LUEROTH’S THEOREM IN DIFFERENTIAL FIELDS

In this paper,we present a constructive proof of Lueroth’s theorem in differential case.We also give a method to fing the inversion maps for general differential rational parametric equations.As a consequence,we prove that a differential rational curve always has a set of proper parametric equations.     

THE PROPER PARAMETRIZATION OF A SPECIAL CLASS OF RATIONAL PARAMETRIC EQUATIONS

We give a proper reparametrization theorem for a set of rational parametric equationswhich is proper for all but one of its parameters.We also give an algorithm to determine whether aset of rational parametric equations belongs to this class,and if it does,we reparametrize it such thatthe new parametric equations are proper.     

IMPLICITIZATION OF PARTIAL DIFFERENTIAL RATIONAL PARAMETRIC EQUATIONS

In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal of P; （2） To find a canonical representation for the image of P; （3）To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; （4） To compute the inversion maps of P, and as a consequence, to decide whether P is proper.     

ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.     

FIXED POINTS OF THE lTH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper, we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations. Because of the control of differential equation, we can obtain some precise estimate of their fixed points.     

FIXED POINTS OF THE ITH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper,we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations.Because of the control of differential equation,we can obtain some precise estimate of their fixed points.     

STABILIZATION OF NONUNIFORM TIMOSHENKOBEAM WITH COUPLED LOCALLY DISTRIBUTED FEEDBACKS

The stabilization problem of a nonuniform Timoshenko beam system With coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equations, we establish the asymptotic decay of the energy corresponding to the closed loop system. Then, by virtue of piecewise multiplier method, we prove the exponential decay of the closed loop system.     

ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations con-tain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.     

Solving the State Equation of a System by Walsh Function

In this paper, We deal with the solution of the state equation of a system by the Walsh function, that is, we shall find the solution of a matrix differential equation by the Walsh function, and introduce a solution of the higher-order matrix differential equation. First, after a certain transform, we turn the higher-order matrix differential equation into a state equation. Then we find the solution of the state equation by the Walsh function. Finally after a certain transform, we obtain a solution of the higher-order matrix differential equation.     

Generation method for five-axis NC spiral tool path based on parametric surface mapping

A new spiral tool path generation algorithm for 5-axis high speed machining is proposed in this paper. Firstly, the voltage contours are calculated to satisfy the machining parameters in the mapping parametric domain by means of the electrostatic field model of partial differential equations. Secondly, the mapping rules are constructed and the machining trajectory is planned out in the standard parametric domain in order to map and generate the spiral trajectory in the corresponding parametric domain. Finally, this trajectory is mapped onto the parametric surface for the obtainment of the spiral tool path. This spiral tool path can realize the machining of complicated parametric surface and trimmed surface without tool retractions. The above-mentioned algorithm has been implemented in several simulations and validated successfully through the actual machining of a complicated cavity. The results indicate that this method is superior to the existing machining methods to realize the high speed machining of the complicate-shaped cavity based on parametric surface and trimmed surface.     

二阶动力学系统输出反馈特征结构配置

考虑了二阶动力学系统的输出反馈特征结构配置设计问题。基于一类广义Sylvester方程的参数化解,给出了闭环系统的右、左特征向量矩阵及反馈增益矩阵的完全参数化表达式。该参数化方法为控制系统设计提供了全部自由度,其中包括待配置特征值和一组自由参量。该参数化方法直接基于二阶动力学系统的参数矩阵,故其计算简单、便于工程应用。数值例子表明二阶动力学系统输出反馈特征结构配置参数化方法简单而有效。     

导弹追逃博弈微分对策建模与求解

针对导弹攻防对抗过程中拦截器追击具备较强机动能力弹头的追逃问题,建立了双方追逃微分对策模型并给出求解方法.一是给出导弹追逃质点动力学模型;二是基于微分对策理论,建立了导弹攻防对抗微分对策模型,模型以推力角为控制变量,高度,速度和经度角为状态变量,并考虑了地球重力和自转的影响;三是针对模型获得解析解的困难,给出高精度四阶Gauss-Lobatto多项式配点法来逼近非线性方程,通过离散化节点和配点上的状态量和控制量将微分方程组转换为代数约束;四是为采用配点法求解模型,给出了将双边最优对策问题转化为单边最优对策问题的具体方法.最后实例分析对本文研究进行了仿真验证.     

短期降雨预测的随机微分模型

在Nakita等的确定型短期降雨预测模型的基础上，利用随机微分方程理论。给出了预测降雨强度的随机模型．通过随机分析理论，求出了随机模型的解，同时研究了求解的近似数值方法和利用Fourier变换转化该随机降雨模型方程为常微分方程组的可行性．最后把文章提出的随机波动模型和NAk．klta提出的确定型短期预测模型运用到Nakita 1996年给出的降雨事件中进行预测和比较，效果良好．     

二阶动力学系统模型的跟踪设计

考虑了基于分散状态反馈控制律的二阶动力学系统输出渐近跟踪设计,该控制律包括被控对象状态和参考模型状态两部分。给出了问题解的存在条件:两个矩阵方程,其中一个为二阶Sylvester矩阵方程。给出了所有控制器增益阵的完全参数化表达式。归纳出了二阶动力学系统模型参考输出跟踪控制律的设计算法。该算法直接基于原系统的参数矩阵,无须对系统增广或变换,仅涉及自由参数的选取和一些简单的代数运算,便于工程应用。仿真结果说明所给出的算法是有效的。     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

Rational Solutions of High-Order Algebraic Ordinary Differential Equations

This paper considers algebraic ordinary differential equations(AODEs) and study their polynomial and rational solutions. The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE. An AODE satisfying this condition is called noncritical. Then the authors prove that some common classes of low-order AODEs are noncritical. For rational solutions, the authors determine a class of AODEs, which are called maximally comparable, such that the possible poles of any rational solutions are recognizable from their coefficients. This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient. Finally, the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs, which is applicable to 78.54% of the AODEs in Kamke's collection of standard differential equations.