正交曲线坐标系中加速度的拉氏方程求法

采用拉格朗日方程给出一种求解正交曲线坐标系中加速度的简捷方法。     

凸多边形上的Bezier曲面片

本文建立了正多边形上的重心坐标，并构造了多边形上的Ｂｅｚｉｅｒ曲面片、     

Polar Interface Optical Phonon Modes and Fr(o*)hlich Electron-Phonon Interaction Hamiltonians in an Arbitrary Layer-Number Quantum Well System

By using determinant method as in our recent work, the IO phonon modes, the orthogonal relation forpolarization vector, electron-IO phonon Frohlich interaction Hamiltonian, the dispersion relation, and the electron-phonon coupling function in an arbitrary layer-number quantum well system have been derived and investigated withinthe framework of dielectric continuum approximation. Numerical calculation on seven-layer Alx Ga1-x As/GaAs systemshave been performed. Via the numerical results in this work and previous works, the general characters of the IO phononmodes in an n-layer coupling quantum well system were concluded and summarized. This work can be regarded as ageneralization of previous works on IO phonon modes in some fixed layer-number quantum well systems, and it providesa uniform method to investigate the effects of IO phonons on the multi-layer coupling quantum well systems.     

联苯乙烯类蓝色发光材料DPVBi的合成及发光性质研究

合成了联苯乙烯类蓝色有机发光材料DPVBi[4，4′-二(2，2-二苯乙烯基)-1，l′-联苯]，用^1H-NMR，IR，元素分析等方法对其结构进行了表征。以DPVBi作发光层制备了电致发光器件，其结构为：ITO／CuPc／NPB／DPVBi/Alq3／LiF／Al，研究了器件的电致发光性质。器件最高亮度达4 373cd/cm^2，最大流明效率为1．24 lm／w，在20mA／cm^2电流密度驱动下的亮度为434cd／cm^2，CIE色坐标为x=0．15，y=0．16，器件的蓝色发光具有较好的色纯度。重点对器件发光色度的稳定性进行了研究，结果表明，随电流密度(4～4 000mA／cm^2)的变化，器件色度具有很好的稳定性。     

Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex and uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pythagorean-type theorem. Earlier, all these results were known only in Hilbert spaces.     

二维平面光栅角色散公式的完整解析形式及分析

在矢量衍射理论基础上给出了任意入射状态下二维平面光栅的光栅方 程，推导出二维平面光栅角色散公式的完整解析形式，确立了二维平面光栅衍射极角 角色散（第一类角色散）和衍射方位角角色散（第二类角色散）的概念. 通过二维平面光栅 衍射极角和衍射方位角角色散的理论分析和数值计算，阐明了当入射波矢偏离光栅法线时， 衍射光斑阵列发生畸变的机理，并明确指出了引起衍射方位角角色散的突变、导致衍射光斑 阵列剧烈变化的条件，因而具有理论上的意义. 在实际应用方面，以晶体和量子点 的x射线衍射、低能电子衍射和反射式高能电子衍射为 关键词： 二维平面光栅 衍射极角角色散 衍射方位角角色散 晶体电子衍射     

Estimates for the low‐frequency electromagnetic fields scattered by two adjacent metal spheres in a lossless medium

Inductive electromagnetic means, currently employed in real physical applications and dealing with voluminous bodies embedded in lossless media, often call for analytically demanding tools of field calculation at modeling stage and later on at numerical stage. Here, one is considering two closely adjacent perfect conductors, possibly almost touching one another, for which the 3D bispherical geometry provides a good approximation. The particular scattering problem is modeled with respect to the two solid impenetrable metallic spheres, which are excited by a time‐harmonic magnetic dipole, arbitrarily orientated in the 3D space. The incident, the scattered, and the total non‐axisymmetric electromagnetic fields yield rigorous low‐frequency expansions in terms of positive integral powers of the real‐valued wave number in the exterior medium. We keep the most significant terms of the low‐frequency regime, that is, the static Rayleigh approximation and the first three dynamic terms, while the additional terms are small contributors and they are neglected. The typical Maxwell‐type problem is transformed into intertwined either Laplace's or Poisson's potential‐type boundary value problem with impenetrable boundary conditions. In particular, the fields are represented via 3D infinite series expansions in terms of bispherical eigenfunctions, obtaining analytical closed‐form solutions in a compact fashion. This procedure leads to infinite linear systems, which can be solved approximately within any order of accuracy through a cutoff technique.     

Hyperkähler metric and GMN ansatz on focus–focus fibrations

In this paper, we study the hyperkähler metric and practise GMN’s construction of hyperkähler metric on focus–focus fibrations. We explicitly compute the action–angle coordinates on the local model of focus–focus fibrations, and show its semi-global invariant should be harmonic to admit a compatible holomorphic 2-form. Then we study the canonical semi-flat metric on it. After the instanton correction, finally we are able to get a reconstruction of the generalized Ooguri–Vafa metric.     

LaTiO3(110)薄膜分子束外延生长的精确控制和表面截止层的研究

LaTiO₃ 是一种典型的强关联电子材料, 其(110) 薄膜为通过晶格对称性、应变等的设计调控外延结构的物理性质提供了新的机会. 本文研究了SrTiO₃(110) 衬底表面金属La 和Ti 沉积所引起的微观结构变化, 进而利用电子衍射信号对分子束外延薄膜生长表面阳离子浓度的灵敏响应, 发展了原位、实时、精确控制金属蒸发源沉积速率的方法, 实现了高质量LaTiO₃(110) 薄膜的生长和对阳离子化学配比的精确控制. 由于LaTiO₃中Ti³⁺ 3d 电子的库仑排斥作用, 氧原子层截止的(110) 表面更容易实现极性补偿, 因此生长得到的薄膜表面暴露出单一类型的氧截止面.