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This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake.Originally published in 1970.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Complex analysis --- Analytic spaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Algebra homomorphism. --- Algebraic curve. --- Algebraic extension. --- Algebraic surface. --- Algebraic variety. --- Analytic continuation. --- Analytic function. --- Associated prime. --- Atlas (topology). --- Automorphism. --- Bernhard Riemann. --- Big O notation. --- Branch point. --- Change of variables. --- Characterization (mathematics). --- Codimension. --- Coefficient. --- Cohomology. --- Complete intersection. --- Complex analysis. --- Complex conjugate. --- Complex dimension. --- Complex number. --- Connected component (graph theory). --- Corollary. --- Critical point (mathematics). --- Diagram (category theory). --- Dimension (vector space). --- Dimension. --- Disjoint union. --- Divisor. --- Equation. --- Equivalence class. --- Exact sequence. --- Existential quantification. --- Finitely generated module. --- Geometry. --- Hamiltonian mechanics. --- Holomorphic function. --- Homeomorphism. --- Homological dimension. --- Homomorphism. --- Hypersurface. --- Ideal (ring theory). --- Identity element. --- Induced homomorphism. --- Inequality (mathematics). --- Injective function. --- Integral domain. --- Invertible matrix. --- Irreducible component. --- Isolated singularity. --- Isomorphism class. --- Jacobian matrix and determinant. --- Linear map. --- Linear subspace. --- Local ring. --- Mathematical induction. --- Mathematics. --- Maximal element. --- Maximal ideal. --- Meromorphic function. --- Modular arithmetic. --- Module (mathematics). --- Module homomorphism. --- Monic polynomial. --- Monomial. --- Neighbourhood (mathematics). --- Noetherian. --- Open set. --- Parametric equation. --- Parametrization. --- Permutation. --- Polynomial ring. --- Polynomial. --- Power series. --- Quadratic form. --- Quotient module. --- Regular local ring. --- Removable singularity. --- Ring (mathematics). --- Ring homomorphism. --- Row and column vectors. --- Scalar multiplication. --- Scientific notation. --- Several complex variables. --- Sheaf (mathematics). --- Special case. --- Subalgebra. --- Submanifold. --- Subset. --- Summation. --- Surjective function. --- Taylor series. --- Theorem. --- Three-dimensional space (mathematics). --- Topological space. --- Vector space. --- Weierstrass preparation theorem. --- Zero divisor. --- Fonctions de plusieurs variables complexes --- Variétés complexes

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This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

Thermodynamics --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mathematics. --- Addition. --- Adiabatic process. --- Applied mathematics. --- Arthur Eddington. --- Asymmetry. --- Available energy (particle collision). --- Axiom. --- Balance equation. --- Banach space. --- Boltzmann's entropy formula. --- Brillouin scattering. --- Carnot cycle. --- Classical mechanics. --- Clausius (crater). --- Compact space. --- Conservation law. --- Conservation of energy. --- Constant of integration. --- Continuous function (set theory). --- Continuous function. --- Control theory. --- Deformation (mechanics). --- Derivative. --- Diathermal wall. --- Diffeomorphism. --- Differentiable function. --- Diffusion process. --- Dimension (vector space). --- Dimension. --- Dissipation. --- Dot product. --- Dynamical system. --- Emergence. --- Energy density. --- Energy level. --- Energy storage. --- Energy. --- Entropy. --- Equation. --- Equations of motion. --- Equilibrium point. --- Equilibrium thermodynamics. --- Equipartition theorem. --- Existential quantification. --- First law of thermodynamics. --- Hamiltonian mechanics. --- Heat capacity. --- Heat death of the universe. --- Heat flux. --- Heat transfer. --- Homeomorphism. --- Hydrogen atom. --- Ideal gas. --- Inequality (mathematics). --- Infimum and supremum. --- Infinitesimal. --- Initial condition. --- Instant. --- Internal energy. --- Irreversible process. --- Isolated system. --- Kinetic theory of gases. --- Laws of thermodynamics. --- Linear dynamical system. --- Lipschitz continuity. --- Local boundedness. --- Lyapunov function. --- Lyapunov stability. --- Mathematical optimization. --- Molecule. --- Non-equilibrium thermodynamics. --- Operator norm. --- Probability. --- Quantity. --- Reversible process (thermodynamics). --- Second law of thermodynamics. --- Semi-infinite. --- Smoothness. --- State variable. --- State-space representation. --- Statistical mechanics. --- Steady state. --- Summation. --- Supply (economics). --- Systems theory. --- Temperature. --- Theorem. --- Theoretical physics. --- Theory. --- Thermal conduction. --- Thermal equilibrium. --- Thermodynamic equilibrium. --- Thermodynamic process. --- Thermodynamic state. --- Thermodynamic system. --- Thermodynamic temperature. --- Thermodynamics. --- Time evolution. --- Zeroth law of thermodynamics.

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About 120 years ago, James Clerk Maxwell introduced his now legendary hypothetical "demon" as a challenge to the integrity of the second law of thermodynamics. Fascination with the demon persisted throughout the development of statistical and quantum physics, information theory, and computer science--and linkages have been established between Maxwell's demon and each of these disciplines. The demon's seductive quality makes it appealing to physical scientists, engineers, computer scientists, biologists, psychologists, and historians and philosophers of science. Until now its important source material has been scattered throughout diverse journals.This book brings under one cover twenty-five reprints, including seminal works by Maxwell and William Thomson; historical reviews by Martin Klein, Edward Daub, and Peter Heimann; information theoretic contributions by Leo Szilard, Leon Brillouin, Dennis Gabor, and Jerome Rothstein; and innovations by Rolf Landauer and Charles Bennett illustrating linkages with the limits of computation. An introductory chapter summarizes the demon's life, from Maxwell's illustration of the second law's statistical nature to the most recent "exorcism" of the demon based on a need periodically to erase its memory. An annotated chronological bibliography is included.Originally published in 1990.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Thermodynamics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Maxwell's demon. --- Adiabatic process. --- Automaton. --- Available energy (particle collision). --- Billiard-ball computer. --- Black hole information paradox. --- Black hole thermodynamics. --- Black-body radiation. --- Boltzmann's entropy formula. --- Boyle's law. --- Calculation. --- Carnot's theorem (thermodynamics). --- Catalysis. --- Chaos theory. --- Computation. --- Copying. --- Creation and annihilation operators. --- Digital physics. --- Dissipation. --- Distribution law. --- Domain wall. --- EPR paradox. --- Energy level. --- Entropy of mixing. --- Entropy. --- Exchange interaction. --- Expectation value (quantum mechanics). --- Extrapolation. --- Fair coin. --- Fermi–Dirac statistics. --- Gibbs free energy. --- Gibbs paradox. --- Guessing. --- Halting problem. --- Hamiltonian mechanics. --- Heat engine. --- Heat. --- Helmholtz free energy. --- Ideal gas. --- Idealization. --- Information theory. --- Instant. --- Internal energy. --- Irreversible process. --- James Prescott Joule. --- Johnson–Nyquist noise. --- Kinetic theory of gases. --- Laws of thermodynamics. --- Least squares. --- Loschmidt's paradox. --- Ludwig Boltzmann. --- Maxwell–Boltzmann distribution. --- Mean free path. --- Measurement. --- Mechanical equivalent of heat. --- Microscopic reversibility. --- Molecule. --- Negative temperature. --- Negentropy. --- Newton's law of universal gravitation. --- Nitrous oxide. --- Non-equilibrium thermodynamics. --- Old quantum theory. --- Particle in a box. --- Perpetual motion. --- Photon. --- Probability. --- Quantity. --- Quantum limit. --- Quantum mechanics. --- Rectangular potential barrier. --- Result. --- Reversible computing. --- Reversible process (thermodynamics). --- Richard Feynman. --- Rolf Landauer. --- Rudolf Clausius. --- Scattering. --- Schrödinger equation. --- Second law of thermodynamics. --- Self-information. --- Spontaneous process. --- Standard state. --- Statistical mechanics. --- Superselection. --- Temperature. --- Theory of heat. --- Theory. --- Thermally isolated system. --- Thermodynamic equilibrium. --- Thermodynamic system. --- Thought experiment. --- Turing machine. --- Ultimate fate of the universe. --- Uncertainty principle. --- Unitarity (physics). --- Van der Waals force. --- Wave function collapse. --- Work output.

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Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an 'unlikely intersection' statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.

MATHEMATICS / Geometry / Algebraic. --- Affine plane. --- Affine space. --- Affine transformation. --- Algebraic closure. --- Algebraic curve. --- Algebraic equation. --- Algebraic extension. --- Algebraic surface. --- Algebraic variety. --- Algebraically closed field. --- Analysis. --- Analytic function. --- Analytic geometry. --- Approximation. --- Arithmetic dynamics. --- Asymmetric graph. --- Ball (mathematics). --- Bifurcation theory. --- Boundary (topology). --- Cantor set. --- Characterization (mathematics). --- Chebyshev polynomials. --- Coefficient. --- Combinatorics. --- Complex manifold. --- Complex number. --- Computation. --- Computer programming. --- Conjugacy class. --- Connected component (graph theory). --- Continuous function (set theory). --- Coprime integers. --- Correspondence theorem (group theory). --- Counting. --- Critical graph. --- Cubic function. --- Datasheet. --- Disk (mathematics). --- Divisor (algebraic geometry). --- Elliptic curve. --- Equation. --- Equidistribution theorem. --- Equivalence relation. --- Euclidean topology. --- Existential quantification. --- Fixed point (mathematics). --- Function space. --- Geometric (company). --- Graph (discrete mathematics). --- Hamiltonian mechanics. --- Hausdorff dimension. --- Hausdorff measure. --- Holomorphic function. --- Inequality (mathematics). --- Instance (computer science). --- Integer. --- Intermediate value theorem. --- Intersection (set theory). --- Inverse-square law. --- Irreducible component. --- Iteration. --- Jordan curve theorem. --- Julia set. --- Limit of a sequence. --- Line (geometry). --- Metric space. --- Moduli space. --- Moment (mathematics). --- Montel's theorem. --- P-adic number. --- Parameter. --- Pascal's Wager. --- Periodic point. --- Polynomial. --- Power series. --- Primitive polynomial (field theory). --- Projective line. --- Quotient ring. --- Rational number. --- Realizability. --- Renormalization. --- Riemann surface. --- Ring of integers. --- Scientific notation. --- Set (mathematics). --- Sheaf (mathematics). --- Sign (mathematics). --- Stone–Weierstrass theorem. --- Subharmonic function. --- Support (mathematics). --- Surjective function. --- Theorem. --- Theory. --- Topology. --- Transfer principle. --- Union (set theory). --- Unit disk. --- Variable (computer science). --- Variable (mathematics). --- Zariski topology. --- Polynomials. --- Dynamics. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Algebra --- Algebraic geometry. --- Mathematics.

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This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Harmonic analysis. Fourier analysis --- Phase space (Statistical physics) --- Harmonic analysis --- 512.54 <043> --- 530.145 <043> --- 517.986.6 --- 51-7 <043> --- 517.986.6 <043> --- Groups. Group theory--Dissertaties --- Quantum theory--Dissertaties --- Harmonic analysis of functions of groups and homogeneous spaces --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc.--Dissertaties --- Harmonic analysis of functions of groups and homogeneous spaces--Dissertaties --- 517.986.6 <043> Harmonic analysis of functions of groups and homogeneous spaces--Dissertaties --- 51-7 <043> Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc.--Dissertaties --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- 530.145 <043> Quantum theory--Dissertaties --- 512.54 <043> Groups. Group theory--Dissertaties --- Space, Phase (Statistical physics) --- Generalized spaces --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Harmonic analysis. --- Analytic continuation. --- Analytic function. --- Antisymmetric tensor. --- Asymptotic expansion. --- Automorphism. --- Bilinear form. --- Bounded operator. --- Calculation. --- Canonical commutation relation. --- Canonical transformation. --- Cauchy–Riemann equations. --- Cayley transform. --- Class function (algebra). --- Classical mechanics. --- Commutative property. --- Complex analysis. --- Configuration space. --- Differential equation. --- Differential geometry. --- Differential operator. --- Eigenvalues and eigenvectors. --- Equation. --- Explicit formula. --- Fock space. --- Fourier analysis. --- Fourier integral operator. --- Fourier transform. --- Functional analysis. --- Gaussian function. --- Gaussian integral. --- Geometric quantization. --- Hamiltonian mechanics. --- Hamiltonian vector field. --- Heisenberg group. --- Hermite polynomials. --- Hermitian symmetric space. --- Hilbert space. --- Hilbert transform. --- Integral transform. --- Invariant subspace. --- Irreducible representation. --- Lebesgue measure. --- Lie algebra. --- Lie superalgebra. --- Lie theory. --- Mathematical physics. --- Number theory. --- Observable. --- Ordinary differential equation. --- Orthonormal basis. --- Oscillator representation. --- Oscillatory integral. --- Partial differential equation. --- Phase factor. --- Phase space. --- Point at infinity. --- Poisson bracket. --- Polynomial. --- Power series. --- Probability. --- Projection (linear algebra). --- Projective Hilbert space. --- Projective representation. --- Projective space. --- Pseudo-differential operator. --- Pullback (category theory). --- Quadratic function. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Representation theory. --- Schrödinger equation. --- Self-adjoint operator. --- Semigroup. --- Several complex variables. --- Siegel disc. --- Sobolev space. --- Spectral theorem. --- Spectral theory. --- State-space representation. --- Stone's theorem. --- Stone–Weierstrass theorem. --- Summation. --- Symmetric space. --- Symmetric tensor. --- Symplectic geometry. --- Symplectic group. --- Symplectic vector space. --- Symplectomorphism. --- Tangent space. --- Tangent vector. --- Theorem. --- Translational symmetry. --- Unbounded operator. --- Unit vector. --- Unitarity (physics). --- Unitary operator. --- Unitary representation. --- Variable (mathematics). --- Wave packet.