三个不同领域实际问题相结合的教学方法探讨

通过建立肿瘤增长动力学模型,研究肿瘤增长动态规律时发现:肿瘤增长的全过程与龚珀兹增长曲线描述的经济增长过程完全相符;进一步给出了龚珀兹增长曲线与描述种群的增长与调节的逻辑斯蒂增长曲线完全相似.将上述三个属性完全不同的实际应用问题打包传授给学生的授课方法是有别于孤立地介绍三个具体问题的,学生的学习效果也会不同.     

基于灰色系统的逻辑斯蒂模型的建模方法

给出了基于灰色系统的逻辑斯蒂(logisitic)模型的建模方法.用实例验证了基于灰色系统的逻辑斯蒂(logisitic)模型的建模过程简便适用,拟合精度较高.     

拟合及预测饱和增长趋势的广义逻辑（Logistic）曲线模型

本文讨论了逻辑（Ｌｏｇｉｓｔｉｃ）曲线与龚柏兹（Ｇｏｍｐｅｒｔｚ）曲线模型结构上的缺点。针对这些缺点，文中提出利用广义逻辑曲线模型拟合及预测饱和增长趋势，解释了该模型包含的实际经济意义，并给出了相应的参数估计算法，以实例说明了该模型具有高于逻辑曲线和龚柏兹曲线的预测精度。     

混沌平话(续完)

续上期）菲根鲍姆常数映射中的倍化周期现象还有更让人惊异逻辑斯蒂映射的分岔图．常数α从（横坐标）２增大到４．纵坐标是状态ｘ．注意混沌带的生长紧随着周期倍化现象图１的奥秘与内涵．将前述逻辑斯蒂映射中的参数α与其映射产生的相应的不动点或定态点（吸引子）值ｘ...     

协方差矩阵扰动生长曲线模型岭估计的影响分析

本文研究了协方差矩阵发生扰动时，生长曲线模型岭估计的影响分析，建立了生长曲线模型、协方差矩阵扰动生长曲线模型岭估计之间的关系式。讨论了协方差扰动和数据删除对岭估计的影响，导出了度量影响大小的基于岭估计的广义Cook距离Di^*（k）最后，用实例说明了用Di^*(k）度量生长曲线模型的影响点是有效的。     

协方差改进法及其应用

协方差改进法是构造更好估计的一个有力工具，本文在系统讨论了这个方法及其重要性质基础上，综述了它在许多模型的参数估计中的应用。这包括半相依回归模型，线性回归模型和生长曲线模型。本文还提出了几个未解决的问题。     

一种半参数ROC曲面估计方法

ROC曲面是诊断医学统计学里评估有多类诊断结果的诊断测试方法准确性的一个重要工具,也是近年来的一个研究热点.本文提出一种半参数的ROC曲面估计方法.该方法可以借助于许多统计软件里的逻辑斯蒂回归程序进行计算,所以它的实施较为方便.相关统计模拟显示,本文提出的方法与传统的非参数方法相比,有效性得到了显著提高.而与参数方法相比,当参数模型假设是正确时仍比参数方法有略高的有效性；而当参数模型假设不正确时,本文提出的半参数方法明显优于参数方法.     

布拉德福曲线的威布尔模型

为了克服原有布拉德福曲线的模型不能描述格鲁斯段的缺陷,通过分析布拉德福数据排列的特点、分析期刊文献产生的机理、提出假设、建立微分方程、解微分方程、参数分析等一系列步骤,获得了布拉德福曲线的威布尔模型.通过实证对比分析,模型优于原有的斯马里科夫统一方程和莱姆库勒模型.     

生长曲线模型的条件BLU估计

研究了线性等式约束下一般生长曲线模型，得到了条件线性可做函数的唯一最优线性无偏估计。     

生长曲线模型中LSE的一个新的相对效率

对于一般生长曲线模型Yq×n＝Aq×nBm×kCk×n＋e，E（e）＝0，本文定义了相对于b·的一个新的相对效率，并给出了它的一个上界．     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].