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Relativity : an introduction to special and general relativity / par Stephani,, Hans. Publication : [S.l.] : Cambridge University Press, 2004 . 420 p. ; , Thoroughly revised and updated, this self-contained textbook provides a pedagogical introduction to relativity. It covers the most important features of special as well as general relativity, and considers more difficult topics, such as charged pole-dipole particles, Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools are provided, most derivations are complete, and exercises are included where appropriate. The bibliography lists the original papers and also directs the reader to useful monographs and review papers. Previous Edition Hb(1990): 0-521-37066-3 Previous Edition Pb(1990): 0-521-37941-5. 23 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Riemannian geometry and geometric analysis / par Jost, Jurgen. Publication : [S.l.] : Springer, 2005 . 566 p. ; , This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. Besides several smaller additions, reorganizations, corrections, and a systematic bibliography, the main new features of the 4th edition are a systematic introduction to KƲhler geometry and the presentation of additional techniques from geometric analysis. From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Math. Reviews. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Rotating fields in general relativity par Islam, Jamal N. Publication : Cambridge [Cambridgeshire] | New York Cambridge University Press 1985 . vi, 122 pages 24 cm Date : 1985 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Self-organised criticality theory, models, and characterisation par Pruessner,, Gunnar, Publication : Cambridge | New York Cambridge University Press 2012 . xxii, 494 pages , "Giving a detailed overview of the subject, this book takes in the results and methods that have arisen since the term 'self-organised criticality' was coined twenty years ago. Providing an overview of numerical and analytical methods, from their theoretical foundation to the actual application and implementation, the book is an easy access point to important results and sophisticated methods. Starting with the famous Bak-Tang-Wiesenfeld sandpile, ten key models are carefully defined, together with their results and applications. Comprehensive tables of numerical results are collected in one volume for the first time, making the information readily accessible to readers. Written for graduate students and practising researchers in a range of disciplines, from physics and mathematics to biology, sociology, finance, medicine and engineering, the book gives a practical, hands-on approach throughout. Methods and results are applied in ways that will relate to the reader's own research"-- | "When Bak, Tang, and Wiesenfeld (1987) coined the term Self-Organised Criticality (SOC), it was an explanation for an unexpected observation of scale invariance and at the same time, a programme of further research. Over the years it developed into a subject area which is concerned mostly with the analysis of computer models that display a form of generic scale invariance. The primacy of the computer model is manifest in the first publication and throughout the history of SOC, which evolved with and revolved around such computer models. That has led to a plethora of computer 'models', many of which are not intended to model much except themselves (also Gisiger, 2001), in the hope that they display a certain aspect of SOC in a particularly clear way. The question whether SOC exists is empty if SOC is merely the title for a certain class of computer models. In the following, the term SOC will therefore be used in its original meaning (Bak et al, 1987), to be assigned to systems with spatial degrees of freedom [which] naturally evolve into a self-organized critical point. Such behaviour is to be juxtaposed to the traditional notion of a phase transition, which is the singular, critical point in a phase diagram, where a system experiences a breakdown of symmetry and long-range spatial and in non-equilibrium, also temporal correlations, generally summarised as (power law) scaling (Widom, 1965a,b; Stanley, 1971)"-- 26 cm. Date : 2012 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

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Soliton equations and hamiltonian systems par Dickey, L. A. Publication : [S.l.] World Scientific Pub Co Inc 2003 . 408 p. , The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics. The second edition is up-to-date and differs from the first one considerably. One third of the book is completely new and the rest is refreshed and edited. 24 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Spectral problems associated with corner singularities of solutions to elliptic equations par Kozlov,, V. A. Publication : [S.l.] American Mathematical Society 2000 . 436 p. , This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order $2m$ in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order $2$ in an $n$-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $mid {Re} lambda - m + /2n mid leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses. 26 cm. Date : 2000 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Statistical mechanics : a concise introduction for chemists / par B.,, Widom. Publication : [S.l.] : Cambridge University Press, 2002 . 180 p. ; , This is an introduction to statistical mechanics, intended to be used either in an undergraduate physical chemistry course or by beginning graduate students with little undergraduate background in the subject. It assumes familiarity with thermodynamics, chemical kinetics, the kinetic theory of gases, quantum mechanics and spectroscopy, at the level at which these subjects are normally treated in undergraduate physical chemistry. Highly illustrated with numerous exercises and worked solutions, it provides a concise, up-to-date treatise of statistical mechanics and is ideally suited to use in one semester courses. 25 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (2),

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Stochastic differential equations : an introduction with applications / par k̲sendal,, Bernt. Publication : [S.l.] : Springer, 2003 . 374 p. ; , This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. 24 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Stochastic numerics for mathematical physics par Milshtein, G. N. Publication : Berlin | New York | London Springer 2004 . ixx [i.e. xix], 594 pages 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Stochastic processes for physicists understanding noisy systems par Jacobs,, Kurt Publication : Cambridge | New York Cambridge University Press 2010 . xiii, 188 pages 26 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Strings and geometry : proceedings of the clay mathematics institute 2002 summer school on strings and geometry, isaac newton institute, cambridge   Publication : [S.l.] Amer Mathematical Society 2004 . 376 p. , This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks. This volume contains a selection of expository and research articles by lecturers at the school and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. The book is suitable for graduate students and research mathematicians interested in relations between mathematical physics and algebraic geometry. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Supergravity par Freedman, Daniel Z. Publication : New York Cambridge University Press 2012 . xvii, 607 pages , "Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Although there are many books on string theory, this is the first-ever authoritative and systematic account of supergravity. Written by two of the most respected workers in the field, it provides a solid introduction to the fundamentals of supergravity. It starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers"-- 26 cm. Date : 2012 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Symmetries, lie algebras and representations a graduate course for physicists par Fuchs, Jürgen Publication : Cambridge Cambridge University Press 1997 . 438 p. , This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers. 25 cm. Date : 1997 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The mathematical language of quantum theory From uncertainty to entanglement par Heinosaari, Teiko Publication : Cambridge | New York Cambridge University Press 2012 . xii, 327 pages , "For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement. The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on mathematically precise formulations, the book summarises the relevant mathematics"-- | "THE MATHEMATICAL LANGUAGE OF QUANTUM THEORY For almost every student of physics, their first course on quantum theory raises puzzling questions and creates an uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation"-- 26 cm. Date : 2012 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The Random-cluster model / par Grimmett, Geoffrey R. Publication : [S.l.] : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2006 . 380 p. ; , Relié. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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The theory of magnetism made simple:an introduction to physical concepts and to some useful mathematical methods par Mattis, Daniel c. Publication : [S.l.] World Scientific Publishing Company 2006 . 580 p. , This new version of a classic updates much of the material in earlier editions, including the first chapter, on the history of the field. Important modifications reflect major discoveries of the past decades. A historical perspective is maintained throughout. The reader is drawn into the process of discovery: starting with a phenomenon, finding plausible explanations and competing theories — and finally, the solution. The theory of magnetism is practically a metaphor for theoretical physics. The very first quantum many-body theory (Bethe’s ansatz) was devised for magnetic chains, just as mean-field theory was invented a century ago by Weiss to explain Curie’s Law. The first two chapters of this book are immensely readable, taking us from prehistory to the “spin valves" of the most recent past. Topics in subsequent chapters include: angular momenta and spin (Chapter 3), quantum theory of simple systems, followed by increasingly technical insights into ordered and random systems, thermal fluctuations, phase transitions, chaos and the like. Contemporary developments in nanotechnology now seek to take advantage of the electron’s spin as well as of its charge. The time is not far off when nano-circuits made entirely of silicon exhibit such many-body properties as superconductivity or ferromagnetism — without any superconducting materials or magnetic ions being present. The reader of this book will be prepared for such exotic twenty-first century applications. Daniel C Mattis, BS, MS, PhD, Fellow of the American Physical Society (APS), is a frequent lecturer at research institutions and the author of several textbooks and numerous research articles. His expertise includes many-body theory, electrical conductivity, quantum theory of magnetism and most recently, nanotechnology. Prof. Mattis is on the editorial panel for high-temperature superconductivity of the International Journal of Modern Physics B and Modern Physics Letters B, both published by World Scientific. Currently serving as Professor in the Physics department at the University of Utah in Salt Lake City, Utah, USA, at various times he has been visiting Professor at Yale University (New Haven), State University of New York (Buffalo), Temple University (Philadelphia), and served as “Wei-Lun Visiting Professor" at the Chinese University of Hong Kong. A founding member of the “Few-Body Physics" section of the APS, he has also served as Chair of the standing committee of the! APS for the “International Freedom of Scientists." 25 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (2),

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Theoretical atomic physics par Friedrich, Harald Siegfried. Publication : [S.l.] Springer 2005 . 520 p. , This established text contains an advanced presentation of quantum mechanics adapted to the requirements of modern atomic physics.The third edition extends the successful second edition with a detailed treatment of the wave motion of atoms, and it also contains an introduction to some aspects of atom optics that are relevant for current and future experiments involving ultra-cold atoms. Included: Various problems with complete soluti 25 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Theory of random sets / par Molchanov,, Ilya. Publication : [berne.] : Springer, 2005 . 504 p. , This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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