Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.

INTEGRABLE TYPES OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION SETS OF HIGHER ORDERS

Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.

Research Progress of Differential Systems for Physiological Races of Plasmodiophora brassicae Wor

Research progress was reviewed on the differential systems for physiologic races of Plasmodiophora brassicae Woron,including Williams,differential system and European clubroot differential（ECD） set.The existing problems and countermeasures of the different differential systems were discussed,and a research status quo on the molecular identification and detection of clubroot pathogen in crucifers were introduced.

STRICT STABILITY OF IMPULSIVE SET VALUED DIFFERENTIAL EQUATIONS

In this paper, we develop strict stability concepts of ODE to impulsive hybrid set valued differential equations. By Lyapunov’s original method, we get some basic strict stability criteria of impulsive hybrid set valued equations.

Conservation Laws of a Class of Combined Equations

In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.

Measures of Semi Noncompactness and Set Valued AM Mappings

In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.

Differential attack on nonlinear combined sequences

By using the coding properties and statistic properties of the plaintext,the differential properties of the key stream sequences generated by a nonlinear combined generator were analyzed.Then a differential attack algorithm on the nonlinear combined sequences was proposed.At last,an attack example adopting the differential attack algorithm was presented.