New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

Asymptotic Behavior on a Competition Model Arising from an Unstirred Chemostat

This paper is concerned with the unstirred chemostat model with two-species and one non-reproducingresource.The global attractivity of the positive steady-state solutions of the original system is established.Moreover,the effects of the growth rate on the unique positive equilibrium of the single population model arestudied.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

微分算子扰动问题的值域研究

本文研究作用在C2周期函数空间上的微分算子u→u″ g(u) ,其中g(u)为连续有界函数.我们将证明上述微分算子的值域限制在周期函数空间的“超曲面”中.     

Ag纳米颗粒的光吸收和透射电镜研究

用硼氢化钠作还原剂,制备出两种相对稳定的含银纳米颗粒的水溶胶,用透射电镜（TEM）和光学吸收谱对这些颗粒进行了表征.当被还原的银离子较少时,所形成的银纳米颗粒较小,吸收峰呈现二极等离子体共振吸收峰.当被还原的银离子较多时,银纳米颗粒尺寸变大,并出现二极和四极共振吸收峰.在Ag纳米颗粒形成后,对其溶液稀释,发现其峰形保持不变,而峰位会出现红移,最大红移量可达到10 nm.透射电镜研究表明,低浓度溶胶中的Ag纳米颗粒尺寸较为均匀,平均直径12 nm.高浓度溶胶中的纳米颗粒尺寸呈双尺寸分布特点,少量颗粒直径小于14 nm,大部分颗粒直径大于20 nm.     

On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.     

非均匀散射层矢量辐射传输(VRT)方程高阶散射解的迭代法

将散射介质层在z轴方向划分成薄层，用薄层的一阶散射强度、Fourier变换和迭代方法求解散射介质整层的矢量辐射传输(VRT)方程的高阶散射解.该方法将一阶散射与高阶散射迭代结合起来，计算公式简明，可计算高阶迭代解，计算时间少.计算结果与一层均匀散射介质的VRT方程一阶Mueller矩阵解、半空间均匀散射介质二阶Mueller矩阵解、以及离散坐标-特征值特征矢量法的VRT热辐射的数值解作了全面的比较.提出并讨论了非均匀散射层主动与被动VRT方程的高阶解.本计算程序可以通用于非球形粒子多层结构及非均匀介质的散射和热辐射计算. 关键词： VRT方程 分层 迭代解     

Effect of Hydrolysis Conditions on the Direct Formation of Nanoparticles of Ceria–Zirconia Solid Solutions from Acidic Aqueous Solutions

The effect of the cation concentration, hydrolysis temperature, and composition in the CeO₂–ZrO₂ system on the direct precipitation of ceria–zirconia solid solutions and the structure of the precipitates from acidic aqueous solutions of (NH₄)₂Ce(NO₃)₆ and ZrOCl₂ by hydrolysis under hydrothermal conditions were investigated. Nanometer-sized (8–10 nm) ceria–zirconia solid solution particles in a composition range of 0 to 60 mol% ZrO₂ were directly precipitated from the solutions with total metal cation concentration less than 0.2 mol/dm³ by simultaneous thermal hydrolysis at 150–240°C. The crystalline phase of the precipitates gradually changed from cubic and/or tetragonal to monoclinic with increasing the cation concentration of the solution from 0.2 to 0.8 mol/dm³ at the starting composition of 50 mol% ZrO₂ under hydrolysis condition of 150°C for 48 h, which was attributed to decrease in the supply of hydrolyzed Ce component caused by decrease in the hydrolysis ratio of (NH₄)₂Ce(NO₃)₆. Ceria–zirconia solid solutions containing large amount of ZrO₂ maintained high specific surface area and small-sized crystallite after heat-treatment at 900–1000°C for 1 h.