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Book Cover
Author Wu, Yong

Title Beyond nonstructural quantitative analysis : blown-ups, spinning currents, and modern science / Yong Wu, Yi Lin
Published River Edge, NJ : World Scientific, ©2002


Description 1 online resource (xx, 324 pages) : illustrations
Contents Ch. 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 -- ch. 2. Nonlinearity: The conclusion of calculus. 2.1. A brief history of calculus. 2.2. The method of differential analysis. 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. 2.6. References -- ch. 3. Blown-up theory: The beginning of the era of discontinuity. 3.1. Looking at whole evolutions. 3.2. Mathematical physics meanings of blown-ups. 3.3. Nonlinear transitional changes: A mathematical character of blown-ups. 3.4. Mapping properties of blown-ups and related observ-control problems. 3.5. Spinning current: A physics characteristic of blown-ups. 3.6. Equal quantitative effects. 3.7. References -- ch. 4. Puzzles of the fluid science. 4.1. Fluids: A historical perspective. 4.2. Convergency (divergency) of moving fluids. 4.3. Dynamic characteristics of Navier-Stokes equation. 4.4. Some problems about atmospheric long waves. 4.5. Problem of objectivity of Hadly circulations. 4.6. Problems related to the modeling and solution of KdV and Burgers equations. 4.7. Is meteorological science a part of geophysics or atmospheric science? 4.8. References -- ch. 5. Questions about nonlinear macro-evolution theory. 5.1. Introduction. 5.2. Does "chaos" objectively exist? 5.3. Some problems about the one-dimensional iteration formula. 5.4. Problems related to thermodynamics. 5.5. Methodological problems of synergetics. 5.6. Some problems regarding catastrophe theory. 5.7. References -- ch. 6. Problems existing in theories of microscopic evolutions. 6.1. Some relevant historical recall. 6.2. Rules of quantum motion and characteristics of singularity. 6.3. Inaccurate measurements and equal quantitative effects. 6.4. Discussion on "quantum chaos". 6.5. Blown-up theory of laser emission. 6.6. References -- ch. 7. Some problems existing in the field theory. 7.1. The concept of fields and its historical importance. 7.2. The blown-up problem of the evolution of Higgs field. 7.3. Some problems about the evolution of SU (2) gauge field. 7.4. Do "gravitational waves" objectively exist? 7.5. Some problems about "universal gravitation". 7.6. References -- ch. 8. Difficulties facing the dynamics of nonlinear chemical reactions. 8.1. Chemical reactions and their rates. 8.2. The blown-up problem on gaseous chemical reactions. 8.3. The blown-up oroblem on liquid chemical reactions. 8.4. The blown-up problem on Schlog reaction model. 8.5. The blown-up problem on chain-reaction models. 8.6. References -- ch. 9. Nonlinearity and problems on theories of ecological evolutions. 9.1. The population evolution equation. 9.2. Evolution problems of logistic models. 9.3. Blown-up characteristics of improved logistic models. 9.4. References -- ch. 10. Nonlinearity and the blown-up theory of economic evolution systems. 10.1. The start of economics and inherent difficulties. 10.2. Evolution problem in merchandise prices. 10.3. The evolution problem on competitions between economic sectors and individual enterprises. 10.4. References
Summary Annotation 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
Bibliography Includes bibliographical references (pages 303-310) and index
Notes Print version record
Subject Nonlinear theories.
SCIENCE -- Physics -- Mathematical & Computational.
Nonlinear theories.
Form Electronic book
Author Forrest, Jeffrey Yi-Lin, 1959-
ISBN 9789812778093