Isotropic polynomial invariants of Hall tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.     

Kink wave determined by parabola solution of a nonlinear ordinary differential equation

By finding a parabola solution connecting two equilibrium points of a planar dynamical system,the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown.Some exact explicit parametric representations of kink wave solutions are given.Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.     

The existence of periodic solutions for nonlinear systems of first-order differential equations at resonance

ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｏｂｌｅｍｉｎｔｈｅＲｅｓｅａｒｃｈｏｆＴｏｒｏｉｄＴｈｉｓｐａｐｅｒｄｅａｌｓｗｉｔｈｔｈｅｅｘｉｓｔｅｎｃｅｏｆ2π＿ｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｔｏｔｈｅｎｏｎｌｉｎｅａｒｓｙｓｔｅｍｏｆｆｉｒｓｔ＿ｏｒｄｅｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈａｄｅｖｉａｔｉｎｇａｒｇｕｍｅｎｔ ｘ(ｔ) =Ｂｘ(ｔ) Ｆ(ｘ(ｔ-τ) ) ｐ(ｔ) ,( 1 )ｗｈｅｒｅｘ(ｔ)∈Ｒ2 , ｘ(ｔ) =ｄｄｔｘ(ｔ) ,τ∈Ｒ ,Ｂ∈Ｒ2×2 ,Ｆ :Ｒ2 →Ｒ2 ｉｓｂｏｕｎｄｅｄａｎｄｐ∈Ｃ(…     

The existence of periodic solutions of impulsive differential equations of mixed type

1　ＰｒｏｂｌｅｍｉｎｔｈｅＲｅｓｅａｒｃｈｏｆＴｏｒｏｉｄＩｍｐｕｌｓｉｖｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｉｓａｎｅｗｉｍｐｏｒｔａｎｔｂｒａｎｃｈｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ.Ｉｎ1989,[1],[2]ｓｙｓｔｅｍａｔｉｃａｌｌｙｓｕｍｍａｒｉｚｅｄｒｅｓｅａｒｃｈｗｏｒｋａｂｏｕｔｉｍｐｕｌｓｉｖｅｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｉｎｒｅｃｅｎｔｙｅａｒｓ,ｔｈｅｒｅａｒｅｍａｎｙｌｉｔｅｒａｔｕｒｅｓｄｅａｌｉｎｇｗｉｔｈｔｈｅｏｓｃｉｌｌａｔｉｏ…     

Differentiator series solution of linear differential ordinary equation

１Ｄｉｆｅｒｅｎｔｉａｔｏｒ,ＩｎｖｅｒｓＯｐｅｒａｔｏｒａｎｄＴｈｅｉｒＰｒｏｐｅｒｔｉｅｓ１．１ＤｉｆｅｒｅｎｔｉａｔｏｒａｎｄｉｎｖｅｒｓｏｐｅｒａｔｏｒＳｕｐｐｏｓｅｔｈｅｌｉｎｅａｒｏｒｄｉｎａｒｙｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆ...     

Numerical solution of nonlinear ordinary differential equation for a turning point problem

By using the method in[3],several useful estimations of the derivatives of the solutionof the boundary value problem for a nonlinear ordinary differential equation with a turningpoint are obtained.With the help of the technique in[4],the uniform convergence on thesmall parameterεfor a difference scheme is proved.At the end of this paper,a numericalexample is given.The numerical result coincides with theoretical analysis.     

Problem of periodic solutions for neutral functional differential equation

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＣ(ｋ- 1)2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓ (ｋ -1 )＿ｔｈｏｒｄｅｒｃｏｎｔｉｎｕｏｕｓｄｉｆｆｅｒｅｎｔｉａｂｌｅａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　Ｃ2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓｃｏｎｔｉｎｕｏｕｓａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　‖ｈ(ｔ)‖ =ｓｕｐｔ∈ [0 ,2π] ｜ｈ(ｔ) ｜ ,　　‖ｈ(ｔ)‖Ｐｋ- 1 =ｍａｘ‖ｈ(ｔ)‖ ,‖ｈ′(ｔ)‖ ,… ,‖ｈ(ｋ- 1) (ｔ)‖ ,　　ｘ(ｍ) (ｔ+ ·) (θ) =ｘ(ｍ) (ｔ+θ)　　θ∈Ｒ (ｍ =0 ,1 ,2 ,… ,ｋ-1 ) .Ｃｌｅａｒｌｙ ,ｘ(ｍ) (ｔ + ·) ∈Ｃ2π, …     

INTEGRABLE TYPES OF NONLINEAR ORDINARY DIFFERENTIAL EQUATION SETS OF HIGHER ORDERS

ＩＮＴＥＧＲＡＢＬＥＴＹＰＥＳＯＦＮＯＮＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＥＴＳＯＦＨＩＧＨＥＲＯＲＤＥＲＳＴａｎｇＧｕａｎｇｓｏｎｇ（汤光宋）（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔ,ＪｉａｎｇｈａｎＵｎｉｖ...     

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATION

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＺｈａｏＪｉｅ－ｍｉｎ（赵杰民）;ＨｕａｎｇＫｅ－ｌｅｉ（黄克累）...     

RESEARCH OF THE PERIODIC SOLUTION FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

ＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦ　ＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＲＥＳＥＡＲＣＨＯＦＴＨＥＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＤＩＦＦＥ...     

A new method for the periodic solution of strongly nonlinear systems

A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found. The project supported by the National Natural Science Foundation of China