基于效用函数的模糊数的比较与排序

对相同的模糊数进行比较,不同风险偏好的决策者,会得到不同的结论.效用函数是对风险偏好的度量,因此,模糊数的比较与排序的方法,一定要结合决策者的效用函数来构造.为此,根据效用函数定义了模糊效用函数,在此基础上定义了效用序.之后,证明效用序为全序,进一步利用结构元理论对效用序进行表述.根据效用函数反映风险偏好的程度,对效用序进行分类.这样,决策者对模糊数进行比较时,依据自身对风险偏好程度来选择效用序.     

基于POT方法的极值理论在基金净值预测中的应用

为对基金净值数据进行建模,根据基金净值样本数据的尾部特点,建立极大,极小值分布的GPD模型,运用POT方法确定临界值,进而对参数进行估计,并对模型进行检验.最后,运用建立的模型对一些极值点进行预测.所得结果很好地描述了数据特点,对极值点的预测符合实际.     

创业板成长型中小企业效率评价

中小企业成长,是质与量的统一.对于创业板中小企业而言,由于多数存在经营业绩不稳定情况,因此其成长问题广受关注.首先,基于单指标识别方法,从175家企业中筛选出31家成长型中小企业,并对成长型企业的成长指数进行了计算.其次,采用数据包络分析方法,对成长型中小企业的效率进行评价,并对技术效率、纯技术效率、规模效率和成长指数进行了分析.最后,对175家企业的效率进行了综合分析,对成长型和非成长型企业效率进行了对比分析,并分别对成长速度、技术效率和企业盈利能力的关系进行了回归分析.     

碳纤维及浸润树脂自然老化性能的模型预测

对目前土木工程加固常用的两种碳纤维片材及树脂耐久性进行了对比性试验研究.截至自然老化3年时,已进行了16组共80个试件的试验.考察在我国自然环境条件下抗拉强度的老化.根据复合材料的中值老化剩余强度半经验数学模型,对其进行拟合,回归出CFRP复合材料及其树脂的剩余强度中值方程的相关参数.预测复合材料自然老化剩余强度.对复合材料进行寿命预估,供进一步研究和工程设计参考使用.     

基于Elman网络预测汇率短期发展趋势

采用神经网络Elman网络模型对汇率进行预测.处理过程对样本序列进行了分类,并对训练与测试样本进行了残差分析.预测结果表明:该方法对汇率涨落方向的预测准确度达到74.54%,对汇率预测值与实际值之间的偏差略为偏大的情况,并分析了产生误差的原因.     

基于残差修正灰色预测模型的北京市道路交通事故预测分析

社会机动车使用量的增加带来的道路交通安全问题日益突出.对北京市道路交通事故预测进行了研究.采用灰色GM(1,1)预测模型对北京市城市道路交通事故进行了预测,并根据预测结果精度等级进行了残差修正,得出了具有科学性的预测结果.此外,通过灰色关联度分析对北京市交通事故的各相关因素进行了比较,为交通管理部门有效地控制交通事故的发生提供参考.     

金融资产收益率尾概率估计研究

在对金融资产进行投资时,投资者所关注的问题往往是金融资产收益率发生大波动的概率,简称尾概率.本文利用大偏差定理对此概率如何进行估计进行深入研究.将收益率按其尾部的分布特征分成三类,分别对其进行研究,得到三种不同的估计公式.本文对收益率序列存在相关性、收益率是多元随机变量情况下的尾概率估计问题也进行了分析.     

基于多属性群决策模型的评教方法

对高校学生网上评教存在的主要问题进行了分析,给出了网上评教的信息处理新方法.首先利用信息熵和正态分布函数对学生可信度函数进行了定义,再根据可信度大小对学生评价的权重进行了分配,最后利用加权算术平均算子对课程班的得分进行集结.数值算例分析了方法的有效性、合理性和可操作性.     

初中数学应用题解题能力培养策略

应用题是初中数学重要教学内容.培养初中生应用题解题技巧能力能帮助学生理解题意,强化学生数学思维,有利于培养学生利用数学思维解决实际问题的能力.基于此,本文对初中数学应用题解题技巧能力培养策略进行分析.首先,本文对初中生解决数学应用题遇到的阻碍进行分析.其次,本文对初中数学应用题解题技巧进行分析.最后,提出有效的初中数学应用题解题技巧能力培养策略.     

基于函数型数据分析的金融数据多层凝聚算法

将多层核心集凝聚算法应用于函数型数据分析,并应用于金融数据聚类.首先,依托金融数据的函数型特征对其进行基函数展开;其次,对产生的高维数据进行特征提取;最后,用多层核心集凝聚算法进行聚类.实验对股票波动率曲线进行聚类,挖掘出股票数据波动的内在特征,可以客观地对股票板块进行划分.     

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

正~~     

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].