Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) ...Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.展开更多
By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained. With the help o...By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained. With the help of the technique in [4], the uniform convergence on the small parameter e for a difference scheme is proved. At the end of this paper, a numerical example is given. The numerical result coincides with theoretical analysis.展开更多
In this paper, we consider the boundary value problems of the form ey″ - f(x, e)y′ + g(x, e)y=0 (-a&lex&leb, 0<e1) y(-a)=a, y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The ...In this paper, we consider the boundary value problems of the form ey″ - f(x, e)y′ + g(x, e)y=0 (-a&lex&leb, 0<e1) y(-a)=a, y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.展开更多
In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an alg...In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT mi...A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.展开更多
Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inc...Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.展开更多
In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t...In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.展开更多
We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, ...We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, f i satisfy 2 f y′ 2 i t =0 =0, we say that F possesses a generalized turning point at t =0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior of the solution when F possesses a generalized turning point at t =0. We mainly discuss regular singular crossings.展开更多
针对实际特高压换流变压器匝间短路故障时的二次谐波制动判据持续闭锁导致差动保护动作速度较慢的问题,该文详细分析特高压换流变匝间短路故障时的保护动作行为,通过理论分析换流变压器三相的相序差动电流变化量,发现匝间短路故障时具...针对实际特高压换流变压器匝间短路故障时的二次谐波制动判据持续闭锁导致差动保护动作速度较慢的问题,该文详细分析特高压换流变匝间短路故障时的保护动作行为,通过理论分析换流变压器三相的相序差动电流变化量,发现匝间短路故障时具有故障相的相序差动电流变化量幅值为非故障相的两倍且相位差为180°的特定关系,在此基础上,提出相序差动电流开放判据。此外,为防止特殊涌流工况时开放判据误闭锁,增设基于涌流间断偏移特征的识别开放判据,并进一步构造整套基于相序差动电流特征差异的换流变压器匝间保护优化方案。通过现场录波及实时数字仿真(real time digital simulation system,RTDS)仿真验证,提出的保护方法在匝间短路故障且二次谐波制动判据误闭锁时具有高快速性,对于暴露问题的实际故障,保护动作时间由56ms缩短为20ms。同时,保护在各类涌流工况时可靠不误动。该保护算法具有计算量小,对数据采样率要求不高的特点。展开更多
文摘Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.
文摘By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained. With the help of the technique in [4], the uniform convergence on the small parameter e for a difference scheme is proved. At the end of this paper, a numerical example is given. The numerical result coincides with theoretical analysis.
文摘In this paper, we consider the boundary value problems of the form ey″ - f(x, e)y′ + g(x, e)y=0 (-a&lex&leb, 0<e1) y(-a)=a, y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.
文摘In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金supported by the National University of Defense Technology Innovation Support Project for Outstanding Graduate Student(B100303)
文摘A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.
文摘Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.
文摘In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.
文摘We consider in this paper the boundary value problems of nonlinear systems the form εY″=F(t,Y,Y′,ε), -1<t<1, Y(-1,ε)=A(ε), Y(1,ε)=B(ε). Supoosing some or all of the components of F , that is, f i satisfy 2 f y′ 2 i t =0 =0, we say that F possesses a generalized turning point at t =0. Our goal is to give sufficient conditions for the existence of solution of the problems and to study the asymptotic behavior of the solution when F possesses a generalized turning point at t =0. We mainly discuss regular singular crossings.
文摘针对实际特高压换流变压器匝间短路故障时的二次谐波制动判据持续闭锁导致差动保护动作速度较慢的问题,该文详细分析特高压换流变匝间短路故障时的保护动作行为,通过理论分析换流变压器三相的相序差动电流变化量,发现匝间短路故障时具有故障相的相序差动电流变化量幅值为非故障相的两倍且相位差为180°的特定关系,在此基础上,提出相序差动电流开放判据。此外,为防止特殊涌流工况时开放判据误闭锁,增设基于涌流间断偏移特征的识别开放判据,并进一步构造整套基于相序差动电流特征差异的换流变压器匝间保护优化方案。通过现场录波及实时数字仿真(real time digital simulation system,RTDS)仿真验证,提出的保护方法在匝间短路故障且二次谐波制动判据误闭锁时具有高快速性,对于暴露问题的实际故障,保护动作时间由56ms缩短为20ms。同时,保护在各类涌流工况时可靠不误动。该保护算法具有计算量小,对数据采样率要求不高的特点。
