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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, {3.) 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

MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROL SYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

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Journal of Systems Science & Complexity 2010年第2期23卷 219-231页

作者： Jingtao SHI·Zhen WU school of mathematics,Shandong University,jinan 250100,{3.. school of mathematics Shandong University

Both necessary and sufficient maximum principles for optimal control of stochastic systemwith random jumps consisting of forward and backward state variables are *** control variableis allowed to enter both diffusion and jump *** result is applied to a mean-varianceportfolio selection mixed with a recursive utility functional optimization *** expressionof the optimal portfolio selection strategy is obtained in the state feedback form.

关键词： Forward-backward stochastic control system maximum principle Poisson random measure recursive utility stochastic optimal control.

The minimal sublinear expectations and their related properties

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Science china mathematics 2009年第4期52卷 785-793页

作者： JIA GuangYan school of mathematics, Shandong University, jinan 250100, {3. 1. school of mathematics Shandong University Jinan 250100 China

In this paper, we prove that for a sublinear expectation ?[·] defined on L 2(Ω, $ \mathcal{F} $ ), the following statements are equivalent: ? is a minimal member of the set of all sublinear expectations defined on L 2(Ω, $ \mathcal{F} $ )? is linearthe two-dimensional Jensen’s inequality for ? holds.Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.

关键词： g-expectation Jensen’s inequality linear expectation subadditive expectation sublinear expectation 60H10

A maximum principle for partially observed optimal control of forward-backward stochastic control systems

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Science china(Information Sciences) 2010年第11期53卷 2205-2214页

作者： WU Zhen school of mathematics, Shandong University, jinan 250100, {3. 1. school of mathematics Shandong University Jinan 250100 China

This paper studies an optimal control problem for partially observed forward-backward stochastic control system with a convex control domain and the forward diffusion term containing control variable. A maximum principle is proved for this kind of partially observable optimal control problems and the corresponding adjoint processes are characterized by the solutions of certain forward-backward stochastic differential equations in finite-dimensional spaces. One partially observed recursive linear-quadratic (LQ) optimal control example is also given to show the application of the obtained maximum principle. An explicit observable optimal control is obtained in this example.

关键词： maximum principle partial information adjoint equation backward stochastic differential equation filtering linear-quadratic optimal control

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, {3. 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

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 3.4000, china 2 school of mathematics and System Sciences, Shandong University, jinan 250100, 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

Construction of convex solutions for the second type of Feigenbaum's functional equations

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Science china mathematics 2009年第8期52卷 1617-1638页

作者： SI JianGuo & ZHANG Min school of mathematics, Shandong University, jinan 250100, {3. school of mathematics Shandong University Jinan 250100 China

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existenc... 详细信息

In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 2-convex solutions of the above equation.

关键词： the second type of Feigenbaum’s functional equations constructive method initial function convex solutions

Adaptive bidirectional diffusion for image restoration

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Science china(Information Sciences) 2010年第12期53卷 2452-2460页

作者： FU ShuJun 1,2 & ZHANG CaiMing 1 1 school of Computer Science and Technology, Shandong University, jinan 250101, china 2 school of mathematics, Shandong University, jinan 250100, china 1. school of Computer Science and Technology Shandong University Jinan 250101 China2. School of Mathematics Shandong University Jinan 250100 China

A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.

关键词： image restoration bidirectional diffusion inverse diffusion anisotropic diffusion stabilizing scheme spatially varying constraint

Range inclusion of operators on non-archimedean Banach space

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Science china mathematics 2010年第12期53卷 3215-3224页

作者： WANG PengHui 1 & ZHANG Xu 2,3.1 school of mathematics, Shandong University, jinan 250100, {3. 2 Key Laboratory of Systems and Control, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, {3. 3.school of mathematics, Sichuan University, Chengdu 610064, {3. 1. school of mathematics Shandong University Jinan 250100 China2. Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. School of Mathematics Sichuan University Chengdu 610064 China

In this paper, we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields. These theorems provide close relationship among range inclusion, majorization and factorization for bounded linear operators. It is found that these results depend strongly on a continuous extension property, which is always true in the classical archimedean case, but may fail to hold for the non-archimedean setting. Several counterexamples are given to show that our results are sharp in some sense.

关键词： range inclusion majorization factorization non-archimedean Banach space continuous extension property