We introduced the useful instrument of Knot Theory Jones polynomial and its formation.

In this paper,we discuss Jones polynomial of Brunnian links mainly from the geometric point of view.

Research of overhead cam characteristic based high order polynomial in high speed-gasoline engine;

To adapt to the high speed of modern rapier looms and the requirement of rapier motion curve,a new design method of transitional curve of modified trapezoid acceleration motion for rapier is put forward,which uses high order polynomial as transitional curve.

By simulating,computing and analyzing FB2,sine-parabolic and high-order polynomial the cam profile of asymmetrical valve train,the influences of characteristic parameters such as velocity at the end of buffering zone,lift at the end of buffering zone,half-angle of base zone on the cam profile,and the valve movement as well as the self characteristic response of every cam profile were analyzed.

Taking the fullness coefficient and wear design as multi-objectives,we study the optimization of the cam profile of a high-order polynomial using MATLAB and its optimization toolbox.

In this paper,it was to be analyzed respectively for cosine acceleration,sinusoidal acceleration,improving trapezoid acceleration of follower motion and SVAJ curve of high degree polynomial based on the characteristic of double-stopping-distance cam mechanism.

In this paper,a new definition of Bernstein Polynomial in convergence region is proposed,and a concise method is used to demonstrate the result of approximate degree of Bernstein Polynomial function.

Then,applying the generalized Bernstein polynomial,the approximation theorem is established,that is,there exists a sequence of αpolynomial{Pn(x,a)}for a continue function f(x) in a closed interval, the sequence{Pn(x,a)}converges the function f(x) uniformly in the interval.