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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 2.0100, 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.

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, 2.0100 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 2.0100, 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 2.0100, 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

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 2.0100, 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 2.0100, 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.

Function S-rough sets and security-authentication of hiding law

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Science in china(Series F) 2008年第7期51卷 924-935页

作者： SHI KaiQuan1,2 & ZHAO JianLi3 1 school of mathematics and Computer sciences, Longyan university, Longyan 364000, china 2.school of mathematics and system sciences, shandong university, jinan 2.0100, china 3 school of mathematics Science, Liaocheng university, Liaocheng 252059, china 1. school of mathematics and Computer sciences Longyan University Longyan 364000 China 2. school of mathematics and system sciences Shandong University Jinan 250100 China 3. school of mathematics Science Liaocheng University Liaocheng 252059 China

Function S-rbugh sets are defined by R-function equivalence class, which have dynamic characteristic. Function S-rough sets have dynamic characteristic, law characteristic and law-hiding characteristic. Function S-rough sets can generate f-hiding law and f-hiding law. By engrafting, crossing, and penetrating between the information security theory and function S-rough sets, the security hiding and the authentication of f-hiding law and f-hiding law are given respectively in this paper. The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system.

关键词： function S-rough sets law-hiding elliptic curve the security-authentication of hiding law

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 2.0100, 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

Mechanical model of vulnerable atherosclerotic plaque rupture

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Science china(Physics,Mechanics & Astronomy) 2004年第4期47卷 452-462页

作者： SU Haijun1, ZHANG Mei2 & ZHANG Yun2 1. school of mathematics and system Science, shandong university, jinan 2.0100, china 2. Qilu Hospital, shandong university, jinan 250012, china 1. school of mathematics and system Science Shandong University 250100 Jinan China 2. Qilu Hospital Shandong University 250012 Jinan China

Rupture of atherosclerotic plaque is the main trigger of acute cardiovascular events, but the mechanism of plaque rupture is still unknown. We have constructed a model describing the motion of the fibrous cap of the plaque using the theory of elastic mechanics and studied the stability of the plaque theoretically. It has shown that plaque rupture is the result of a dynamic interplay between factors intrinsic to the plaque itself and extrinsic factors. We have proposed a new mechanism of plaque rupture, given a new explanation about the nonlinear dynamic progress of atherosclerosis and suggested a method to identify the vulnerable plaques to manage atherosclerosis.

关键词： fibrous cap, parametric resonance, stability, mechanism, identification.

ON SOME RESULTS OF YI AND THEIR APPLICATIONS IN THE FUNCTIONAL EQUATIONS

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Acta Mathematica Scientia 2010年第5期30卷 1649-1660页

作者：杨连中张继龙 school of mathematics and system sciences Shandong University LMIB and school of mathematics and system sciences Beihang University

In this article, we establish some uniqueness theorems that improves some results of H. X. Yi for a family of meromorphic functions, and as applications, we give some results about the non-existence of meromorphic sol... 详细信息

关键词： functional equations meromorphic functions uniqueness