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区间数多指标决策的相对隶属度法

系统工程与电子技术 2004年第7期26卷 903-905,913页

作者：刘华文姚炳学山东大学数学与系统科学学院山东济南250100

对区间数多指标决策问题 ,基于模糊集下论给出一种新的处理方法 :相对隶属度法 ,首先 ,构造优等与劣等方案 ,借助每一方案与优、劣等方案的综合加权距离求得每个方案相于优等方案的隶属度 ,再按隶属度的大小进行决策 ,该方法克服了以往... 详细信息

对区间数多指标决策问题 ,基于模糊集下论给出一种新的处理方法 :相对隶属度法 ,首先 ,构造优等与劣等方案 ,借助每一方案与优、劣等方案的综合加权距离求得每个方案相于优等方案的隶属度 ,再按隶属度的大小进行决策 ,该方法克服了以往研究此类问题时所遇到的区间数难以排序的困难。通过分析表明相对隶属度法的择优与排序能力要比传统的逼近理想解法强。最后。

关键词：多指标决策相对隶属度法模糊集区间数

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基于椭圆曲线的盲签署系统

山东大学学报（工学版） 2004年第6期34卷 94-98页

作者：胡海清王洪凯山东大学数学与系统科学学院三明学院计算机科学系福建三明365004

介绍了椭圆曲线的基本概念与其特性 ,以椭圆曲线密码理论为依据 ,给出基于椭圆曲线的盲签署算法 ,并给出实际例子 ,评估了算法的安全性 ,给出算法性能分析 .研究结果表明基于椭圆曲线的盲签署算法是安全的 ,高效的 .它将在诸多领域中得... 详细信息

介绍了椭圆曲线的基本概念与其特性 ,以椭圆曲线密码理论为依据 ,给出基于椭圆曲线的盲签署算法 ,并给出实际例子 ,评估了算法的安全性 ,给出算法性能分析 .研究结果表明基于椭圆曲线的盲签署算法是安全的 ,高效的 .它将在诸多领域中得到广泛的应用 ,现在已经成为信息安全研究的热点之一 .

关键词：椭圆曲线盲签署离散对数应用

LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

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Journal of Computational mathematics 2002年第2期20卷 153-164页

作者： Dan-ping Yang (school of mathematics and system Science, shandong university, jinan 250100, china) school of mathematics and system Science Shandong University Jinan 250100

Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio... 详细信息

关键词： least-squares algorithm mixed finite element nonlinear parabolic problems convergence analysis

An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model

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Acta Mechanica Sinica 2009年第4期25卷 463-469页

作者： Jianhong Kang Mingyu Xu Institute of Applied mathematics,school of mathematics and system Science,shandong university, 250100 jinan, china Institute of Applied mathematics School of Mathematics and System Science Shandong University 250100 Jinan China

In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.

关键词： Generalized Oldroyd-B model Rotating fluid Accelerated plate Exact solution

ON JENSEN'S INEQUALITY FOR g-EXPECTATION

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Chinese Annals of mathematics,Series B 2004年第3期25卷 401-412页

作者： JIANG LONG CHEN ZENGJING school of mathematics and system sciences, shandong university, jinan 250100, china. Department of mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu,china. E-mail: jianglong@*** school of mathematics and system sciences, shandong university, jinan 250100, china. shandong Univ Sch Math & Syst Sci Jinan 250100 Peoples R China china Univ Min & Technol Dept Math Jiangsu 221008 Peoples R China shandong Univ Sch Math & Syst Sci Jinan 250100 Peoples R China

Briand et al. gave a counterexample showing that given g, Jensen's inequality for g-expectation usually does not hold in general This paper proves that Jensen's inequality for g-expectation holds in general if and onl... 详细信息

关键词： Backward stochastic differential equation Jensen's inequality g-expectaation Conditional g-expectation Comparison theorem

S-rough sets and knowledge separation

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Journal of systems Engineering and Electronics 2005年第2期16卷 403-410页

作者： Shi Kaiquan 1,21. school of mathematics and system sciences, Liaocheng university, Liaocheng 252059, P. R. china 2. school of mathematics and system sciences, shandong university, jinan 250100, P. R. china school of mathematics and system sciences Liaocheng University Liaocheng 252059 P. R. China school of mathematics and system sciences Shandong University Jinan 250100 P. R. China

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separ... 详细信息

关键词： S- rough sets f- screen - screen f-filter theorem - filter theorem knowledge separation.

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of mathematics, china university of Mining and Technology, Xuzhou 221008, Jiangsu, china school of Mathematical sciences, Fudan university, Shanghai 200433, china school of mathematics and system sciences, shandong university, jinan 250100, china. Department of mathematics China University of Mining Technology Xuzhou 221008 Jiangsu China school of Mathematical sciences Fudan University Shanghai 200433 China school of mathematics system sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs

Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long Department of mathematics, china university of Mining and Technology, Xuzhou 221008, china Institute of mathematics, Fudan university, Shanghai 200433, china school of mathematics and system sciences, shandong university, jinan 250100, china 1. Department of mathematics China University of Mining and Technology Xuzhou 221008 China 2. Institute of mathematics Fudan University Shanghai 200433 China 3. school of mathematics and system sciences Shandong University Jinan 250100 China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

Infinite Interval Backward Stochastic Differential Equations in the Plane

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 485-490页

作者： Yan-ling Guschool of mathematics and system sciences, shandong university, jinan 250100, china school of mathematics and system sciences Shandong University Jinan 250100 China

This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet.

关键词： Two-parameter mixed type BSDE