局部传输信息不等式和曲率维数条件的等价性

本文得到了曲率维数条件CD(ρ,∞) 和CD(0, n)与相应的局部传输信息不等式的等价性.     

A Class of Finite-Dimensional Representations of U_q（sl_2）

In order to study a class of finite-dimensional representations of Uq（sl2）, we deal with the quotient algebra Uq （m, n, b） of quantum group Uq（sl2） with relations Kr=1, Emr=b, Fnr=0 in this paper, where q is a root of unity. The algebra Uq（m, n, b） is decomposed into a direct sum of indecomposable （left） ideals. The structures of indecomposable projective representations and their blocks are determined.     

零维理想的一般准素分解

本文对零维理想关于某个变元是否为正常位置进行讨论,给出零维理想关于某个变元是否为正常位置的等价条件,得到一种较容易的求零维理想准素分解的方法,对某些理想能较快地得到部分准素分支,更有利于对理想进行准素分解.     

一类板弯曲方程的辛本征函数展开方法

本文研究一边简支对边滑支边界条件的矩形板方程的无穷维Hamilton算子本征函数系,证明该无穷维Hamilton算子广义本征函数系在Cauchy主值意义下是完备的,为应用辛本征函数展开法求解该平面弹性问题提供理论基础.进而推导出原方程的通解,并对该平面弹性问题指出什么样的边界条件可按此方法求解.最后应用具体的算例说明所得结论的合理性.     

牺牲层腐蚀二维数值模拟与仿真

建立了基于扩散方程的二维腐蚀模型,并给出相应的边界条件.为求解二维扩散方程,分别给出了有限差分显式和隐式求解算法.得到了每一时刻溶液在具体位置的浓度值,再由Topography模型计算腐蚀前端面的腐蚀情况得到腐蚀前端行进轮廓线.编程实现了对多种不同牺牲层几何结构以及组合结构腐蚀过程的仿真,最后实验验证了模拟的真实性.     

The single-longitudinal-mode operation of a ridge waveguide laser based on two-dimensional photonic crystals

An electrically driven, single-longitudinal-mode GaAs based photonic crystal (PC) ridge waveguide (RWG) laser emitting at around 850 nm is demonstrated. The single-longitudinal-mode lasing characteristic is achieved by introducing the PC to the RWG laser. The triangle PC is etched on both sides of the ridge by photolithography and inductive coupled plasma (ICP) etching. The lasing spectra of the RWG lasers with and without the PC are studied, and the result shows that the PC purifies the longitudinal mode. The power per facet versus current and current-voltage characteristics have also been studied and compared.     

High-mobility two-dimensional electron gases at oxide interfaces： Origin and opportunities

Our recent experimental work on metallic and insulating interfaces controlled by interfacial redox reactions in SrTiO3-based heterostructures is reviewed along with a more general background of two-dimensional electron gas(2DEG)at oxide interfaces.Due to the presence of oxygen vacancies at the SrTiO3surface,metallic conduction can be created at room temperature in perovskite-type interfaces when the overlayer oxide ABO3has Al,Ti,Zr,or Hf elements at the B sites.Furthermore,relying on interface-stabilized oxygen vacancies,we have created a new type of 2DEG at the heterointerface between SrTiO3and a spinelγ-Al2O3epitaxial film with compatible oxygen ion sublattices.This 2DEG exhibits an electron mobility exceeding 100000 cm2·V 1·s 1,more than one order of magnitude higher than those of hitherto investigated perovskite-type interfaces.Our findings pave the way for the design of high-mobility all-oxide electronic devices and open a route toward the studies of mesoscopic physics with complex oxides.     

转轮优化设计二元能量收支控制新理念

大流量贯流式水轮机转轮叶片由轮毂至轮缘形状变化很大,流动特征变化亦非常明显,采用代表半径处能量平均的一元设计将不能满足要求。为了使转轮叶片设计达到更细致的优化设计目标,非常有必要进行二元的转轮叶片翼型优化设计。本文提出将一元能量概念及技术扩张至二元能量收支的新概念。研究中由CFD三维数值解析结果求得叶片进出口二元能量收支状况并对其进行评价及控制,为转轮叶片翼型优化设计提供依据。研究结果表明,二元能量收支方法对优化设计具有实际意义,用此方法设计的贯流式水轮机效率比一元设计提高了0.5%。     

一类分层三角剖分下三次样条空间的维数

本文定义了平面单连通多边形域的一类较任意的三角剖分－分层三角剖分，并通过分析二元样条的积分协调条件，确定了分层三角剖分卜三次Ｃ^１作条函数空间的维数．     

自仿函数分数阶导数的分形维数

研究一类自仿函数的分数阶导数,获得了自仿函数的Weyl-Marchaud分数阶导数的图像盒维数,证明了分数阶导数的阶与分形维数之间的线性关系.