Yi Lin

Yong Wu

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 the current, active research widely carried out in the natural sciences. Along the lines of the analyses, they introduce new points of view and the corresponding methods. Also, they point out that the blown-up theory originated from the idea of mutual slavings of materials' structures so that “numbers are transformed into forms”. This discovery reveals that nonlinearity is not a problem solvable in the first-push system, and that the materials' property of rotation is not only an epistemology but also a methodology. The authors then point to the fact that nonlinearity is a second stir of mutual slavings of materials. Contents: Nonlinearity: The Conclusion of CalculusBlown-Up Theory: The Beginning of the Era of DiscontinuityPuzzles of the Fluids ScienceQuestions About Nonlinear Macro-Evolution TheoryProblems Existing in Theories of Microscopic EvolutionsSome Problems Existing in the Field TheoryDifficulties Facing the Dynamics of Nonlinear Chemical ReactionsNonlinearity and Problems on Theories of Ecological EvolutionsNonlinearity and the Blown-Up Theory of Economic Evolution Systems Readership: Undergraduates and scientists, as well as general readers interested in popular science, nonlinear science or general mathematics. Keywords:Reviews:“In the book a lot of examples in several situations are given, complemented by historical excursions and critical remarks.”Zentralblatt MATH

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