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

By Yi Lin

This booklet summarizes the most medical achievements of the blown-up thought of evolution technology, which was once first noticeable in released shape in 1994. It explores - utilizing the point of view and technique of the blown-up concept - attainable generalizations of Newtonian particle mechanics and computational schemes, constructed on Newton's and Leibniz's calculus, in addition to the medical structures and the corresponding epistemological propositions, brought and polished long ago 300 years.

The authors in short clarify the elemental suggestions, then learn a sequence of subject matters and difficulties of the present, lively examine greatly conducted within the average sciences. alongside the strains of the analyses, they introduce new issues of view and the corresponding equipment. additionally, they indicate that the blown-up concept originated from the assumption of mutual slavings of fabrics' constructions in order that ''numbers are remodeled into forms''. This discovery finds that nonlinearity isn't really an issue solvable within the first-push approach, 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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Lin (1989), Y. Lin (1990), Y. Lin, Y. Ma and R. Port (1990), S. C. OuYang (1994), I. Prigogine (1967), R. Thorn (1975), L. Y. Xu (1983), Y. Z. 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.

Instead, their changes follow certain underlying laws and are related. For example, the atmospheric pressure changes with the altitude. So, the variables pressure and altitude vary at the same time and are related. This fact provides the n a t u r a l basis on which the concept of functions was introduced and studied. 1 ( D e f i n i t i o n of F u n c t i o n s ) : W h e n a variable x assumes a value out of a set of the real number line, if based on a certain rule, another 22 Nonlinearity: The Conclusion of Calculus variable y has to take a certain number value or a certain set of number values, then the variable y is called a function of the variable x.

To this end, OuYang has clearly said: "Determinacy is a problem about materials' structures and is not simply a problem of formal mathematical quantifications". We think that such conclusion should be an important epistemological progress of the 20th century; and at the same time, it ends the hundred-year old debate between determinacy and indeterminacy. What's more important is that this conclusion points to a forthcoming revolution in scientific methodology: Dwelling exclusively on the traditional equation-type quantitative relations and statistical schemes will not reveal the essence and origins of materials' evolutions.

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