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.     

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.     

长三角地区省级雾霾影响综合风险评价

为全面评估雾霾天气对经济社会生态的安全状况,基于自然灾害系统理论构造了雾霾危害综合风险评估体系并结合层次分析法和熵权法计算了各子因素权重,采用物元可拓模型计算长三角三省市雾霾危害综合风险的关联系数、判定等级.计算结果表明:上海市综合风险等级判定为严重,江苏省综合风险等级处于轻度,浙江省综合风险等级处于微度,同时使用综合指数法的计算结果验证了结果可信.最后根据三省市各项风险因素的权重大小、风险等级和改变难度综合评价各项风险因素,确定了长三角各省市降低雾霾危害风险水平的关键因素.     

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.     

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.     

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.     

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     

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     

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).     

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.     

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.