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The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.

Anbieter: Dodax

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76,76 € *

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The second edition deals with all essential aspects of non-relativistic quantum physics up to the quantisation of fields. In contrast to common textbooks of quantum mechanics, modern experiments are described both for the purpose of foundation of the theory and in relation to recent applications. Links are made to important research fields and applications such as elementary particle physics, solid state physics and nuclear magnetic resonance in medicine, biology and material science. Special emphasis is paid to quantum physics in nanoelectronics such as resonant tunnelling, Coulomb blockade and the realisation of quantum bits.This second edition also considers quantum transport through quantum point contacts and its application as charge detectors in nanoelectronic circuits. Also the realization and the study of electronic properties of an artificial quantum dot molecule are presented. Because of its recent interest a brief discussion of Bose-Einstein condensation has been included, as well as the recently detected Higgs particle. Another essential new addition to the present book concerns a detailed discussion of the particle picture in quantum field theory. Counterintuitive aspects of single particle quantum physics such as particle-wave duality and the Einstein-Podolski-Rosen (EPR) paradox appear more acceptable to our understanding if discussed on the background of quantum field theory. The non-locality of quantum fields explains non-local behaviour of particles in classical Schrödinger quantum mechanics. Finally, new problems have been added.The book is suitable as an introduction into quantum physics, not only for physicists but also for chemists, biologists, engineers, computer scientists and even for philosophers as far as they are interested in natural philosophy and epistemology.

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101,71 € *

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Many open questions in Theoretical Physics pertain to strongly interacting quantum systems such as the quark-gluon plasma (QGP) produced in heavy-ion collisions or the strange-metal phase observed in many high-temperature superconductors. These systems are notoriously difficult to study using traditional methods such as perturbation theory, but the gauge/gravity duality offers a successful alternative approach, which maps strongly interacting quantum gauge theories to computationally tractable, classical gravity theories. This book begins with a pedagogical introduction to how the duality can be used to extract transport properties of quantum systems from their gravity dual. It then presents new results on hydrodynamic transport in strongly interacting quantum fluids, providing strong evidence that the Haack-Yarom identity between second-order transport coefficients holds for all fluids with a classical gravity dual and may be a universal feature of all strongly coupled quantum fluids such as the QGP. Newly derived Kubo formulae, expressing transport coefficients in terms of quantum correlators, hold independently of the duality. Lastly, the book discusses new results on magnetic impurities in strongly correlated metals, including the first dual gravity description of an inter-impurity coupling, crucial for the quantum criticality underlying the strange-metal phase.

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113,00 CHF *

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This book provides a comprehensive introduction to gauge/string duality and its applications to the study of the thermal and transport properties of quark-gluon plasma. It is an ideal reference for students and researchers in string theory, quantum field theory, quantum many-body physics, heavy ion physics and lattice QCD.

Anbieter: Orell Fuessli CH

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76,90 CHF *

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Anbieter: Orell Fuessli CH

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164,00 CHF *

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In modern mathematical physics, classical together with quantum, geometrical and functional analytic methods are used simultaneously. Non-commutative geometry in particular is becoming a useful tool in quantum field theories. This book, aimed at advanced students and researchers, provides an introduction to these ideas. Researchers will benefit particularly from the extensive survey articles on models relating to quantum gravity, string theory, and non-commutative geometry, as well as Connes' approach to the standard model. From the contents: -Notes on Equivariant Localization - An Introduction to Spin Foam Models of BF Theory and Quantum Gravity - T-Duality and the Gravitational Description of Gauge Theories - Noncommutative Geometry and Basic Physics - An Introduction to Noncommutative Geometry - Geometric Properties of Transport in Quantum Hall Systems - q-Deformed Heisenberg Algebras - Abstracts of the Seminars

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The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience--including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.

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69,90 CHF *

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Invariant sets for semilinear parabolic and elliptic systems.- On the numerical solution of nonlinear partial differential equations on divergence form.- Application of the averaging method for the solution of boundary problems for ordinary differential and integro-differential equations.- Solution set properties for some nonlinear parabolic differential equations.- Asymptotic invariant sets of autonomous differential equations.- Algebraic methods in the theory of global properties of the oscillatory equations Y?=Q(t)Y.- Stability problems in mathematical theory of viscoelasticity.- On the branching of solutions and Signorini's perturbation procedure in elasticity.- Differential subspaces associated with pairs of ordinary differential operators.- Control and the Van der Pol equation.- On properties of spectral approximations.- Singular perturbations and linear feedback control.- On some inverse problems for partial differential equations.- Nonlinear noncoercive boundary value problems.- On the iterative solution of some nonlinear evolution equations.- Exponential representation of solutions of ordinary differential equations.- The Rayleigh and Van der Pol wave equations, some generalizations.- The Dirichlet problem.- Multiple solutions of some asymptotically linear elliptic boundary value problems.- Dual finite element analysis for some unilateral boundary value problems.- Gradient alternating-direction methods.- Nonlinear parabolic boundary value problems with the time derivative in the boundary conditions.- Variational and boundary value problems for differential equations with deviating argument.- On a general conception of duality in optimal control.- Boundary value problems for systems of nonlinear differential equations.- Boundary behavior of potentials.- Some modifications of sobolev spaces and non-linear boundary value problems.- Some problems in neutron transport theory.- On formulation and solvability of boundary value problems for viscous incompressible fluids in domains with non-compact boundaries.- Boundary value problems at resonance for vector second order nonlinear ordinary differential equations.- Behaviour of solutions to the dirichlet problem for the biharmonic operator at a boundary point.- Asymptotic methods for singularly perturbed linear differential equations in Banach spaces.- Non linear quasi variational inequalities and stochastic impulse control theory.- On the regularity of weak solutions to variational equations and inequalities for nonlinear second order elliptic systems.- The solution of parabolic models by finite element space and A-stable time discretization.- Global properties of the nth order linear differential equations.- A forced quasilinear wave equation with dissipation.- Energetic estimates analogous to the Saint-Venant principle and their applications.- A priori bounds for a semilinear wave equation.- The method of least squares on the Boundary and very weak solutions of the first biharmonic problem.- Application of bounded operators and Lyapunov's majorizing equations to the analysis of differential equations with a small parameter.- On linear problems in the space BV.- A partially ordered space connected with the de la Vall¿poussin problem.- Abstract Cauchy problem.- Solution of symmetric positive systems of differential equations.- Some problems concerning the functional differential equations.- A-stability and numerical solution of abstract differential equations.- Mapping properties of regular and strongly degenerate elliptic differential operators in the besov spaces B p,p s (?). The case 0

Anbieter: Orell Fuessli CH

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72,90 CHF *

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Heavy ion collision experiments recreating the quark-gluon plasma that filled the microseconds-old universe have established that it is a nearly perfect liquid that flows with such minimal dissipation that it cannot be seen as made of particles. String theory provides a powerful toolbox for studying matter with such properties. This book provides a comprehensive introduction to gauge/string duality and its applications to the study of the thermal and transport properties of quark-gluon plasma, the dynamics of how it forms, the hydrodynamics of how it flows, and its response to probes including jets and quarkonium mesons. Calculations are discussed in the context of data from RHIC and LHC and results from finite temperature lattice QCD. The book is an ideal reference for students and researchers in string theory, quantum field theory, quantum many-body physics, heavy ion physics and lattice QCD.

Anbieter: Orell Fuessli CH

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