三次Bézier曲线的快速生成算法

本文给出了一种三次Ｂéｚｉｅｒ曲线的生成算法，在曲线的逐点生成过程中，只用到加减法，故效率极高．而且，此方法可推广到一般多项式或有理参数曲线     

二元数字期权定价与copula的关系

首先简要介绍了 copula的一些基本概念和性质 ,然后探讨了一种多元未定权益——二元数字期权的价格与 copula的关系 .结论表明 ,一个二元数字期权的价格恰好是一个 copula函数 ,由此结论进而给出了根据实际数据获得二元数字期权价格的基本思路和步骤 .     

Existence of solutions to a class of nonlinear second order two-point boundary value problems

In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u^″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u^′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role.     

关于一类高阶Liénard型方程周期解的注记

本文研究一类具偏差变元的高阶 Liénard型方程的周期解存在性 ,给出了这类方程周期解存在性的若干充分条件 .     

LIMIT CYCLES OF A GENERALIZED LINARD DIFFERENTIAL EQUATION VIA AVERAGING THEORY

We apply the averaging theory of first and second orders to a generalized Liénard differential equation to study the maximum number of limit cycles of the system.     

一类广义Liénard型系统解振荡的充要条件

给出了一类广义Liénard型系统(x)=p(y)k(x),(y)=-f(x,y)p(y)q(y)-g(x)h(y).解振荡的充要条件,文中的引理也有助于研究这类系统周期解的存在性.     

Cubic spline for a class of singular two-point boundary value problems

In this paper we have presented a method based on cubic splines for solving a class of singular two-point boundary value problems. The original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by Thomas algorithm. Some model problems are solved, and the numerical results are compared with exact solution.     

关于错排数与Bell数的一些循环公式

In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the generating function methods and Padé approximation techniques. Illustrative special cases of the main results are also presented.     

关于凸函数的新不等式

考虑由Fejér不等式的右边部分生成的差值.通过建立积分恒等式,在导函数满足M-Lipschitz条件和导函数有界这两种情况下,给出这个差值的界的估计.