水质富营养化评价的状态矩阵方法

本首先利用曲线拟合的方法构造出各湖泊水质富营养化的状态矩阵，然后确定各评价指标的权重，进而通过加权平均计算综合评价值，取得了水质富营养化等级评估的满意结果。     

基于贝叶斯网络的新冠肺炎区域风险等级划分准确性评估

新冠肺炎在我国爆发后，分区分级管控措施已经取得了良好的效果，但研判的准确度有待商榷。提出基于不精确概率的贝叶斯网络决策模型，评估疫情区域风险等级划分的准确度。采用贝叶斯网络结构表征风险等级划分过程，并进行了数学描述。通过分析疫情防控中收集的证据，提炼出网络节点状态的不精确概率数值，并将其转化成真、假、不确定三个状态的基本概率分配函数；运用扩展的证据合成技术传递节点的不确定性，评估风险等级划分的准确性。结果表明：区域风险等级划分为中风险的判断准确性较高，而低、高风险的判断准确性较低；疫情防控进入常态化后，精准防控还应结合风险等级的准确度重点考虑低、高风险区域经济社会的秩序安排，以适应应急管理科学化、专业化、智能化、精细化的需要。     

基于模糊综合评判法的保密风险定量评估

根据保密工作现状和实际情况,针对保密风险的的特点,分析了其相关影响因素,建立了保密风险评估的指标体系,给出了评估指标的量化处理方法,并对评价指标进行了无量纲化处理．在此基础上,提出了保密风险的模糊综合评估模型,划分了保密风险的5类等级．     

评价污水处理系统的Fuzzy模式识别方法

综合考虑了所有对污水处理系统的相关因素,应用Fuzzy模式识别的数学方法,对评价污水处理系统建立了数学模型.由于此模型对污水处理系统给出了等级划分和对各相关因素等级指数之间的中介状态进行了恰当处理,所以它应用于评价污水处理系统将更科学.     

一类搜索型随机格斗的获胜概率研究

把随机过程分析引入Lanchester方程就形成了随机格斗理论.运用随机格斗理论研究了潜艇协同隐蔽攻击水面舰艇编队获胜概率的数学模型,利用状态转移图和Laplace变换的性质推导出了2对2搜索型随机格斗中双方的获胜概率公式,并结合潜艇协同隐蔽攻击水面舰艇的实际,计算分析了格斗双方的获胜概率.利用这一公式可以得到概率上的精确解,能够被用来定量评估潜艇协同隐蔽攻击水面舰艇编队的作战效能.     

“人口-生态-空间-经济-社会”多维城镇化状态评估——基于改进证据理论

针对目前城镇化状态评估中"非此即彼"的问题,在全方位理解新型城镇化"内涵式发展"的基础上,建立了"人口-生态-空间-经济-社会"五维评价指标体系;综合模糊集理论与隶属度函数,将城镇化状态划分为最高、较高、中等、较低和最低五个等级,并完成基本概率赋值;在对证据源修正的基础上,对经典证据理论合成公式进行改进.以新疆为例,验证了方法的正确性、有效性及良好的泛化能力,为城镇化状态评估提供一个新的思路.     

基于三角模糊层次分析法的农产品滞销风险等级决策评价

为了有效预警和弱化农产品滞销事件危害,提出农产品滞销风险等级评估方法.首先,搜集近3年来发生的农产品滞销较大事件209起,分析确定农产品滞销风险等级评价指标体系.其次,考虑到决策过程的复杂性和不确定,提出三角模糊数的层次分析法确定评价指标权重.将农产品滞销风险划分为五个等级,构建各等级的标准模糊状态向量,利用模糊模式识别法计算农产品与等级标准模糊状态向量之间的贴近度.然后,基于权重和贴进度建立农产品滞销风险等级决策模型.最后,实例和对比分析研究验证了基于三角模糊数的层次分析法和模糊模式识别的农产品滞销风险等级评估模型的有效性和可行性.     

基于云模型的地下商城火灾防范能力评估

将逆向云发生器与一维前件云发生器综合集成,比对待评估地下商城与地下工程"火灾防范能力数据库"各项指标之间的确定度,并利用Matlab云发生器工具箱对各个等级的确定度进行大量随机计算,通过比较各个等级的中值与均值,判断待评估地下商城的火灾防范能力等级.结论表明,综合云发生器不仅可以客观全面的保留原始评价信息,而且评价结果更加立体直观.     

基于集对分析的输电工程造价综合评价研究

合理评估输电工程造价水平对于提高电网资产效率,推动经济发展具有重要意义.综合考虑影响输电工程造价的量、价因素,构建了输电工程造价技术经济指标体系;基于AHP-熵权法确定指标基本权重,并建立三维权重模型反映电压等级与地区差异性对指标权重的影响;然后建立基于集对分析理论的综合评价模型,评估输电工程方案的造价水平;最后选取8个110kV、220kV输电工程进行分析,结果表明模型评价结果直观,能充分体现电压等级、地区的差异.     

信息化部队指挥管理类干部综合能力评估模型

首先根据部队当前军事斗争需要和未来任务的要求构建了指挥管理类干部综合能力评估指标体系,再采用层次分析法把各个指标量化表示为权重.经过比较,基于三角白化函数的综合评估模型能有效避免极端数据的影响,权重的取值分布较合理,而且还具有稳定的排序功能.以2009年武警杭州指挥学院干部综合考评为例,评估结果显示排名顺序与实际排名一致,不仅能有效区分不同等级,而且还能对同一等级的数据给出相对排序.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

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.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

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].