提高验证牛顿第二定律实验精度的创新和改进

在验证牛顿第二定律实验中,除了教会学生动手操作、数据采集与处理外,还要向学生传授物理实验思想、实验设计方案、数学模型建立、误差分析与误差纠正等方面的内容。笔者撰写此论文,意在通过挖掘该实验创新知识点,以便达到培养学生创新思维和创造力的目的。     

SIM在使用中应注意的条件

本文介绍了Hausdorff与Box分形维数及测度，首次引入了周积规范比的概念，给出了SIM的正确数学描述及证明，提出了使用SIM的充分条件，并将该方法进行了修正．     

Preparation of a novel polymeric fluorescent nanoparticle

A new type of narrowly dispersed fluorescent crosslinked polystyrene (PS) nanoparticles (20-50 nm) was synthesized via a modified microemulsion copolymerization of styrene, crosslinker divinyl benzene (DVB) and a hydrophilic comonomer amino ethyl methacrylate hydrochloride (AEMH), in the presence of pyrene. Characterized by steady-state fluorescence spectra, these nanoparticles show high luminescent intensity and the embedded pyrene has a negligible desorption from the nanoparticles. The emission intensity I₁ of the pyrene in the crosslinked nanoparticles is 40 times higher than that of pyrene in toluene or styrene solution with the same concentration. The fluorescence emission intensity can be varied by the amount of the monomer, crosslinker and pyrene, but is influenced little by the amount of AEMH in the range of investigation. The surface of the nanoparticles is modified by amino and amidino functional groups introduced by the comonomer and the initiator 2, 2'-azobis(2-amidinopropane) dihydrochloride (V₅₀), which controls the zeta potential on the particle surface.     

像散法离焦检测中的像散透镜参数设计

推导出了离焦量与聚焦误差信号功率的关系式。利用MATLAB软件仿真,详细分析了像散透镜系统各个参数对离焦量、灵敏度、光斑大小等的影响,得到了像散圆透镜与像散柱透镜焦距之间的距离关系。结果发现聚焦物镜和探测器参数对最小离焦量、灵敏度、精度有决定性的影响。提出了像散透镜系统各光学参数选择的原则和方法,并以德国Silicon Sensor公司的QP50-6型四象限探测器为例,详细分析了离焦量与聚焦误差信号功率的线性关系。这些工作对建立满足应用对象要求的像散法离焦检测系统具有重要的指导意义。     

Geometric decay in level-expanding QBD models

Level-expanding quasi-birth-and-death (QBD) processes have been shown to be an efficient modeling tool for studying multi-dimensional systems, especially two-dimensional ones. Computationally, it changes the more challenging problem of dealing with algorithms for two-dimensional systems to a less challenging one for block-structured transition matrices of QBD type with varying finite block sizes. In this paper, we focus on tail asymptotics in the stationary distribution of a level-expanding QBD process. Specifically, we provide sufficient conditions for geometric tail asymptotics for the level-expanding QBD process, and then apply the result to an interesting two-dimensional system, an inventory queue model.     

On Projective Modules in Category \mathcal{O}_{int} of Quantum \mathfrak{sl}_{2}

The restriction of a Verma module of ${\bf U}(\mathfrak{sl}_3)$ to ${\bf U}(\mathfrak{sl}_2)$ is isomorphic to a Verma module tensoring with all the finite dimensional simple modules of ${\bf U}(\mathfrak{sl}_2)$ . The canonical basis of the Verma module is compatible with such a decomposition. An explicit decomposition of the tensor product of the Verma module of highest weight 0 with a finite dimensional simple module into indecomposable projective modules in the category $\mathcal O_{\rm{int}}$ of quantum $\mathfrak{sl}_2$ is given.     

Analysis of exact tail asymptotics for singular random walks in the quarter plane

In this paper, we consider all singular cases of random walks in the quarter plane. Specifically, exact light tail asymptotics for stationary probabilities are obtained for all singular random walks.     

Characterizations of QF Rings

A ring R is called “left GP-injective” if for any 0 ≠ a ∈ R, there exists n > 0 such that a ⁿ  ≠ 0 and a ⁿ R = r(l(a ⁿ )). It is proved that (1) every right Noetherian left GP-injective ring such that every complement left ideal is a left annihilator is a QF ring, (2) every left GP-injective ring with ACC on left annihilators such that every complement left ideal is a left annihilator is a QF ring, and (3) every left P-injective left CS ring satisfying ACC on essential right ideals is a QF ring. Several well-known results on QF rings are obtained as corollaries.     

Rings in which elements are uniquely the sum of an idempotent and a unit that commute

A ring is called uniquely clean if every element is uniquely the sum of an idempotent and a unit. The rings described by the title include uniquely clean rings, and they arise as triangular matrix rings over commutative uniquely clean rings. Various basic properties of these rings are proved and many examples are given.