Beyond Nonstructural Quantitative Analysis - Blown-Ups, by Yi Lin

By Yi Lin

This e-book summarizes the most clinical achievements of the blown-up conception of evolution technology, which used to be first noticeable in released shape in 1994. It explores - utilizing the point of view and technique of the blown-up conception - attainable generalizations of Newtonian particle mechanics and computational schemes, constructed on Newton's and Leibniz's calculus, in addition to the clinical structures and the corresponding epistemological propositions, brought and polished some time past 300 years.

The authors in brief clarify the basic options, then research a sequence of issues and difficulties of the present, energetic examine broadly conducted within the common sciences. alongside the strains of the analyses, they introduce new issues of view and the corresponding tools. additionally, they indicate that the blown-up idea originated from the belief of mutual slavings of fabrics' buildings in order that ''numbers are remodeled into forms''. This discovery finds that nonlinearity isn't an issue solvable within the first-push procedure, and that the fabrics' estate of rotation is not just an epistemology but additionally a technique. The authors then element to the truth that nonlinearity is a moment stir of mutual slavings of fabrics.

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Extra info for Beyond Nonstructural Quantitative Analysis - Blown-Ups, Spinning Currents and Modern Science

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If successful, we would hope to reach the goal that scientific explorations will ultimately describe the Tao of the nature instead of trying to fit the Tao into the tools employed. The organization of this book can be outlined as follows: Chapter two is devoted to the presentation of the so-called mystery of nonlinearity and how the modern study, entitled "nonlinear science", has been originated, after a brief introduction to an array of basic concepts of calculus. After showing that discontinuity is a fundamental characteristic of nonlinear evolutions, it is concluded that in order to revolve problems of nonlinearity, new methodology and thinking logic are needed.

Zhu (1985). For more details, please consult with these references. This page is intentionally left blank Chapter 2 Nonlinearity: The Conclusion of Calculus In this chapter, we will look at a brief history of calculus, its achievements, fundamental concepts and results of the differential and integral analysis. As soon as the concepts of well-psedness and singularity of differential equations are looked at, one starts to see the limitations of calculus and all theories developed on calculus. Then, by considering a list of examples, it is argued that discontinuity is a mathematical characteristic of nonlinear evolutions.

Quoted from Natural Dialectics). In the past one hundred plus years, scholars had tried whatever they could to change this situation. Especially after the 1970s, with the rapid development of computer technology, a heat wave of mathematical modeling and computer simulation has been spreading across the entire spectrum of science and technology to such a degree 12 Introduction that to some people, it seems that all natural events and matters can be modeled and simulated by employing mathematics and that all problems can be resolved by using numerical computations.

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