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Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value

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Acta Mathematica Sinica,English Series 2001年第2期17卷 197-206页

作者： Yuan Di WANG department of mathematics, shanghai university, shanghai 200436. P. R. c.ina department of mathematics Shanghai University Shanghai 200436 P. R. China

Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces and generalized Poincare operators play an important role in proving the existence of solutions.

关键词： Nonlocal problem Nonlinear boundary condition Palabolic equation Solution Existence Generalized Poincaree operator

chen's Theorem with Small Primes

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Acta Mathematica Sinica,English Series 2002年第3期18卷 597-604页

作者： Ying chun cAI department of mathematics, shanghai university, shanghai 200436. P. R. c.ina department of mathematics Shanghai University Shanghai P. R. China

Let N be a sufficiently large even integer. In this paper it is proved that the equation N=p+P_2, p≤N^(0.95), is solvable, where p denotes a prime and P_2 denotes an almost prime with at most two prime factors.

关键词： chen's theorem Sieve Mean value theorem

Advanced technology for functionalization of carbon nanotubes

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Progress in Natural Science:Materials International 2009年第7期19卷 801-810页

作者： Lingjie Meng, chuanlong Fu, Qinghua Lu School of chemistry and chemical Technology, shanghai jiaotong university, shanghai 200240, c.ina [a]School of chemistry and chemical Technology Shanghai Jiaotong University Shanghai 200240 China

Functionalization of carbon nanotubes (cNTs) has attracted considerable interest in the fields of physics, chemistry, material science and biology. The functionalized cNTs exhibit improved properties enabling facile fabrication of novel nanomaterials and *** of the functionalization approaches developed at present could be categorized into the covalent attachment of functional groups and the non-covalent adsorption of various functional molecules onto the surface of cNTs. This review highlights recent development and our work in functionalization of carbon nanotubes, leading to biocompatible cNTs, fluorescent cNTs and transition metal functionalized cNTs. These novel methods possess advantages such as simplified technical procedures and reduced cost of novel nanomaterials and nanodevices fabrication.

关键词： carbon nanotubes (cNTs) Functionalization Bio-compatibility Fluorescence Transition metal

Parametric estimation of discretely sampled Gamma-OU processes

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Science c.ina mathematics 2006年第9期49卷 1231-1257页

作者： ZHANG Shibin,ZHANG Xinsheng & SUN Shuguang School of Management, Fudan university, shanghai 200433, c.ina department of mathematics, shanghai Maritime university, shanghai 200135, c.ina School of Management Fudan University Shanghai 200433 China department of mathematics Shanghai Maritime University Shanghai 200135 China

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter A and its convergence result are given, and the simulations show that the estimation is quite accurate. Assuming that the parameter A is estimated, the maximum likelihood estimation of shape parameter c and scale parameter a, whose likelihood function is not explicitly computable, is considered. By means of the Gaver-Stehfest algorithm, we construct an explicit sequence of approximations to the likelihood function and show that it converges the true (but unkown) one. Maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and the approximation shares the asymptotic properties of the true maximum likelihood estimator. Some simulation experiments reveal that this method is still quite accurate in most of rational situations for the background of volatility.

关键词： Gamma-OU process transition function Lévy process Lévy density stochastic volatility background driving Lévy process Laplace transformation maximum likelihood estimation

SYNERGY OF WALL SHEAR STRESS AND cIRcUMFERENTIAL STRESS IN STRAIGHT ARTERIES

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Journal of Hydrodynamics 2005年第6期17卷 752-757页

作者： QIN Kai-rong XU Zhe WU Hao JIANG Zong-lai LIU Zhao-rong Institute of Mechanobiology and Medical Engineering Shanghai Jiaotong University Shanghai 200240 China department of Mechanics and Engineering Science Fudan University Shanghai 200433 China Institute of Mechanobioiogy and Medical Engineering Shanghai Jiaotong University Shanghai 200240China

The Wall Shear Stress （WSS） generated by blood flow and circumferential Stress （cS） driven by blood pressure have been thought to play an important role in blood flow-dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis. The WSS and cS in straight arteries were calculated by measuring the blood pressure, center-line velocity, wall thickness, and radius of vessels. The WSS and cS in the time domain were then decomposed into the amplitude and phase in the frequency domain. The cS amplitude to the WSS amplitude ratio （referred as stress ampli tude ratio, Zs ） and the phase difference between the cS and the WSS （referred as stress phase difference, SPA） in the fre quency domain were calculated to characterize the synergy of the cS and WSS. Numerical results demonstrated that the cS is not in phase with the WSS, a time delay in the time domain or a stress phase difference in the frequency domain between the WSS and the cS exists. Theoretical analysis demonstrated that the Zs and SPA are primarily determined by the local fac tors （blood viscosity, local inertial effects, local geometry, loeal elasticity） and the input impedance of whole downstream arterial beds. Because the arterial input impedance has been shown to reflect the physiological and pathological states of whole downstream arterial beds, the stress amplitude ratio Zs and stress phase difference SPA would be thought to be the appropriate indices to reflect the effects of states of whole downstream arterial beds on the local blood flow dependent phenomena such as angiogenesis, vascular remodeling, and atherosgenesis.

关键词： Wall Shear Stress (WSS) circumferential Stress (cS) wall shear stress-circumferential stress synergy,angiogenesis vascular remodeling atherosgenesis

A saliency model based on wavelet transform and visual attention

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Science c.ina(Information Sciences) 2010年第4期53卷 738-751页

作者： LI ZhiQiang, FANG Tao* & HUO Hong Institute of Image Processing and Pattern Recognition, shanghai jiaotong university, shanghai 200240, c.ina 1. Institute of Image Processing and Pattern Recognition Shanghai Jiaotong University Shanghai 200240 China

This paper presents a novel wavelet transform saliency model to detect salient objects. In this model, a saliency map is generated by combining orientation feature maps obtained from wavelet transform of different scale images derived from the same image. Then, the order map of a saliency map is obtained by using Fourier descriptor, which could be used as a guidance to process the most important objects. Experiments indicate that this saliency model is robust to noise and superior to other saliency models in the literature.

关键词： bottom-up attentional mechanism center-surround inhibition phenomenon Fourier descriptor top-down attentional mechanism visual attention wavelet transform

THE STABILITY ANALYSIS OF THE θ-METHODS FOR DELAY DIFFERENTIAL EQUMIONS

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Journal of computational mathematics 1996年第3期14卷 203-212页

作者： H.J.Tian J-X.Kuang(department of mathematics, shanghai Normal university, shanghai, c.ina) shanghai NORMAL UNIV DEPT MATH SHANGHAI PEOPLES R CHINA

This paper deals with the stability analysis of θ-methods for the numericalsolution of delny dmerential equations (DDEs). We focus on the behavioux of suchmethods in the solution of the linear test equation y'(t) = a(t)y(t) + b(t)y(t - T),where T > o, a(t) and b(t) are functions from R to c. It is proved that the linearθ-method and the one-leg θ-method are TGP-stable if and only if θ = 1.

关键词： METHODS FOR DELAY DIFFERENTIAL EQUMIONS THE STABILITY ANALYSIS OF THE Math

central simple Poisson algebras

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Science c.ina mathematics 2004年第2期47卷 245-263页

作者： SU Yucai & XU Xiaopingdepartment of mathematics, shanghai jiaotong university, shanghai 200030, c.ina Institute of mathematics, Academy of mathematics and System Sciences, chinese Academy of Sciences, Beijing 100080, c.ina 1.department of mathematics Shanghai Jiaotong University 200030 Shanghai China 2.Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic *** Lie algebra structures of these Poisson algebras are in general not finitely-graded.

关键词： Poisson algebra, locally-finite operator, derivation, finitely-graded, isomorphism class.

Design and Analysis of Ways to Improve System MTTF on Massive Storage clusters

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微计算机信息 2007年第22期 181-183+180页

作者： cHEN YAN XU GUOZHI (EE department,shanghai jiaotong university,shanghai 200240,c.ina)

Nowadays clusters have been widely deployed as platforms for massive data storage. For applications with high reliability requirement,how to improve system MTTF is one of the key problems. This paper proposes a new dynamic replication scheme,called "concurrent data replication". Through extensive theoretical analysis,it shows that this scheme can improve system MTTF significantly,and the results are further proved by simulation. Additionally,this paper also gives key design techniques.

关键词： massive storage cluster MTTF