一类图的强最大亏格嵌入

图的嵌入理论是拓扑图论中一个中心课题.图的最大亏格嵌入的刻画和研究已较完善.但对于强嵌入,这方面的讨论却很少.本文对于平面上的不含不交(指无公共节点)圈的图以及完全图K5,利用构造强最大亏格嵌入的方法,给出了强最大亏格.同时,也给出了完全二部图K3,k(k≥3)的不可定向强最大亏格的一个下界.     

固体间界面的物理模型和界面对声波的反射

简要描述了模拟两固体间界面特性的弹簧模型，该模型最早是根据静力学方法提出的，后来用固体间界面薄层的声波反射方法加以改进，从界面弹簧模型可以方便地得到界面外近似边界条件，其中包含界面“弹簧”振子的劲度常数和质量，文章还给出了两相间固体中界面声反射系数的表达式，介绍了测量界面劲度常数的超声反射谱方法。最后讨论了仍关声波与界面相互作用研究领域中最近的一些研究进展。     

四角晶相HfO2(001)表面原子和电子结构研究

采用基于第一性原理的密度泛函理论研究了四角晶相二氧化铪(t-HfO₂)体相及 其(001)表面的原子几何与电子结构.理论计算结果表明，t-HfO₂(001)表面不会 产生重构现象.与体相电子结构相比, t-HfO₂(001)表面态密度明显高于体相态 密度.其次，表面原子的态密度更靠近费米能级(E_F)，价带往低能量处移动，并 有表面态产生.计算结果表明了t-HfO₂表面禁带宽度明显低于体相的禁带宽度. t-HfO₂(001)的表面态产生以及表面禁带宽度减小是由于Hf原子与O原子的配位 数减少，表面原子周围的环境发生变化而引起的. 关键词： 密度泛函理论 2(001)')" href="#">t-HfO₂(001) 表面电子结构     

Ag+掺杂的立方相Y2O3:Eu纳米晶体粉末发光强度研究

采用化学自燃烧法制备了不同Ag⁺掺杂浓度的Y₂O₃:Eu纳米晶体粉末样品(［Y³⁺］∶［Eu³⁺］∶［Ag⁺］=99∶1∶X，X=0—3.5×10^-2)，以及通过退火处理得到了相应的体材料.根据X射线衍射谱确定所得纳米和体材料样品均为纯立方相.实验表明在纳米尺寸样品中随着Ag离子浓度的增加，荧光发射强度随之增加，当X=2×10^-2时达到最大值，其发光强度比X=0时提高了近50%.当Ag离子浓度继续增加，样品发光强度保持不变.在相应的体材料样品中则没有观察到此现象.通过对各样品的发射光谱，激发光谱，X射线衍射图谱，透射电镜(TEM)照片和荧光衰减曲线的研究，分析了引起纳米样品荧光强度变化的原因是由于Ag离子与表面悬键氧结合，从而使这一无辐射通道阻断，使发光中心Eu³⁺的量子效率提高；Ag⁺的引入所带来的另一个效应是使激发更为有效.这两方面原因使发光效率得到了提高.     

纳米级精度分光路双频干涉度量系统的设计

为完成快速、精确的外观轮廓度量,设计了一种新型纳米级精度分光路双频干涉度量系统。系统由低频差双频激光干涉度量模块和微探头及二维工作台两部分组成。微探针以轻敲式接近样品至几十纳米时,受原子力作用发生偏转,利用双频干涉模块度量其纵向偏转量,并对样品进行梳状式度量得到外观形貌。根据双频激光的实际光源,对原有双频干涉度量理论进行了改进提高。进行了系统组建和实验验证。结果表明:系统具有纳米级精度,可用于超精样品外观轮廓度量。     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

水斗非定常自由水膜流三维贴体数值模拟

本研究采用水斗三维非正交贴体坐标系进行了非定常自由水膜流动的数值解析。对不规则水斗内表面采用三维非正交贴体坐标系下离散点进行拟合,推导了曲面离散点的法向矢量和曲面微元面高斯曲率、平均曲率等几何特征量的计算公式,进而导出流体粒子在运动方向上曲率计算式。在水斗三维贴体坐标系中,还推导了流体粒子在水斗曲面上的运动控制方程。最后对某水轮机水斗内表面非定常自由水膜流进行了数值模拟,得到其非定常水膜流态分布。     

Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)