FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES （II）

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].     

层状地基中埋管地基阻抗函数的分析方法

本文首先利用波函数展开法推导了弹性半空间中埋管的地基轴向阻抗函数计算公式.然后采用层状地基中无限长线激振荷载薄层法基本位移解,结合容积法求解了层状地基中埋管的地基轴向、垂直及水平阻抗函数.分别用两种方法计算了弹性全空间、弹性半空间地基内埋管的地基轴向阻抗函数,两者的计算结果符合良好,验证了用薄层法求解的可行性.本文还利用薄层法分析了弹性半空间内埋管的埋深对地基水平、垂直及轴向阻抗函数的影响;计算了弹性半空间内埋管的轴向刚度系数并与我国及日本的相关规范对比分析;计算分析了上海典型层状地基内地铁隧道的地基阻抗函数.     

非齐次边界条件下两点边值问题单调解的存在性

研究了一类二阶非线性微分方程在非齐次边界条件下的两点边值问题单调解的存在性.运用锥拉伸与锥压缩不动点定理,分别得到了边值问题单调递增正解和单调递减负解存在的充分条件.     

LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT

In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin‘s function corresponding to the Green‘s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.     

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHROEDINGER-POISSON EQUATIONS

In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.     

岩石块体滑动的界面摩擦阻抗时效研究

基于岩石块体摩擦滑动试验反映的特征规律 ,本文分析了岩块随时间滑动的界面阻抗机理 ,并建立粘滑位移弱化时反映滑动界面阻抗时间效应的模型公式阻抗松弛模型。     

一个非局部边界流问题解的存在性和渐近性

一个带有非局部第三边界条件的抛物型方程问题解的存在性和渐近性质将在这里被讨论.使用的办法包括比较原理、Sobolev-Slobodetskii 空间等.     

Verification and Calculation of Negative Refractive Indices of a Meta-Material by Numerical Method

The verification and calculation of the negative refractive index of a meta-material is carried out by the finitedifference time-domain method. A slab and a prism of the meta-material are simulated. A genuine plane wave is generated by a two-direction periodic boundary condition (PBC) in the slab model. Based on an advanced phase extraction technique, the negative refractive index of the meta-material is verified by phase velocity measurement in the slab and prism measurement. From our results, not only the phenomenon of backward phase propagation but also the negative refraction is clearly observed. The index is also calculated precisely. The results from the two models are consistent.     

格子Boltzmann方法中的边界条件

比较并讨论了几种格子Boltzmann方法(LBM)中的边界条件处理方法，对标准的壁面全反弹方法进行了改进，提高了壁面反弹方法的精度．通过采用d2q9模型对Poiseuille流和非定常Coueue流进行数值模拟，获得了与分析解比较吻合的结果．针对不同的松弛时间τ和Re数，还给出了采取不同边界条件处理时的收敛精度，验证了小Re数时，LBM可以完全模拟N-S方程，由计算发现松弛时间τ接近1时的精度最高，τ较大时，误差较大。     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。