A METHOD FOR CALCULATING THE LYAPUNOV EXPONENT SPECTRUM OF A PERIODICALLY EXCITED NON-AUTONOMOUS DYNAMICAL SYSTEM

The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.

Dynamic Analysis of a Single-Column Platform

In this paper, a single-column structure used as well-head platform is studied. The loads of wave and current exerted on the single-column will be greatly reduced, therefore the cost of the structure will be decreased. The advantages of the single-column structure compared with ordinary jacket structure are explained. A dynamic analysis of this type of structure is made and some problems related to dynamic analysis are solved. In order to check the reliability of computation theory and programme, model tests have been carried out. However, as space is limited, the conclusion of tests will be introduced in another paper. Therefore, this type of structure is applicable for proctical engineering.

Study on microbial protein and the mechanism of solid-state fermentation with periodical dynamic changes of air

The effect of different extraction and purification conditions on the microbial protein obtained from solid-state fermentation(SSF)and the effect of periodical dynamic changes of air on protein have been studied.The mechanism of solid-state fermentation with periodical dynamic changes of air is also discussed.Compared with static solid-state fermentation,periodical dynamic changes of air afford a higher protein mass;from 1 g of the fermentation microbe,5.3 mg of the intracellular protein(an increase of 34.63%)and 9.09 mg of the extracellular protein(an increase of 17.8%)were obtained on the sixth day of fermentation.The filter paper activity and carboxymethyl cellulose activity(FPA and CMCase)of the extracellular protein are 1.739μmol/s and 109.592μmol/s,respectively,which represent increases of 60.1%and 21.2%over the corresponding values for static solid-state fermentation.The FPA and CMCase of the intra-cellular protein are 0.245μmol/s and 6.392μmol/s,respec-tively,which represent decreases of 22.2%and 38.7%over the corresponding values for static solid-state fermentation.The enzyme activity of the microbial extracellular protein in solid-state fermentation with periodical dynamic changes of air on the fifth day is nearly equal to that on the sixth day without periodical dynamic changes of air,so the period of fermentation can be shortened.The sodium dodecyl sulfate-polyacrylamide gel electrophoresis(SDS-PAGE)experiments suggest that pulsating air pressure stimulation leads to a decrease in the amount of protein component with molecule mass of about 80400Da,and an increase in the amount of protein component with molecule mass of about 28520Da.

BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.