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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, Shandong {1., jinan 2501.1. china 2.school of mathematics, Shandong {1., 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

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 {1.,Qufu 2731.5,china 2school of mathematics,Shandong {1.,jinan 2.01.0,china 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

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.

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 {1.,Fuzhou 350002,china 2.school of mathematics,Shandong {1.,jinan 2.01.0,china 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

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1.and Liu Shenquan2(1. Department of mathematics, Hangzhou Normal {1., Hangzhou 31.036, china 2. Department of Applied mathematics, school of Mathematical Sciences, South china {1. of Technology, Guangzhou 51.640, china) Department of mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

An investigation of hadronization mechanism at a Z^0 factory

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Science china(Physics,Mechanics & Astronomy) 2010年第11期53卷 1998-2004页

作者： JIN Yi 1.SI ZongGuo 2,XIE QuBing 2 & YAO Tao 2 1.Department of Physics,university of {1.,{1. 250022,china 2.school of Physics,Shandong university,{1. 2.01.0,china 1. Department of Physics University of Jinan Jinan 250022 China2. School of Physics Shandong University Jinan 250100 China

We briefly review the hadronization pictures adopted in the LUND String Fragmentation Model (LSFM),Webber Cluster Fragmentation Model (WCFM) and Quark Combination Model (QCM),*** of hadron multiplicity,baryon to meson ratios and baryon-antibaryon flavor correlations,especially those related to heavy hadrons at a Z 0 factory obtained by LSFM and QCM,are reported.

关键词： Z0 factory hadronization model baryon to meson ratio B correlation

Note on the number of integral ideals in Galois extensions

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Science china {1. 2010年第9期53卷 2417-2424页

作者： L GuangShi1.& WANG YongHui2 1.0} of {1.,Shandong university,jinan 2.01.0,china 2Department of {1.,Capital Normal university,Beijing 1.0048,china 1. school of {1. Shandong University Jinan 250100 China2. Department of Mathematics Capital Normal University Beijing 100048 China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2,3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

Error analysis of the semi-discrete local discontinuous Galerkin method for semiconductor device simulation models

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Science china {1. 2010年第12期53卷 3255-3278页

作者： LIU YunXian 1. & SHU Chi-Wang 2 1.school of {1., Shandong university, jinan 2.01.0, china 2 Division of Applied {1., Brown university, Providence, RI 0291., USA 1. school of {1. Shandong University Jinan 250100 China2. Division of Applied Mathematics Brown University Providence RI 02912 USA

In this paper we continue our effort in Liu-Shu (2004) and Liu-Shu (2007) for developing local discontinuous Galerkin (LDG) finite element methods to discretize moment models in semiconductor device simulations. We consider drift-diffusion (DD) and high-field (HF) models of one-dimensional devices, which involve not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. Error estimates are obtained for both models with smooth solutions. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. A simulation is also performed to validate the analysis.

关键词： local discontinuous Galerkin method error estimate semiconductor