Error bounds of two smoothing approximations for semi-infinite minimax problems

In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., the one dimensional semi-infinite minimax problems）, the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature.     

HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

GBF_n（g）的商群性质

证明对于任一正交基函数ｇ，广义布尔函数具有商群性质，并提出同态核的构造，从而得到广义布尔函数的一种生成方法．     

一种广义互补问题的稳定点与非奇异性条件

广义互补问题是互补问题的推广，它在工农业生产等实际问题中有重要的应用．文章借助磨光函数将其转化为一个光滑方程系统和无约束光滑优化问题，讨论了优化问题的稳定点与广义互补问题的解之间的关系．     

Strong Stability and Non-smooth Data Error Estimates for Discretizations of Linear Parabolic Problems

We study smoothing properties of discretizations of a linear parabolic initial boundary value problem with a possibly non-selfadjoint elliptic operator. The solution at time t > 0 of this problem, as well as its time derivatives, are in L _r for initial values in L _s even when r > s. We show that similar strong stability results hold for discrete solutions obtained by discretizing in space by linear finite elements and in time by a class of A()-stable implicit rational multistep methods (including single step methods as a special case) with good smoothing properties, as well as for certain combinations of single step methods. Most of our results are derived from the corresponding L ₂-bounds, shown by semigroup techniques, together with a discrete Gagliardo-Nirenberg inequality, and generalize previously known estimates with respect to admissible problems and time discretization methods. Our techniques make it possible to obtain, e.g., supremum norm error estimates for initial data which are only required to be in L ₁.     

Vondrak数据平滑方法及其在微机上的实现

从Ｖｏｎｄｒａｋ的基本假设出发，比较详细地介绍了Ｖｏｎｄｒａｋ数据平滑方法，该方法适用于等间距和不等间距的测量数据，并且可以通过选择不同的平滑因子控制平滑的程度，因此它是一种实用的数据处理方法，文中用Ｆｏｒｔｒａｎ语言编写了完整的程序，对实际测量数据进行了平滑处理，并研究了本方法的幅频特性。     

广义滤波与建立矿体数学模型的自动化

在地质统计学中,采用变异函数来描述区域化变量的变化特征。但变异函数的实验曲线很不稳定,特别是在抽样观测数据比较少和抽样点比较分散时,很难得到比较理想的实验曲线。克里金法在建立数学模型的时候,往往要用手工法来拟合数学模型。在“杨赤中滤波与推估”法中,采用一种广义滤波法,即采用逐步增大游动区间半径取二项式系数加权游动平均的方法来建立随机特征函数的实验曲线。这种实验曲线是自然的光滑曲线,能够灵敏地反映变量的变化特征,并且采用一种特殊形式的与实验曲线有很好的吻合性的负幂指数函数来拟合它。用它来作数学模型,既能反映变量的宏观变化特征,又能反映局部变化特征,建立数学模型的全过程,可以通过一个计算程序来实现。不需要很多的已知点,也不要求点位很规则,只要把已知值输入计算机(点位不规则时,还要同时输入点的坐标),就可以很快打印输出数学模型的函数式。各向异性的数学模型也不需要用手工来套合。这样就完全实现了建立数学模型的自动化。上述自动建立数学模型的方法,不论用于金属或非金属矿,都取得了完满成功。建立矿体数学模型的完全自动化,是数学地质领域的一个重要创造。     

第一类积分方程三次光顺样条配置解法

引入并分析数值解第一类积分子方程的三次光顺样条配置解法,证明了极值问题的解存在唯一且是一个三次样条函数,得到了极值问题等价的线性方程组.     

快速傅里叶变换在喇曼光谱信号噪声平滑中的应用

 通过快速傅里叶变换(FFT)处理水的普通喇曼散射光谱信号,实现对其干扰噪声的抑制,获得信噪比较高的喇曼光谱.结果表明,通过快速傅里叶变换,获得弱信号源的目标信号和噪声信号的频谱,针对实验获得的弱信号喇曼光谱进行低通滤波和门限滤波,可以分别将具有高频和较低振幅的噪声信号去除,从而实现噪声平滑并获得高信噪比的喇曼光谱.