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Mathematical physics --- Fluides, Mécanique des --- Fluid mechanics --- Korteweg-de Vries equation --- Korteweg-de Vries, Équation de --- Fluid mechanics. --- Korteweg-de Vries equation. --- Fluides, Mécanique des --- Korteweg-de Vries, Équation de --- Equations aux derivees partielles non lineaires

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Differential equations, Partial --- Hamiltonian systems --- Mathematical physics --- Solitons --- Equations aux dérivées partielles --- Systèmes hamiltoniens --- Physique mathématique --- Equations aux dérivées partielles --- Systèmes hamiltoniens --- Physique mathématique --- Solitons. --- Korteweg-de Vries equation --- Korteweg-de Vries, Équation de --- Differential equations, Nonlinear --- Équations différentielles non linéaires --- Lie groups --- Lie, Groupes de --- Lie algebras --- Lie, Algèbres de

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Mathematical physics --- Differential equations, Partial --- Solitons --- Scattering (Mathematics) --- Equations aux dérivées partielles --- Dispersion (Mathématiques) --- Numerical solutions --- Solutions numériques --- 517.93 --- -Scattering (Mathematics) --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Scattering theory (Mathematics) --- Boundary value problems --- Scattering operator --- Partial differential equations --- Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems --- Solitons. --- Numerical solutions. --- Scattering (Mathematics). --- 517.93 Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems --- Equations aux dérivées partielles --- Dispersion (Mathématiques) --- Solutions numériques --- Numerical analysis --- Korteweg-de Vries equation --- Korteweg-de Vries, Équation de --- Korteweg-de Vries equation. --- Korteweg-de Vries, Équation de --- Dynamique différentiable --- Differential equations, Partial - Numerical solutions --- Equations aux derivees partielles --- Scattering

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Symmetry and complexity are the focus of a selection of outstanding papers, ranging from pure Mathematics and Physics to Computer Science and Engineering applications. This collection is based around fundamental problems arising from different fields, but all of them have the same task, i.e. breaking the complexity by the symmetry. In particular, in this Issue, there is an interesting paper dealing with circular multilevel systems in the frequency domain, where the analysis in the frequency domain gives a simple view of the system. Searching for symmetry in fractional oscillators or the analysis of symmetrical nanotubes are also some important contributions to this Special Issue. More papers, dealing with intelligent prognostics of degradation trajectories for rotating machinery in engineering applications or the analysis of Laplacian spectra for categorical product networks, show how this subject is interdisciplinary, i.e. ranging from theory to applications. In particular, the papers by Lee, based on the dynamics of trapped solitary waves for special differential equations, demonstrate how theory can help us to handle a practical problem. In this collection of papers, although encompassing various different fields, particular attention has been paid to the common task wherein the complexity is being broken by the search for symmetry.

History of engineering & technology --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes --- fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes

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This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff.The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space.Originally published in 1995.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.

Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Congresses --- Analysis, Fourier --- -Analysis, Fourier --- -Theory of the Fourier integral --- -517.518.5 Theory of the Fourier integral --- 517.518.5 --- 517.518.5 Theory of the Fourier integral --- Theory of the Fourier integral --- Mathematical analysis --- Analytic function. --- Banach fixed-point theorem. --- Bessel function. --- Blaschke product. --- Boundary value problem. --- Bounded operator. --- Cauchy–Riemann equations. --- Coefficient. --- Commutative property. --- Convolution. --- Degeneracy (mathematics). --- Differential equation. --- Differential geometry. --- Differential operator. --- Dirichlet problem. --- Distribution (mathematics). --- Eigenvalues and eigenvectors. --- Elias M. Stein. --- Elliptic integral. --- Elliptic operator. --- Equation. --- Ergodic theory. --- Error analysis (mathematics). --- Estimation. --- Existential quantification. --- Fourier analysis. --- Fourier integral operator. --- Fourier series. --- Fourier transform. --- Fundamental matrix (linear differential equation). --- Fundamental solution. --- Geometry. --- Green's function. --- Haar measure. --- Hardy space. --- Hardy–Littlewood maximal function. --- Harmonic analysis. --- Harmonic function. --- Harmonic measure. --- Hausdorff dimension. --- Heisenberg group. --- Hermitian matrix. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hopf lemma. --- Hyperbolic partial differential equation. --- Integral geometry. --- Integral transform. --- Julia set. --- Korteweg–de Vries equation. --- Lagrangian (field theory). --- Lebesgue differentiation theorem. --- Lebesgue measure. --- Lie algebra. --- Linear map. --- Lipschitz continuity. --- Lipschitz domain. --- Mandelbrot set. --- Martingale (probability theory). --- Mathematical analysis. --- Maximal function. --- Measurable Riemann mapping theorem. --- Minkowski space. --- Misiurewicz point. --- Morera's theorem. --- Möbius transformation. --- Nilpotent group. --- Non-Euclidean geometry. --- Numerical analysis. --- Nyquist–Shannon sampling theorem. --- Ordinary differential equation. --- Orthonormal basis. --- Orthonormal frame. --- Oscillatory integral. --- Partial differential equation. --- Plurisubharmonic function. --- Pseudo-Riemannian manifold. --- Pseudo-differential operator. --- Pythagorean theorem. --- Radon transform. --- Regularity theorem. --- Representation theory. --- Riemannian manifold. --- Riesz representation theorem. --- Riesz transform. --- Schrödinger equation. --- Schwartz kernel theorem. --- Sign (mathematics). --- Simultaneous equations. --- Singular integral. --- Sobolev inequality. --- Sobolev space. --- Special case. --- Symmetrization. --- Theorem. --- Trigonometric series. --- Uniqueness theorem. --- Variable (mathematics). --- Variational inequality. --- Analyse harmonique