LEADER 04977nam 22006014a 450 001 9910784818103321 005 20230607221546.0 010 $a981-277-809-8 035 $a(CKB)1000000000410418 035 $a(EBL)1681243 035 $a(OCoLC)879025122 035 $a(SSID)ssj0000110978 035 $a(PQKBManifestationID)11139211 035 $a(PQKBTitleCode)TC0000110978 035 $a(PQKBWorkID)10074951 035 $a(PQKB)11180548 035 $a(MiAaPQ)EBC1681243 035 $a(WSP)00004877 035 $a(Au-PeEL)EBL1681243 035 $a(CaPaEBR)ebr10201233 035 $a(CaONFJC)MIL505443 035 $a(EXLCZ)991000000000410418 100 $a20020514d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBeyond nonstructural quantitative analysis$b[electronic resource] $eblown-ups, spinning currents, and modern science /$fYong Wu, Yi Lin 210 $aRiver Edge, NJ $cWorld Scientific$dc2002 215 $a1 online resource (344 p.) 300 $aDescription based upon print version of record. 311 $a981-02-4839-3 320 $aIncludes bibliographical references (p. 303-310) and index. 327 $aContents ; Foreword ; Chapter 1 Introduction ; 1.1 Scientific Discoveries ; 1.2 Nonlinear Science ; 1.3 Some Ancient Thoughts of the East and the West ; 1.4 Determinacy and Randomness ; 1.5 Equal Quantitative Effects ; 1.6 Organization of This Book ; 1.7 References 327 $aChapter 2 Nonlinearity: The Conclusion of Calculus 2.1 A Brief History of Calculus ; 2.2 The Method of Differential Analysis ; 2.2.1 Functions and Their Properties ; 2.2.1.1 Representations of Functions ; 2.2.1.2 General Properties of Function ; 2.2.2 Limits of Functions 327 $a2.2.3 Continuous Functions 2.2.4 The Concept and Properties of Differentials ; 2.3 The Well-Posedness and Singularity of Differential Equations ; 2.4 Discontinuity: The Mathematical Characteristic of Nonlinear Evolutions ; 2.5 Question the Traditional Treatments of Nonlinearity 327 $a2.5.1 Linearization 2.5.2 Stabilization ; 2.5.3 Comparison between Spectral Method and Numerical Schemes ; 2.5.4 Limitations of Lyapunov Exponents ; 2.6 References ; Chapter 3 Blown-Up Theory: The Beginning of the Era of Discontinuity ; 3.1 Looking at Whole Evolutions 327 $a3.2 Mathematical Physics Meanings of Blown-Ups 3.3 Nonlinear Transitional Changes: A Mathematical Character of Blown-Ups ; 3.3.1 Blown-Ups of Quadratic Nonlinear Models ; 3.3.2 Blown-Ups of Cubic Polynomial Models ; 3.3.3 Blown-Ups of nth Degree Polynomial Models 327 $a3.3.4 Blown-Ups of Higher Order Nonlinear Evolution Systems 330 $a This book summarizes the main scientific achievements of the blown-up theory of evolution science, which was first seen in published form in 1994. It explores - using the viewpoint and methodology of the blown-up theory - possible generalizations of Newtonian particle mechanics and computational schemes, developed on Newton's and Leibniz's calculus, as well as the scientific systems and the corresponding epistemological propositions, introduced and polished in the past three hundred years. The authors briefly explain the fundamental concepts, then analyze a series of topics and problems of t 606 $aNonlinear theories 615 0$aNonlinear theories. 676 $a530.15 700 $aWu$b Yong$0695842 701 $aLin$b Yi$f1959-$0768255 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784818103321 996 $aBeyond nonstructural quantitative analysis$93775497 997 $aUNINA