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Padé approximant. --- Painlevé equations. --- Equations, Painlevé --- Functions, Painlevé --- Painlevé functions --- Painlevé transcendents --- Transcendents, Painlevé --- Differential equations, Nonlinear --- Approximant, Padé --- Approximation theory --- Continued fractions --- Polynomials --- Power series

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Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.

chemie --- analyse (wiskunde) --- Differential equations --- informatietheorie --- Mathematical physics --- Chemistry --- Mathematics --- Ergodic theory. Information theory --- Engineering sciences. Technology --- differentiaalvergelijkingen --- ingenieurswetenschappen --- wiskunde --- Partial differential equations --- fysica --- Painlevé equations. --- Mathematical physics. --- Painlevé equations --- 517.91 --- Equations, Painlevé --- Functions, Painlevé --- Painlevé functions --- Painlevé transcendents --- Transcendents, Painlevé --- Differential equations, Nonlinear --- Physical mathematics --- Physics --- 517.91 Ordinary differential equations: general theory --- Ordinary differential equations: general theory

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Functions, Special. --- Integral equations. --- Funcions especials --- Equacions integrals --- Equacions funcionals --- Càlcul operacional --- Equacions de Fredholm --- Equacions de Volterra --- Equacions integrals estocàstiques --- Transformacions integrals --- Anàlisi funcional --- Funcions --- Funcions transcendents --- Equations, Integral --- Functional equations --- Functional analysis --- Special functions --- Mathematical analysis

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517.91 --- 517.95 --- Mathematical physics --- Painleve equations --- Equations, Painlevé --- Functions, Painlevé --- Painlevé functions --- Painlevé transcendents --- Transcendents, Painlevé --- Differential equations, Nonlinear --- Physical mathematics --- Physics --- Ordinary differential equations: general theory --- Partial differential equations --- Mathematics --- Painlevâe equations --- Engineering & Applied Sciences --- Applied Physics --- 517.95 Partial differential equations --- 517.91 Ordinary differential equations: general theory --- Painlevé equations. --- Mathematical physics. --- Painlevé equations --- Applied mathematics. --- Engineering mathematics. --- Theoretical, Mathematical and Computational Physics. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Painlevé equations. --- Equations differentielles non lineaires

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In late classical and early medieval China, ascetics strove to become transcendents--deathless beings with supernormal powers. Practitioners developed dietetic, alchemical, meditative, gymnastic, sexual, and medicinal disciplines (some of which are still practiced today) to perfect themselves and thus transcend death. Narratives of their achievements circulated widely. Ge Hong (283-343 C.E..) collected and preserved many of their stories in his Traditions of Divine Transcendents, affording us a window onto this extraordinary response to human mortality. Robert Ford Company's groundbreaking and carefully researched text offers the first complete, critical translation and commentary for this important Chinese religious work, at the same time establishing a method for reconstructing lost texts from medieval China. Clear, exacting, and annotated, the translation comprises over a hundred lively, engaging narratives of individuals deemed to have fought death and won. Additionally, To Live as Long as Heaven and Earth systematically introduces the Chinese quest for transcendence, illuminating a poorly understood tradition that was an important source of Daoist religion and a major social, cultural, and religious phenomenon in its own right.

Taoists --- Ge, Hong, --- Taoists - China - Biography --- Ge, Hong, - 284-364. - Shen xian zhuan --- alchemy. --- ancient china. --- archival work. --- ascetics. --- buddhism. --- china. --- chinese history. --- chinese texts. --- classicism. --- daoism. --- discipline. --- divinity. --- eastern philosophy. --- gymnastics. --- immortals. --- lost texts. --- medicine. --- medieval china. --- meditation. --- mortality. --- nonfiction. --- paranormal. --- philosophy. --- religion. --- sexual discipline. --- sexual practices. --- spirituality. --- supernatural being. --- supernatural powers. --- supernatural. --- taoism. --- to live as long as heaven and earth. --- traditions of the divine transcendents. --- transcend death. --- transcendents. --- transfiguration.