抛物线的参数方程及其参数的应用

抛物线的参数方程中参数的几何意义,课本中没有作任何介绍,往往被人们所忽略,本文只对抛物线参数方程的一种形式中的参数的意义略作探讨;为了展现出该曲线方程中的参数在解答一类题型中的效果,现仅就其参数几何意义的应用,特提出一些实例,供读者们参考,下面先引出一个命题。命题过形如抛物线     

一类分布参数系统的参数辨识问题

双重孔隙裂缝储集层的反求参数问题是石油(或天燃气)开发中的非常重要的问题,在流体,运动方程中的综合压缩系数和渗透率是未知的几何参数,在本文中,我们从分布参数系统的参数辨识观点来讨论反求参数问题。我们讨论了具有非齐次边值问题的流体运动方程的可解性问题。得来了参数可辨识性的必要条件。     

联合监测过程位置参数和尺度参数的非参数Shewhart控制图

用于检测生产服务过程的传统控制图多数都假定过程的分布是已知的。这些控制困经常是在正态分布的假设下构建的,然而在服务质量实时监控中数据往往是非正态的。在这种情况下,基于正态分布假设的控制图的结果是不可靠的。为了解决这个问题,通常考虑非参数方法,因为在过程分布未知情况下,非参数控制图比参数图更加稳健有效。本文提出一个新的基于Van der Waerden和Klotz检验的Lepage型非参数Shewhart控制图(称为LPN图)用于同时检测未知连续过程分布的位置参数和尺度参数。文中给出了LPN图在不同参数下的控制限。依据运行长度分布的均值,方差和分位数,分析了LPN图在过程受控和失控时的性能,并与其他一些现有的非参数控制图进行比较。基于蒙特卡洛的模拟结果表明,LPN图对非正态分布具有很好的稳健性,并且在不同的过程分布下对检测位置参数和尺度参数,尤其对检测尺度参数的漂移都具有很好的性能。最后通过监控出租车服务质量说明LPN图在实际中的应用。     

两参数Weibull分布参数的联合置信区间

本文推广了文献[1]的方法,给出了定数截尾情况下两参数Weibull分布的形状参数的区间估计,并通过大量的Monte-Carlo模拟考察了优选问题。另外还讨论了两参数的联合区间估计。文章最后通过实例说明了本文方法的应用。     

三参数Weibull分布参数的Bayes估计

给出了三参数Weibull分布参数Bayes估计的两种方法,其一基于Laplace数值积分法,其二基于Gibbs抽样方法.模拟例子说明了估计方法的有效性.     

截断参数分布族参数的可容许估计

在平方损失下Karlin[1]讨论了截断参数分布族参数的可容许估计问题．本文讨论了当待估参数为单调函数和多项式函数时的可容许估计问题.文[1]讨论的待估参数，形式上较特殊，有关结果可视为本文结论的一个特例．     

限制参数空间时参数的 minimax 估计

一、引言在实际问题中,我们有时事先就对参数有一些认识,因此有必要考虑参数空间被限制时参数的估计问题.但令人吃惊的是,这给理论上的讨论带来了许多困难,尤其是求参数的 minimax 估计等问题,迄今结果不多.     

双参数指数分布位置参数的统计推断

通过次序统计量 ,得到了双参数指数分布 E(μ,λ)中位置参数μ的一致最小方差无偏估计为nn-1 T(1) -1n-1 T,推导出了 ( T-μ) / ( T-T(1) )的分布与参数μ,λ无关 ,从而得到了μ的置信区间与检验统计量 .     

两总体下双参数指数分布门限参数的比较

本文研究了当刻度参数未知时,双参数指数分布门限参数的检验问题.利用了似然比检验的方法,获得了检验统计量及检验水平的上下界.该方法应用在两个截尾数相等情形下,所得到的检验水平是真实的.     

用分离参数法求参数的取值范围

求参数的取值范围问题是中学数学教学的难点之一,也常为高考的热点。教学实践中发现,确定参数取值范围问题常可转化为方程或不等式中参数取值范围问题来处理,因而探讨方程或不等式中参数取值范围的确定方法很有必要。本文介绍求方程或不等式     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.