OnQ-order andR-order of convergence

We give sufficient conditions for a sequence to have theQ-order and/or theR-order of convergence greater than one. If an additional condition is satisfied, then the sequence has an exactQ-order of convergence. We show that our results are sharp and we compare them with older results.This work was supported in part by the National Science Foundation under Grant No. DMS-85-03365. The author wishes to thank J. E. Dennis and R. A. Tapia for helpful comments, and the referee for pointing out a number of typographical and mathematical errors in the original version of this paper.     

基于顺序形态变换的生物芯片图像网格化

生物芯片图像网格化是对由生物芯片扫描得到的荧光成像中的信号(Foreground)和背景(Background)进行划分,以便提取各点的吸光度值、面积和吸光度比等荧光点的数据。网格化的准确与否决定了数据提取的正确性。提出了一种运用顺序形态变换理论实现生物芯片荧光图像网格化的方法,通过对百分位值在0~1之间的顺序形态进行变换,可实现像素灰度的极小值、中间值等多刻度值的灰度取值运算。理论分析表明,该算法能够识别信号与背景的边界,可去除噪声等非边界信息,能判断信号区域,可确定荧光点的边界和范围,可实现荧光点阵图像的网格化。试验结果表明,该算法对不同信噪比的荧光图像来说有很强的适应性,可用于高密度生物芯片图像的处理。     

线性规划问题的一种新的摄动法

在用单纯形方法解线性规划的问题时，不可避免会出现退化情况，而某些退化情况会导致循环。目前采用的避免循环的方法一共有两类：传统的摄动法（字典序）和Bland方法。本分析了传统摄动法的一些不足，给出了一种新的摄动法。     

对G.Ladas的一个开问题的解答

本文获得了一个高阶非线性差分方程具有无界正解的充分条件，所得结果解决了G.Ladas提出的一个开问题。     

一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

双贴合无光焦度校正板在双球面镜次镜后的系统的像差特性研究

讨论了双贴合无光焦度校正板放在次镜后的双反射球面系统.根据像差理论分析了消像差的条件，研究了主镜的相对孔径变化、校正板在次镜后的位置变化以及无光焦度校正板的正负透镜的不同组合形式对系统高级残余像差的影响.结果表明：当主镜的相对孔径增加或校正板靠近次镜时，系统的残余像差增加；无论校正板的第一个透镜是正透镜还是负透镜，系统在某一光焦度处残余像差最小，并且靠近次镜的透镜最好采用负透镜.     

Uniform convergence of Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity

In this article we prove uniform convergence estimates for the recently developed Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity. These multigrid methods are defined in terms of the “Galerkin approach,” where quadratic forms over coarse grids are constructed using the quadratic form on the finest grid and iterated coarse‐to‐fine intergrid transfer operators. Previously, uniform estimates were obtained for problems with full elliptic regularity, whereas these estimates are derived with less than full elliptic regularity here. Applications to the nonconforming P₁, rotated Q₁, and Wilson finite elements are analyzed. The result applies to the mixed method based on finite elements that are equivalent to these nonconforming elements. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 203–217, 2002; DOI 10.1002/num.10004     

双面金属包覆介质波导模序数的判别方法

在双面金属包覆介质波导中 ,随着介质层厚度的变化 ,会出现TM0 模与TM1 模的分离和简并两种状态 ,从而影响衰减全反射 (ATR)谱中模序数的确认。通过对金属波导的理论分析和实验研究 ,提出了三种模序数确认方法 :本征角计算法、吸收峰全峰半宽比较法和吸收峰峰间距比较法 ,实现了两种状态下对模序数的准确判断     

f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

Multivariate Gini Indices

Two extensions of the univariate Gini index are considered:R_D, based on expected distance between two independent vectors from the same distribution with finite meanμ ^d; andR_V, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofR_Das proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.R_Vis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothR_DandR_Vequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:R_Dis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileR_Vis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.