The mathematical principle of the generation of cone roller′s centerless super roller guide spiral camber;

Based on the explanation to the process of an ancient interesting mathematical game by formula,the mathematical principle of this game is analyzed.

With the introduction of mathematic principles in fractal art,the paper explores the application of fractal art in dress pattern design from the perspectives of point,line,surface and color.

From the angle of the mathematical and geometrical bases,this paper makes brief discussion on the compensation of the lining and measuring system in D09―32 continuous tamping machine,emphatically introduces the compensation principles of the "three points" lining operation and "four points" lining operation,and probes into the lining compensation control of the traveling bogie.

One of them deals detailedly with the logical relation between the principle of mathematical induction (type I sa well as type I )and the well-ordering principle under a certain condition and the other introduces an axiom concerning the natural numbers and demonstrates the equivalence between it and the system of Peano axioms.