In this paper the theory of Mandelbrot-Julia sets of high degree complex polynomials is introduced, a series of the Mandelbrot-Julia sets of high degree complex polynomials is constructed through escape-time technique.

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.

Qualitative analysis for a class of higher polynomial system;

Study on limit cycles for a class of higher polynomial system;

By transformation, we change a class of higher polynomial system into a Lienard s system.