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Polygons, polyominoes and polycubes   Publication : [S.l.] Springer 2009 . 518 p. , This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems. In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology and bio-informatics – can be expressed as counting problems, in which specified graphs, or shapes, are counted. One very special class of shapes is that of polygons. These are closed, connected paths in space. We usually sketch them in two-dimensions, but they can exist in any dimension. The typical questions asked include "how many are there of a given perimeter?", "how big is the average polygon of given perimeter?", and corresponding questions about the area or volume enclosed. That is to say "how many enclosing a given area?" and "how large is an average polygon of given area?" Simple though these questions are to pose, they are extraordinarily difficult to answer. They are important questions because of the application of polygon, and the related problems of polyomino and polycube counting, to phenomena occurring in the natural world, and also because the study of these problems has been responsible for the development of powerful new techniques in mathematics and mathematical physics, as well as in computer science. These new techniques then find application more broadly. The book brings together chapters from many of the major contributors in the field. An introductory chapter giving the history of the problem is followed by fourteen further chapters describing particular aspects of the problem, and applications to biology, to surface phenomena and to computer enumeration methods. 24 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),
Quantum field theory a modern perspective par Nair, V. Parameswaran. Publication : [S.l.] Springer 2005 . 556 p. , Based on lecture notes for a graduate course given for many years at the City University of New York.  At present, there is no. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (2),

Quantum integrable systems par Chowdhury, Asesh Roy. Publication : [S.l.] : Chapman and Hall/CRC 2004 . 412 p. , The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the more recent advances. This book presents and clarifies the developments of the last ten years in quantum integrable systems. After a preliminary discussion of the fundamentals of classical nonlinear integrable systems, the authors explore the quantum domain. Their approach emphasizes physical systems and the use of concrete examples, and they take care to establish the relationship between new and older methods. The presentation includes the first comprehensive discussion of the quantum Bcklund transformation Q-operator and various techniques related to algebraic Bethe Ansatz that are not available elsewhere in book form. In Quantum Integrable Systems, researchers active in the field have an up-to-date source for recent advances and new techniques, and nonspecialists finally have an accessible introduction to the concepts and basic tools they need to explore and exploit the wide-ranging applicability of the subjec 32 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Quantum mathematical physics Atoms, molecules and large systems par Thirring, Walter Publication : New York Springer 2002 . xvi, 582 pages , This edition combines the earlier two volumes on Quantum mechanics of atoms and molecules, and Quantum mechanics of large systems, published separately in 1981 and 1983 as a volumes 3 and 4 of the Lehrbuch der mathematischen Physik. 24 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Quantum trajectories and measurements in continuous time the diffusive case par Barchielli, Alberto Publication : Berlin | Heidelberg Springer 2009 . 325 p. , This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the line width narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output. 25 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Relativistic numerical hydrodynamics / par Wilson,, James R. Publication : [S.l.] : Cambridge University Press, 2003 . 232 p. ; , Calculations of relativistic hydrodynamics are crucial to several areas of current research in the physics of supernovae and stellar collapse. This book provides an overview of the computational framework in which such calculations have been developed, with examples of applications to real physical systems. Beginning with the development of the equations and differencing schemes for special relativistic hydrodynamics, the book stresses the viability of the Euler-Lagrange approach to most astrophysical problems. It details aspects of solving the Einstein equations together with the fluid dynamics for various astrophysical systems in one, two and three dimensions. 25 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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),

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),

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),

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),

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),

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),

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),

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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