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MULTI-DIMENSIONAL REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND THE COMPARISON THEOREM

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Acta Mathematica Scientia 2010年第5期30卷 1819-1836页

作者：吴臻消华 school of {1. Shandong University school of {1. and Statistics Shandong University at Weihai

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.

关键词： backward stochastic differential equations comparison theorem local time

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, {1. University, jinan 2501.1. china 2.school of mathematics, {1. University, jinan 2.01.0, 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

DFT study of the conductance of molecular wire:The effect of coupling geometry and intermolecular interaction on the transport properties

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Science china Chemistry 2006年第6期49卷 492-498页

作者： QI Yuanhua1.2, GUAN Daren1.& LIU Chengbu1.1. Institute of Theoretical Chemistry, shandong University, {1., china 2. school of Physics and Microelectronics, shandong University, jinan 250061. china 1. Institute of Theoretical Chemistry Shandong University Jinan 250100 China 2. school of Physics and Microelectronics Shandong University Jinan 250061 China

The density functional theory (DFT) combining with the non-equilibrium Green functions (NEGF) method is applied to the study of the electronic transport properties for a Di-thiol-benzene (DTB) molecule coupled to two Au(1.1. surfaces. The dependence of the transport properties on the bias, the coupling geometry of the molecule-electrode interface, and the intermolecular interaction are examined in detail. The results show that the existence of the hydrogen atom at the end of the DTB molecule would significantly decrease the transmission coefficients, and then the differential conductance (dI/dV). By changing the position of the DTB molecule located between two electrodes a maximum value of calculated current is observed. It is also found that the intermolecular interaction will strongly influence the transport properties of the system studied.

关键词： non-equilibrium Green functions method, transmission spectrum, the molecular projected selfconsistent Hamiltonian, projected density of state.

Moment bounds for IID sequences under sublinear expectations

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Science china {1. 2011年第10期54卷 2155-2160页

作者： HU Feng1.2 1.epartment of mathematics,Qufu Normal University,Qufu 2731.5,{1. 2school of mathematics,shandong University,jinan 2.01.0,{1. 1. Department of mathematics Qufu Normal University Qufu 273165 China2. School of Mathematics Shandong University Jinan 250100 China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1.+ |x|p) for some C > 0,p 1.depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

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 {1. and System Science, shandong University, jinan 2.01.0, china) school of {1. 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

Prediction for RNA planar pseudoknots

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Progress in Natural Science:Materials International 2007年第6期17卷 717-724页

作者： Li Hengwu1.2, Zhu Daming1. Liu Zhendong1.and Li Hong2(1. school of Computer Science and Technology, {1. University, jinan 2.01.0, china 2. Department of Computer, {1. Economic University, jinan 25001., china) [a]school of Computer science and Technology Shandong University Jinan China [b]Department of Computer Shandong Economic University Jinan China

Based on m-stems and semi-extensible structure, a model is presented to represent RNA planar pseudoknots, and corresponding dynamic programming algorithm is designed and implemented to predict arbitrary planar pseudoknots and simple non-planar pseudoknots with O(n4) time and O(n3) space. The algorithm folds total 245 sequences in the Pseudobase database, and the test results indicate that the algorithm has good accuracy, sensitivity and specificity.

关键词： algorithm RNA secondary structure pseudoknot dynamic programming.

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 {1.,shandong University,jinan 2.01.0,china. school of {1. 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.

Total coloring of embedded graphs of maximum degree at least ten

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Science china {1. 2010年第8期53卷 2127-2133页

作者： HOU JianFeng 1.2,WU JianLiang 2,LIU GuiZhen 2 & LIU Bin 2 1.Center for Discrete mathematics,Fuzhou University,Fuzhou 350002,{1. 2.school of mathematics,shandong University,jinan 2.01.0,{1. 1. Center for Discrete mathematics Fuzhou University Fuzhou 350002 China2. School of Mathematics Shandong University Jinan 250100 China

A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same *** total chromatic number χ〃(G) is the smallest integer k such that G has a total *** this paper,it is proved that the total chromatic number of any graph G embedded in a surface Σ of Euler characteristic χ(Σ)≥0 is Δ(G) + 1.if Δ(G)≥1.,where Δ(G) denotes the maximum degree of G.

关键词： surface Euler characteristic total coloring total chromatic number

The minimal sublinear expectations and their related properties

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Science china {1. 2009年第4期52卷 785-793页

作者： JIA GuangYan school of {1., shandong University, jinan 2.01.0, china 1. school of {1. 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 60H1.