4–30 Prolate spheroid, 154. 4–31 Elongated rod, 156. 4–32 Axisymmetric flow past a spherical cap, 157..- 5. The Motion of a Rigid Particle of Arbitrary Shape in an Unbounded Fluid.- 5–1. Introduction, 159. 5–2 Translational motions, 163. 5–3 Rotational motions, 169. 5–4 Combined translation and rotation, 173. 5–5 Symmetrical particles, 183. 5–6 Nonskew bodies, 192. 5–7 Terminal settling velocity of an arbitrary particle, 197. 5–8 Average resistance to translation, 205. 5–9 The resistance of a slightly deformed sphere, 207. 5–10 The settling of spherically isotropic bodies, 219. 5–11 The settling of orthotopic bodies, 220..- 6. Interaction between Two or More Particles.- 6–1 Introduction, 235. 6–2 Two widely spaced spherically isotropic particles, 240: 6–3 Two spheres by the method of reflections and similar techniques, 249. 6–4 Exact solution for two spheres falling along their line of centers, 270. 6–5 Comparison of theories with experimental data for two spheres, 273. 6–6 More than two spheres, 276. 6–7 Two spheroids in a viscous liquid, 278. 6–8 Limitations of creeping motion equations, 281..- 7. Wall Effects on the Motion of a Single Particle.- 7–1 Introduction, 286. 7–2 The translation of a particle in proximity to container walls, 288. 7–3 Sphere moving in an axial direction in a circular cylindrical tube, 298. 7–4 Sphere moving relative to plane walls, 322. 7–5 Spheroid moving relative to cylindrical and plane walls, 331. 7–6 k-coefficients for typical boundaries, 340. 7–7 One- and two-dimensional problems, 341. 7–8 Solid of revolution rotating symmetrically in a bounded fluid, 346. 7–9 Unsteady motion of a sphere in the presence of a plane wall, 354..- 8. Flow Relative to Assemblages of Particles.- 8–1 Introduction, 358. 8–2 Dilute systems—no interaction effects, 360. 8–3 Dilute systems—first-order interaction effects, 371. 8–4 Concentrated systems, 387. 8–5 Systems with complex geometry, 400. 8–6 Particulate suspensions, 410. 8–7 Packed beds, 417. 8–8 Fluidization, 422..- 9. The Viscosity of Particulate Systems.- 9–1 Introduction, 431. 9–2 Dilute systems of spheres—no interaction effects, 438. 9–3 Dilute systems—first-order interaction effects, 443. 9–4 Concentrated systems, 448. 9–5 Nonspherical and nonrigid particles, 456. 9–6 Comparison with data, 462. 9–7 Non-newtonian behavior, 469..- Appendix A. Orthogonal Curvilinear Coordinate Systems.- A-l Curvilinear coordinates, 474. A-2 Orthogonal curvilinear coordinates, 477. A-3 Geometrical properties, 480. A-4 Differentiation of unit vectors, 481. A-5 Vector differential invariants, 483. A-6 Relations between cartesian and orthogonal curvilinear coordinates, 486. A-7 Dyadics in orthogonal curvilinear coordinates, 488. A-8 Cylindrical coordinate systems, 490. A-9 Circular cylindrical coordinates, 490. A-10 Conjugate cylindrical coordinate systems, 494. A-ll Elliptic cylinder coordinates, 495. A-12 Bipolar cylinder coordinates, 497. A-l3 Parabolic cylinder coordinates, 500. A-14 Coordinate systems of revolution, 501. A-l5 Spherical Coordinates, 504. A-l6 Conjugate coordinate systems of revolution, 508. A-17 Prolate spheroidal coordinates, 509. A-18 Oblate spheroidal coordinates, 512. A-19 Bipolar coordinates, 516. A-20 Toroidal coordinates, 519. A-21 Paraboloidal Coordinates, 521..- Appendix B. Summary of Notation and Brief Review of Polyadic Algebra.- Name Index.

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Book SynopsisVery few people have contributed as much to twentieth-century physics as Julian Schwinger. It is therefore appropriate to offer a retrospective of his work on the occasion of his sixtieth birthday (February 12, 1978). We hope, in offering this selection of his papers, to bring to light ideas and results that may have been partly overlooked at the time of the original publication. Schwinger has published prodigiously on a great variety of subjects, as is evident from the comprehensive list of publications arranged in chronological order which appears on p. xiii. Needless to say, only a small subset could be included in the present modest volume. In the selection, great weight was assigned to papers that seem to be less widely known or appreciated than they deserve. Many important papers are therefore omitted. (Examples: Paper [64] 'On Gauge Invariance and Vacuum Polarization' and Paper [69] 'On Angular Momentum', both of which have been reprinted elsewhere. ) The collection is a personal one, having been chosen by Schwinger himself, and is therefore of particular interest. It would probably not be interesting to offer an analysis, by the editors, of Schwinger's contributions to physics. However, we are very pleased to be able to include Schwinger's own informal and very personal comments about each article that appears in this volume. These comments indicate his reasons for choosing these particular articles and, in many cases, provide a capsule synopsis of what he considers most valuable.Table of Contents[8] ‘The Scattering of Neutrons by Ortho- and Parahydrogen’ (with E. Teller), Phys. Rev.52, 286 (1937)..- [11] ‘The Neutron-Proton Scattering Cross Section’ (with V. Cohen and H. Goldsmith), Phys. Rev.55, 106 (1939)..- [15] ‘On Pair Emission in the Proton Bombardment of Fluorine’ (with J. R. Oppenheimer), Phys. Rev.56, 1066 (1939)..- [25] ‘On a Theory of Particles with Half-Integral Spin’ (with W. Rarita), Phys. Rev.60, 61 (1941)..- [26] ‘On the Interaction of Mesotrons and Nuclei’ (with J. R. Oppenheimer), Phys. Rev.60, 150 (1941)..- [31] ‘On a Field Theory of Nuclear Forces’, Phys. Rev.61, 387 (1942)..- [34] ‘Polarization of Neutrons by Resonance Scattering in Helium’, Phys. Rev.69, 681 (1946)..- [42] ‘On the Polarization of Fast Neutrons’, Phys. Rev.73, 407 (1948)..- [43] ‘On Quantum-Electrodynamics and the Magnetic Moment of the Electron’, Phys. Rev.73, 416 (1948)..- [44] ‘A Note on Saturation in Microwave Spectroscopy’ (with R. Karplus), Phys. Rev.73, 1020 (1948)..- [58] ‘On the Charge Independence of Nuclear Forces’, Phys. Rev.78, 135(1950)..- [66] ‘On the Green’s Functions of Quantized Fields I, II’, Proc. Natl. Acad. Sci., U.S.A.37, 452, 455 (1951)..- [74] ‘The Theory of Quantized Fields. III’, Phys. Rev.91, 728 (1953)..- [76] ‘The Theory of Quantized Fields. IV’, Phys. Rev.92, 1283 (1953)..- [78] ‘The Quantum Correction in the Radiation by Energetic Accelerated Electrons’, Proc. Natl. Acad. Sci., U.S.A.40, 132 (1954)..- [82] ‘A Theory of the Fundamental Interactions’, Ann. Phys. (N. Y.)2, 407 (1957)..- [86] ‘On the Euclidean Structure of Relativistic Field Theory’, Proc. Natl. Acad. Sci., U.S.A.44, 956 (1958)..- [88] ‘Euclidean Quantum Electrodynamics’, Phys. Rev.115, 721 (1959)..- [91] ‘The Algebra of Microscopic Measurement’, Proc. Natl. Acad. Sci., U.S.A.45, 1542 (1959)..- [98] ‘The Special Canonical Group’, Proc. Natl. Acad. Sci., U.S.A.46, 1401 (1960)..- [100] ‘On the Bound States of a Given Potential’, Proc. Natl. Acad. Sci., U.S.A.47, 122 (1961)..- [101] ‘Brownian Motion of a Quantum Oscillator’, J. Math. Phys.2, 407(1961)..- [104] ‘Gauge Invariance and Mass’, Phys. Rev.125, 397(1962). 188.- [105] ‘Non-Abelian Gauge Fields. Commutation Relations’, Phys. Rev.125, 1043 (1962)..- [106] ‘Exterior Algebra and the Action Principle. I’, Proc. Natl. Acad. Sci., U.S.A.48, 603 (1962)..- [107] ‘Non-Abelian Gauge Fields. Relativistic Invariance’, Phys. Rev.127, 324(1962)..- [108] ‘Gauge Invariance and Mass. II’, Phys. Rev.128, 2425 (1962)..- [109] ‘Quantum Variables and Group Parameters’, IlNuovo Cimento30, 278(1963)..- [111] ‘Commutation Relations and Conservation Laws’, Phys. Rev.130, 406 (1963)..- [112] ‘Energy and Momentum Density in Field Theory’, Phys. Rev.130, 800(1963)..- [114] ‘Quantized Gravitational Field.II’ Phys. Rev.132, 1317(1963)..- [116] ‘Coulomb Green’s Function’, J. Math. Phys.5, 1606 (1964)..- [117] ‘Non-Abelian Vector Gauge Fields and the Electromagnetic Field’, Rev. Mod. Phys.26, 609 (1964)..- [118] ‘Field Theory of Matter’, Phys. Rev.135, B816 (1964)..- [124] ‘Field Theory of Matter. II’, Phys. Rev.136, B1821 (1964)..- [128] ‘Field Theory of Matter.IV’, Phys. Rev.140, B158 (1965)..- [132] ‘Relativistic Quantum Field Theory’, Nobel Lecture, in Nobel Lectures — Physics, 1963–1970, Elsevier, Amsterdam, 1972..- [135] ‘Particles and Sources’, Phys. Rev.152, 1219 (1966)..- [137] ‘Chiral Dynamics’, Phys. Letters24B, 473 (1967)..- [139] ‘Partial Symmetry’, Phys. Rev. Letters18, 923 (1967)..- [144] ‘Gauge Fields, Sources and Electromagnetic Masses’, Phys. Rev.165, 1714 (1968); Phys. Rev.167, 1546 (1968)..- [147] ‘Sources and Magnetic Charge’, Phys. Rev.173, 1536 (1968)..- [150] ‘A Magnetic Model of Matter’, Science, 165, 757(1969)..- [151] ‘Theory of Sources’, Contemporary Physics (Trieste Symposium 1968), IAEA Vienna, 1969, Vol. II, p. 59..- [155] ‘How Massive is the W Particle?’, Phys. Rev.D7, 908 (1973)..- [156] ‘Classical Radiation of Accelerated Electrons. II. A Quantum Viewpoint’, Phys. Rev.D7, 1696 (1973)..- [157] ‘How to Avoid ?Y=1Neutral Currents’, Phys. Rev.D8, 960 (1973)..- [160] ‘A Report on Quantum Electrodynamics’, in The Physicist’s Conception of Nature, edited by J. Mehra, Reidel, Dordrecht, 1973, p. 413..- [164] ‘Photon Propagation Function: Spectral Analysis of Its Asymptotic Form’, Proc. Natl. Acad. Sci., U.S.A.71, 3024 (1974)..- [167] ‘Source Theory Viewpoints in Deep Inelastic Scattering’, Proc. Natl. Acad. Sci., U.S.A.72, 1 (1975)..- [172] ‘Magnetic Charge and the Charge Quantization Condition’, Phys. Rev.D12, 3105 (1975)..- [174] ‘Casimir Effect in Source Theory’, Lett. Math. Phys.1, 43 (1975)..- [178] ‘Deep Inelastic Scattering of Leptons’, Proc. Natl. Acad. Sci., U.S.A.73, 3351 (1976)..

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Table of ContentsMathematical and Quantum-Mechanical Background.- General Concepts of the Theory of Resonance States and Processes.- Theory of Resonance States Based on the Hilbert-Schmidt Expansion.- Projection Methods.- Theory of Resonance States and Processes Based on Analytical Continuation in the Coupling Constant.- S-matrix Parametrization of Scattering Data. Extraction of Resonance Parameters from Experimental Data.- Resonances in Atomic Physics.- Conclusion, Open Problems.

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Book SynopsisThe Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations. Trade Review`I recommend Adomian's new book to all researchers in the area of mathematical modeling and solving complex dynamical systems.' Foundations of Physics, 1994 Table of ContentsPreface. Foreword. 1. On Modelling Physical Phenomena. 2. The Decomposition Method for Ordinary Differential Equations. 3. The Decomposition Method in Several Dimensions. 4. Double Decomposition. 5. Modified Decomposition. 6. Applications of Modified Decomposition. 7. Decomposition Solutions for Neumann Boundary Conditions. 8. Integral Boundary Conditions. 9. Boundary Conditions at Infinity. 10. Integral Equations. 11. Nonlinear Oscillations in Physical Systems. 12. Solution of the Duffing Equation. 13. Boundary-Value Problems with Closed Irregular Contours or Surfaces. 14. Applications in Physics. Appendix I: Padé and Shanks Transform. Appendix II: On Staggered Summation of Double Decomposition Series. Appendix III: Cauchy Products of Infinite Series. Index.

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Book SynopsisFor many physicists quantum theory contains strong conceptual difficulties, while for others the apparent conclusions about the reality of our physical world and the ways in which we discover that reality remain philosophically unacceptable. This book focuses on recent theoretical and experimental developments in the foundations of quantum physics, including topics such as the puzzles and paradoxes which appear when general relativity and quantum mechanics are combined; the emergence of classical properties from quantum mechanics; stochastic electrodynamics; EPR experiments and Bell's Theorem; the consistent histories approach and the problem of datum uniqueness in quantum mechanics; non-local measurements and teleportation of quantum states; quantum non-demolition measurements in optics and matter wave properties observed by neutron, electron and atomic interferometry. Audience: This volume is intended for graduate students of physics and those interested in the foundations of quantum theory.Table of Contents1. The subject of our discussions; E. Santos. 2. Measurement of the Schrödinger wave of a single particle; Y. Aharonov, L. Vaidman. 3. The emergence of classical properties from quantum mechanics: New problems from old; L.E. Ballentine. 4. Deformations of space-time symmetries and fundamental scales; A. Ballesteros, et al. 5. Aspects of quantum reality; S. Bergia. 6. Kochen-Specker diagram of the Peres--Mermin example; A. Cabello. 7. Zeropoint waves and quantum particles; A.M. Cetto, L. de la Peña. 8. Results of atom interferometry experiments with potassium; J.F. Clauser. 9. On the uncertainty relations; J.R. Croca. 10. Continuously diagonalized density operator of open systems; L. Diósi. 11. The hazy spacetime of the Károlyházy model of quantum mechanics; A. Frenkel. 12. Can the experiments based on parametric-down conversion disprove Einstein locality? A. Garuccio. 13. Quantum-mechanical histories and the uncertainty principle; J.J. Halliwell. 14. Experiments with coherent electron wave packets; F. Hasselbach. 15. The ontological interpretation of quantum field theory applied in a cosmological context; B.J. Hiley, A.H. Aziz Muft. 16. State vector reduction via spacetime imprecision; F. Károlyházy. 17. Analyses of classical and thermodynamic limits of quantum mechanics and quantum measurements on the basis of nonstandard analysis; T. Kobayashi. 18. A realistic interpretation of lattice gauge theories; M. Lorente. 19. Is there abridge connecting stochastic and quantum electrodynamics? T.W. Marshall. 20. Action-angle variables inherent in quantum dynamics; J. Martínez-Linares. 21. A philosopher struggles to understand quantum theory: Particle creations and wavepacket reduction; N. Maxwell. 22. Consistent histories and the interpretation of quantum mechanics; R. Omnès. 23. Is quantum mechanics a limit cycle theory? L. de la Peña, A.M. Cetto. 24. Realization and characterization of quantum nondemolition measurements in optics; J.Ph. Poizat, et al. 25. Fuzzy sets and infinite-valued Łukasiewicz logic in foundations of quantum mechanics; J. Pykacz. 26. A model of topological quantization of the electromagnetic field; A.F. Rañada. 27. Postselection and squeezing in neutron interferometry and EPR-experiments; H. Rauch. 28. Macroscopic decoherence and classical stochastic gravity; J.L. Sanchez-Gomez. 29. Dynamics and measurement of the absolute phase in macroscopic quantum systems; F. Sols, R.A. Hegstrom. 30. Realistic quantum theory and relativity; E.J. Squires. 31. On the empirical law of epistemology: Physics as an artifact of mathematics; N.A. Tambakis. 32. Search of a first principle for quantum physics; A.C. de la Torre. 33. Decoherence in an isolated macroscopic quantum system: A parameter-free model involving gravity; J. Unturbe. 34. Nonlocal measurements and teleportation of quantum states; L. Vaidman. 35. Quantum noise in optical photon detectors; A. Vidiella-Barranco, E. Santos.

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Book SynopsisThere exist essentially two levels of investigation in theoretical physics. One is primarily descriptive, concentrating as it does on useful phenomenological approaches toward the most economical classifications of large classes of experimental data on particular phenomena. The other, whose thrust is explanatory, has as its aim the formulation of those underlying hypotheses and their mathematical representations that are capable of furnishing, via deductive analysis, predictions - constituting the particulars of universals (the asserted laws)- about the phenomena under consideration. The two principal disciplines of contemporary theoretical physics - quantum theory and the theory of relativity - fall basically into these respective categories. General Relativity and Matter represents a bold attempt by its author to formulate, in as transparent and complete a way as possible, a fundamental theory of matter rooted in the theory of relativity - where the latter is viewed as providing an explanatory level of understanding for probing the fundamental nature ofmatter indomainsranging all the way fromfermis and lessto light years and more. We hasten to add that this assertion is not meant to imply that the author pretends with his theory to encompass all ofphysics or even a tiny part of the complete objective understanding of our accessible universe. But he does adopt the philosophy that underlying all natural phenomena there is a common conceptualbasis,and then proceeds to investigate how far such a unified viewcan take us at its present stage of development.Trade Review`...to read it should be a rewarding experience for anyone who is concerned with understanding the most fundamental features of the physicist's world view. ...well written and contains some very useful material on both the conceptual and technical aspects of relativity.' Foundations of Physics, 15 (1985) Table of ContentsA.- 1 / Concepts.- B : Mathematical Preliminaries.- 2 / Vector-Tensor Analysis in Relativity Theory.- 3 / Spinor-Quaternion Analysis in Relativity Theory.- C: The Field Equations.- 4 / The Matter Field Equations.- 5 / The Electromagnetic Field Equations.- 6 / The Gravitational Field Equations and Unification with Inertia and Electromagnetism.- 7 / Astrophysics and Cosmology.- Selections from the Author’s Bibliography.

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Book SynopsisAddressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.Table of ContentsThe conception, gestation, birth and infancy of FCT.- The design of flux-corrected transport (FCT) algorithms for structured grids.- On monotonically integrated large eddy simulation of tubulent flows based on FCT algorithms.- Large scale urban simulations with FCT.- 30 years of FCT.- Algebraic flux corretion I.- Algebraic flux correction II.- Algebraic flux correction III.- Algebraic flux correction IV.- An evaluation of the FCT method for high-speed flows.- Flux-corrected and optimization-based remap.

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Book SynopsisOur book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.Table of ContentsDiscrete stochastic processes and time series.- Trend definition.- Finite AR(1) stochastic process.- Monte Carlo experiments. - Monte Carlo statistical ensembles.- Numerical generation of trends.- Numerical generation of noisy time series.- Statistical hypothesis testing.- Testing the i.i.d. property.- Polynomial fitting.- Linear regression.- Polynomial fitting.- Polynomial fitting of artificial time series.- An astrophysical example.- Noise smoothing.- Moving average.- Repeated moving average (RMA).- Smoothing of artificial time series.- A financial example.- Automatic estimation of monotonic trends.- Average conditional displacement (ACD) algorithm.- Artificial time series with monotonic trends.- Automatic ACD algorithm.- Evaluation of the ACD algorithm.- A paleoclimatological example.- Statistical significance of the ACD trend.- Time series partitioning.- Partitioning of trends into monotonic segments.- Partitioning of noisy signals into monotonic segments.- Partitioning of a real time series.- Estimation of the ratio between the trend and noise.- Automatic estimation of arbitrary trends.- Automatic RMA (AutRMA).- Monotonic segments of the AutRMA trend.- Partitioning of a financial time series.

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Book SynopsisMean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.Table of Contents

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Book SynopsisODE/IM Correspondence.- Exact WKB Analysis and TBA Equations.- Massive ODE/IM Correspondence.- Integrable Models and Functional Relations.

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Book Synopsis.- Foundations of Computational Thermokinetics in RPUF..- Modeling Techniques..- Key Factors in Computational Modeling of RPUF..- Implications and Future Outcomes.

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Book SynopsisChapter 1 Introduction.- Chapter 2 Density Functional Theory.- Chapter 3  Anharmonic Phonon Theory.- Chapter 4 Modern Theory and Machine Learning of Polarization.- Chapter 5 Dielectric Properties of Strongly Anharmonic TiO2.- Chapter 6 Dielectric Properties of Liquid Alcohols and Its Polymers.- Chapter 7 Conclusion.

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Book SynopsisMathematics and Statistics.- Physics.- Chemistry.- Biology.- Engineering Sciences.- Artificial Intelligence.

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Book SynopsisPreface.- Chapter 1. Survey on the Prandtls Equations and Related Boundary Layer Equations.- Chapter 2. Global Well-posedness of Solutions to the 2D Prandtl-Hartmann Equations in Analytic Framework.- Chapter 3. Local Existence of Solutions to the 2D Prandtl Equations in A Weighted Sobolev Space.- Chapter 4. Local Well-posedness of Solutions to the 2D Mixed Prandtl Equations in A Sobolev Space Without Monotonicity or Lower Bound.- Chapter 5. Local Well-posedness of Solutions to 2D Magnetic Prandtl Model in the Prandtl-Hartmann regime.- Chapter 6. Local Existence of Solutions to 3D Prandtl Equations with a Special Structure.- Bibliography.

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Book SynopsisChapter 1. Introduction to Chemical transformations in far from equilibrium systems.- Chapter 2. A brief introduction to vectors spaces: succinct but pertinent summary for scientists.- Chapter 3. White noise probability spaces (Hermite polynomials and functions and their use in defining Weiner Chaos expansion).- Chapter 4. Introduction to Skorohod integration and Malliavian derivativespractical interpretations.- Chapter 5. Introduction to Wick Product and its algebra (analytical solutions to Wick product driven stochastic differential equations; Hermite transformations).- Chapter 6. Numerical solutions to stochastic chemical reactions.- Chapter 7. Stochastic coupled reactions systems: Numerical solutions.- Chapter 8. Modelling chiral symmetry breaking and stability in a noisy environment using Wick productsA case study.

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Book SynopsisTable of Contents1. Introduction 2. The Basis of Monte Carlo 3. Pseudorandom Number Generators 4. Sampling, Scoring, and Precision 5. Variance Reduction Techniques 6. Markov Chain Monte Carlo 7. Inverse Monte Carlo 8. Linear Operator Equations 9. The Fundamentals of Neutral Particle Transport 10. Monte Carlo Simulation of Neutral Particle Transport 11. Monte Carlo Applications

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Book SynopsisEquations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case.Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.Table of ContentsSome Preliminaries from Analysis and the Theory of Wave Processes. Integral Equations of Diffraction Theory for Obstacles in Unbounded Medium. Wave Fields in a Layer of Constant Thickness. Analytical Methods for Simply Connected Bounded Domains. Integral Equations in Diffraction by Linear Obstacles. Short-Wave Asymptotic Methods on the Basis of Multiple Integrals. Inverse Problems of the Short-Wave Diffraction. Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary. Numerical Methods for Irregular Operator Equations.

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Book SynopsisThis book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson''s work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson'Table of ContentsThe infinitesimal rule of threeNonstandard methods in the precalculus curruculumDifference quotients and smoothnessContinuous maps with special propertiesSome nonstandard methods in geometric topologyDelayed bifurcations in perturbed systems analysis of slow passage of Suhl-thresholdFunctional analysis and NSANear-standard compact internal linear operatorsDiscrete Fredholm's equationsNonstandard theory of generalized functionsRepresenting distributions by nonstandard polynomialsContributions of nonstandard analysis to partial differential equationsLoeb measure theoryUnions of Loeb nullsets: the contextGredient lines and distributions of functionals in infinite dimensional Euclidean spacesNonstandard flat integral representation of the free Euclidean field and a large deviation bound for the exponential interactionNonstandard analysis in selective uniersesLattices and monadsA neometric surveyLong sequences and neocompact sets

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Book SynopsisThis volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum groups.Table of ContentsLifting of Nichols algebras of type A2 and pointed Hopf algebras of order p4; survey of cross product bialgebras; a Morita-Takeuchi context for graded coalgebras; coalgebra-Galois extensions from the extension theory point of view; separable functors for the category of Doi-Hopf modules II; cyclic cohomology of coalgebras, coderivations and De Rham cohomology; Schur-Weyl categories and non-quasiclassical Weyl type formula; a generalized power map for Hopf algebras; associated varieties for classical lie superalgebras; algebraic versions of a finite-dimensional quantum groupoid; quasi-Hopf algebras and the centre of a tensor category; an easy proof for the uniqueness of integrals; the coquasitriangular Hopf algebra associated to a rigid Yang-Baxter coalgebra; on regularity of the algebra of covariants for actions of pointed Hopf algebras on regular commutative algebras; a survey on multiplier Hopf algebras.

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Book SynopsisThe increasing power of computer resources along with great improvements in observational data in recent years have led to some remarkable and rapid advances in astrophysical fluid dynamics. The subject spans three distinct but overlapping communities whose interests focus on (1) accretion discs and high-energy astrophysics; (2) solar, stellar, and galactic magnetic fields; and (3) the geodynamo, planetary magnetic fields, and associated experiments. This book grew out of a special conference sponsored by the London Mathematical Society with the support of EPSRC that brought together leading researchers in all of these areas to exchange ideas and review the status of the field.The many interesting problems addressed in this volume concern:Table of ContentsAccretion Discs. Discs with Mhd Turbulence and Their Response to Orbiting Planets. Mixing at the Surface of White Dwarf Stars. Pulsar Magnetospheres. Magnetic Fields in Galaxies. Self-Consistent Mean Field Electrodynamics in Two and Three Dimensions. The Solar Tachocline: Formation, Stability and Its Role in the Solar Dynamo. Magnetoconvection. Alfvén Waves Within the Earth's Core. Turbulence Models and Plane Layer Dynamos. Planetary and Stellar Dynamos: Challenges for Next Generation Models. Convection in Rotating Spherical Fluid Shells and Its Dynamo States. Laboratory Experiments on Liquid Metal Dynamos and Liquid Metal Mhd Turbulence. Index.

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Book SynopsisAn Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand''s representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann''s double commutant theorem, Kaplansky''s density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

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Book SynopsisHydrogen Recycling Studies in Tokamaks and Other Facilities.- 1. Hydrogen Isotopes Retention in Fusion Reactor Plasma-facing Materials: An Abbreviated Review.- 2. Trapping Effect in Hydrogen Retention in Metals.- 3. Recent Progress in Tritium Codeposition Modeling.- 4. The Effect of Deuterium Ion Bombardment on the Optical Properties of Beryllium Mirrors.- 5. Hot Liner Divertor Concept Analysis of Dust Formation and Locations.- Hydrogen Sputtering, Retention, Codeposition in Graphite.- 6. Hydrogen Isotope Retention Analysis for Tokamak Plasma-facing Materials.- 7. Surface Microrelief Influence on Hydrogen Interaction with Materials.- Hydrogen Recycling in Liquid Metals.- 8. Deuterium Treatment Effects on Lithium and TiN-Lithium Sputtering in Solid and Liquid Phase.- 9. Helium Entrapment in Liquid Metal Plasma-facing Surfaces in Tokamak Fusion Reactors.- Fundamental Permeation Studies I.- 10. A Model for the Steady State Plasma- and Gas-driven Hydrogen Isotope Permeation through Multi-layer Metal.- 11. Effect of Hydrogen Sorption on Surface Morphology of Pyrolytic Graphite.- Fundamental Permeation Studies II.- 12. General Model of Hydrogen Transport through Solid Membranes.- 13. Influence of Hydrogen and Helium on Radiation Damage of Structural Materials.- Hydrogen Recycling in Tungsten, Niobium, and Nickel.- 14. Deuterium Retention in Tungsten and Tungsten Carbides Irradiated with D Ions.- 15. An Interpretation of the Retention of Low Energy Deuterium Ions in Tungsten.- General Hydrogen and Helium Issues and Other Metals.- 16. Hydrogen Interaction with TiN Films.- 17. Bimetallic Diffusion Membranes: Possible Use for Active Hydrogen Recycling Control.- 18. Surface Evolution of Nickel under He and H Ion Irradiation by means of Kelvin Probe.- Measurements and Control of Hydrogen Recycling I.- 19. Development of an Innovative Carbon-based Ceramic Material; Application in High Temperature, Neutron and Hydrogen Environment.- 20. Nonmonotone Temperature Dependence of Plasma Driven Permeation through Nb Membrane.- Measurements and Control of Hydrogen Recycling II.- 21. Usage of Hydrogen-saturated Getter for Sputtering Protection of Construction Elements in Vacuum-plasma Installations.- 22. Laser Induced Breakdown Spectroscopy Technique for In-situ Dust Detecting in a Next-step Tokamak.- Authors.Table of ContentsPreface. 1. Hydrogen Isotopes Retention in Fusion Reactor Plasma-facing Materials: An Abbreviated Review; R.A. Causey, T.J. Venhaus. 2. Trapping Effect in Hydrogen Retention in Metals; O.V. Ogorodnikova. 3. Recent Progress in Tritium Codeposition Modeling; J.N. Brooks. 4. The Effect of Deuterium Ion Bombardment on the Optical Properties of Beryllium Mirrors; L.A. Jacobson, et al. 5. Hot Liner Divertor Concept Analysis of Dust Formation and Locations; V.M. Kozhevin. 6. Hydrogen Isotope Retention Analysis for Tokamak Plasma-facing Materials; T.A. Burtseva. 7. Surface Microrelief Influence on Hydrogen Interaction with Materials; A.V. Golubeva, et al. 8.Deuterium Treatment Effects on Lithium and TiN-Lithium Sputtering in Solid and Liquid Phase; J.P. Allain, D.N. Ruzic. 9. Helium Entrapment in Liquid Metal Plasma-facing Surfaces in Tokamak Fusion Reactors; A. Hassanein. 10. A Model for the Steady State Plasma- and Gas-driven Hydrogen Isotope Permeation through Multi-layer Metal; O.V. Ogorodnikova. 11. Effect of Hydrogen Sorption on Surface Morphology of Pyrolytic Graphite; E.A. Denisov, et al. 12. General Model of Hydrogen Transport through Solid Membranes; K. Habib, A. Habib. 13. Influence of Hydrogen and Helium on Radiation Damage of Structural Materials; B.A. Kalin, et al. 14. Deuterium Retention in Tungsten and Tungsten Carbides Irradiated with D Ions; V.Kh. Alimov, et al. 15. An Interpretation of the Retention of Low Energy Deuterium Ions in Tungsten; R.G. Macaulay-Newcombe, et al. 16. Hydrogen Interaction with TiN Films; E.A. Denisov, et al.17. Bimetallic Diffusion Membranes: Possible Use for Active Hydrogen Recycling Control; G.P. Glazunov, et al. 18. Surface Evolution of Nickel and He and H Ion Irradiation by means of Kelvin Probe; G.-N. Luo, et al. 19. Development of an Innovative Carbon-based Ceramic Material; Application in High Temperature, Neutron and Hydrogen Environment; C.H. Wu. 20. Nonmonotone Temperature Dependence of Plasma Driven Permeation through Nb Membrane; A. Spitsyn, et al. 21. Usage of Hydrogen-saturated Getter for Sputtering Protection of Construction Elements in Vacuum-plasma Installations; V.V. Bobkov, et al. 22. Laser Induced Breakdown Spectroscopy Technique for In-situ Dust Detecting in a Next-step Tokamak, V.M. Kozhevin, et al. Authors.

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