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Resonance between automorphic forms and exponential functions

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Science china mathematics 2010年第9期53卷 2463-2472页

作者： REN XiuMin1,& ye yangbo1,2 1school of mathematics,shandong university,jinan 2.0100,china 2Department of mathematics,The university of Iowa,Iowa City,Iowa 52242-1419,USA school of mathematics Shandong University Jinan China Department of mathematics The University of Iowa Iowa City USA

Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier *** this paper,the exponential sum X2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of siz... 详细信息

关键词： automorphic form exponential sum resonance

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 2.0100, china school of Computer Science and Technology Shandong University Jinan China school of mathematics Shandong University Jinan 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

Total coloring of embedded graphs of maximum degree at least ten

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Science china mathematics 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,china 2 school of mathematics,shandong university,jinan 2.0100,china Center for Discrete mathematics Fuzhou University Fuzhou China school of mathematics Shandong University Jinan 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)≥10,where Δ(G) denotes the maximum degree of G.

关键词： surface Euler characteristic total coloring total chromatic number

Genetic diversity of the endangered species Rosa rugosa *** china and implications for conservation strategies

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Journal of Systematics and Evolution 2009年第6期47卷 515-524页

作者： ~1Ji-Hong YANG ~1Shu-Ping ZHANG ~2Jian liu ~1Wen ZHAI ~(1,2)Ren-Qing WANG~* 1(school of Life Sciences,shandong university,jinan 2.0100,china) 2(Institute of Environment Research,shandong university,jinan 2.0100,china) (school of Life Sciences Shandong University Jinan 250100 China) (Institute of Environment Research Shandong University Jinan 250100 China)

Rosa rugosa *** one of the dominant and important shrub species in estuary dunes and shingle beaches of northern ***,its area of distribution,the number of populations,and the size of each population have decreased rapidly in the past two decades because of habitat degradation and *** amplified polymorphic DNA markers were used to determine the genetic diversity of four remaining large natural populations of *** and to discuss an effective conservation strategy for this endangered species in *** genetic variations were detected in *** populations in *** mean percentage of polymorphic loci(P%) within four local populations was 57.99%,with the P%of the total population being 75.30%.Mean Shannon’s information index(H0) was 0.2826,whereas total H0was *** genetic differentiation among populations was 0.1878, which indicates that most genetic diversity occurs within *** Tumenjiang(TMJ) showed the highest genetic diversity(P%= 66.27%;H0= 0.3117) and contained two exclusive *** Changshandao (CSD) showed higher genetic diversity(P%= 59.04%;H0= 0.3065).Populations TMJ and CSD contained 95.33% and 99.33%,respectively,of loci with moderate to high frequency(P>0.05) of the total *** results indicate that populations TMJ and CSD should be given priority for in situ conservation and regarded as seed or propagule sources for ex situ *** results of the present study also suggest that *** in china has become endangered as a result of human actions rather than genetic depression of populations;thus,human interference should be absolutely forbidden in *** habitats.

关键词： china genetic diversity in situ conservation random amplified polymorphic DNA(RAPD) Rosa rugosa

Stability for a class of nonlinear time-delay systems via Hamiltonian functional method

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Science china(Information Sciences) 2012年第5期55卷 1218-1228页

作者： YANG RenMing 1,2 & WANG YuZhen 1 1 school of Control Science and Engineering,shandong university,jinan 250061,china 2 shandong Jiaotong university,jinan 250023,china school of Control Science and Engineering Shandong University Jinan China shandong Jiaotong university Jinan China

This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of ***,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are ***,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) ***,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.

关键词： nonlinear time-delay systems stability Hamiltonian functional method generalized Hamiltonian realization

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, jinan 2.0100, china 2. school of Physics and Microelectronics, shandong university, jinan 250061, china Institute of Theoretical Chemistry Shandong University Jinan China school of Physics and Microelectronics Shandong University Jinan 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(111) 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 mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2 1Department of mathematics,Qufu Normal university,Qufu 273165,china 2school of mathematics,shandong university,jinan 2.0100,china Department of mathematics Qufu Normal University Qufu China school of mathematics Shandong University Jinan 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

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 school of mathematics and System Science Shandong University Jinan China Qilu Hospital Shandong University 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.

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

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Science china mathematics 2010年第12期53卷 3255-3278页

作者： liu YunXian 1, & SHU Chi-Wang 2 1 school of mathematics, shandong university, jinan 2.0100, china 2 Division of Applied mathematics, Brown university, Providence, RI 02912, USA school of mathematics Shandong University Jinan China Division of Applied mathematics Brown University Providence 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