The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

齐次核的Hilbert型多重级数不等式取最佳常数因子的等价条件及应用

利用实分析技巧和权函数方法, 讨论具有齐次核的多重级数Hilbert型不等式, 得到了其取最佳常数因子的充分必要条件, 并给出其应用.     

高速实时可见光通信技术研究及应用

 介绍了可见光通信技术的发展历史及研究现状。基于带宽拓展技术搭建了1 W荧光型LED做光源、PIN光电二极管做探测器、单路速率610 Mb/s的实时传输演示系统，该系统在传输距离为6.2 m时的误码率为3.48×10^-5。在此基础上搭建了荧光型LED为光源、PIN光电二极管做探测器的、双向100 Mb/s无线光上网演示系统。     

不饱和烃同系物凝聚型物理性质递变规律的数学描述

以H-(CH2)n-CH=CH2和H-(CH2)n-C≡CH型同系物结构重复单元数值连续变化为模型,获得了描述该同系物凝聚型物理性质递变规律的数学表达式:P=(a0+a1n+a2n2)/(1+b2n2),式中a0、a1、a2、b2均为常数,n为结构重复单元数值,P为同系物的凝聚型物理性质。通过非线性回归分析,得到回归方程,结果表明同系物的凝聚型物理性质与重复结构单元数值之间满足上述关系式,并显示优良的相关性。     

论住宅户型设计

为适应现代人居住观念的变化，结合设计工作的实践，分别就住宅户型设计中的户内空间序列以及起居室、卧室、厨房、卫生间的设计理念、设计原则和有关具体问题进行了探讨。     

A new molecular rectifier device and some research in its processing

Organic materials of D-π-A type MR-X (MR-1: p-dimethylaminophenylethenetrica-rbonitrile and MR-2: p-diphenylaminophenylethene tricarbonitrile) were designed and synthesized. The device with a sandwich structure shows good rectificative phenomena. The highest rectification ratio 10000 was achieved in device Cu/MR-1/Ag, and about 100 in other device M/MR-X/M (M: Cu, Ag). It has been found that rectificative phenomena exist only in the atmosphere-liquid interface region by means of liquid adsorption, and electric field could help form the oriented molecular film. __________ Translated from Journal of Fudan University (Natural Science), 2005, 44(4) (in Chinese)     

On the Local Uniqueness of Solutions of Variational Inequalities Under H-Differentiability

In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C ¹ and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C ² and C ¹ nonlinear complementarity problems.