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Heuristic programming. --- Algorithms. --- Combinatorial optimization. --- Programmation heuristique --- Algorithmes --- Optimisation combinatoire --- Complex analysis --- Computer. Automation --- Discrete mathematics --- Operational research. Game theory
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Tensor analysis is an essential tool in any science (e.g. engineering,physics, mathematical biology) that employs a continuum description. This concise text offers a straight forward treatment of the subject suitable for the student or practicing engineer.
Calculus of tensors. --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Complex analysis
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Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Mathematical analysis. --- Functions of complex variables. --- Complex analysis --- Analysis (Mathematics). --- Functions of a Complex Variable. --- Analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables
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Complex analysis --- Analytic sheaves --- Analytic spaces --- Hypersurfaces --- Milnor fibration --- Singularities (Mathematics) --- Geometry, Algebraic --- Fibering theorem, Milnor --- Fibers, Milnor --- Fibration, Milnor --- Milnor fibering theorem --- Milnor fibers --- Milnor fibres --- Hyperspace --- Surfaces --- Spaces, Analytic --- Analytic functions --- Functions of several complex variables --- Sheaf theory --- Hypersurfaces. --- Analytic sheaves. --- Analytic spaces. --- Faisceaux analytiques. --- Espaces analytiques. --- Singularités (mathématiques)
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Complex analysis --- Harmonic analysis. --- Convex bodies. --- Representations of groups. --- Laplace transformation. --- Convex bodies --- Harmonic analysis --- Laplace transformation --- Representations of groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics) --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Convex domains
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Complex analysis --- Functions of complex variables --- Mathematical analysis --- Fonctions d'une variable complexe --- Analyse mathématique --- Functions of complex variables. --- Mathematical analysis. --- 517.53 --- Functions of a complex variable --- 517.53 Functions of a complex variable --- Analyse mathématique --- 517.1 Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- 517.1. --- 517.1
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Complex analysis --- 517.53 --- Functions of a complex variable --- 517.53 Functions of a complex variable --- Monogenic functions. --- Small divisors. --- Quasianalytic functions. --- Continued fractions. --- Fractions continues --- Fonctions quasi-analytiques --- Fonctions monogènes --- Continued fractions --- Monogenic functions --- Quasianalytic functions --- Small divisors --- Divisors, Small --- Small divisors problem --- Differentiable dynamical systems --- Functions, Quasianalytic --- Quasi-analytic functions --- Quasientire functions in the sense of Bernstein --- Analytic functions --- Functions, Monogenic --- Functions of complex variables --- Fractions, Continued --- Series --- Processes, Infinite --- Fractions continues. --- Fonctions quasi-analytiques. --- Fonctions monogènes.
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This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.
Schrodinger equation. --- Wave mechanics. --- Equation, Schrödinger --- Schrödinger wave equation --- Electrodynamics --- Matrix mechanics --- Mechanics --- Molecular dynamics --- Quantum statistics --- Quantum theory --- Waves --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Schrödinger equation. --- Schrödinger, Équation de. --- Solitons. --- Abelian integral. --- Analytic continuation. --- Analytic function. --- Ansatz. --- Approximation. --- Asymptote. --- Asymptotic analysis. --- Asymptotic distribution. --- Asymptotic expansion. --- Banach algebra. --- Basis (linear algebra). --- Boundary (topology). --- Boundary value problem. --- Bounded operator. --- Calculation. --- Cauchy's integral formula. --- Cauchy's integral theorem. --- Cauchy's theorem (geometry). --- Cauchy–Riemann equations. --- Change of variables. --- Coefficient. --- Complex plane. --- Cramer's rule. --- Degeneracy (mathematics). --- Derivative. --- Diagram (category theory). --- Differentiable function. --- Differential equation. --- Differential operator. --- Dirac equation. --- Disjoint union. --- Divisor. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic integral. --- Energy minimization. --- Equation. --- Euler's formula. --- Euler–Lagrange equation. --- Existential quantification. --- Explicit formulae (L-function). --- Fourier transform. --- Fredholm theory. --- Function (mathematics). --- Gauge theory. --- Heteroclinic orbit. --- Hilbert transform. --- Identity matrix. --- Implicit function theorem. --- Implicit function. --- Infimum and supremum. --- Initial value problem. --- Integrable system. --- Integral curve. --- Integral equation. --- Inverse problem. --- Jacobian matrix and determinant. --- Kerr effect. --- Laurent series. --- Limit point. --- Line (geometry). --- Linear equation. --- Linear space (geometry). --- Logarithmic derivative. --- Lp space. --- Minor (linear algebra). --- Monotonic function. --- Neumann series. --- Normalization property (abstract rewriting). --- Numerical integration. --- Ordinary differential equation. --- Orthogonal polynomials. --- Parameter. --- Parametrix. --- Paraxial approximation. --- Parity (mathematics). --- Partial derivative. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Pole (complex analysis). --- Polynomial. --- Probability measure. --- Quadratic differential. --- Quadratic programming. --- Radon–Nikodym theorem. --- Reflection coefficient. --- Riemann surface. --- Simultaneous equations. --- Sobolev space. --- Soliton. --- Special case. --- Taylor series. --- Theorem. --- Theory. --- Trace (linear algebra). --- Upper half-plane. --- Variational method (quantum mechanics). --- Variational principle. --- WKB approximation.
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