Mappings of finite distortion: the degree of regularity

This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)1 be a measurable function defined on a domain ΩRⁿ, n2, and such that exp(βK(x))L_loc¹(Ω), β>0. We show that there exist two universal constants c₁(n),c₂(n) with the following property: Let f be a mapping in W_loc^1,1(Ω,Rⁿ) with |Df(x)|ⁿK(x)J(x,f) for a.e. xΩ and such that the Jacobian determinant J(x,f) is locally in L¹ log^−c₁(n)βL. Then automatically J(x,f) is locally in L¹ log^c₂(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion. Namely, we obtain novel results on the size of removable singularities for bounded mappings of finite distortion, and on the area distortion under this class of mappings.     

基于LabVIEW的砝码自动检定系统设计与实现

针对目前砝码检定工作操作过程复杂、检定效率低等问题,设计了一种基于LabVIEW的砝码自动检定系统。在符合砝码检定规程的情况下,系统实现了检定数据实时采集、数据处理、生成原始记录、管理标准器、查询历史数据和衡器控制等功能。相对现有的砝码检定方法有操作简单、高效、程序移植性好等优点。系统由主控计算机、串口转无线扩展卡、多台衡器设备及相应的标准砝码装置组成。通过使用串口转Wi-Fi模块,系统可实现控制多台衡器设备的需求。实验结果证明,系统运行稳定可靠,采集数据准确,容易扩展,且大幅度减轻了检定人员的劳动强度,在计量检定工作中具有一定的实用和推广价值。     

Core-level photoemission of the Si(1 1 1)– -Ag surface using synchrotron radiation

The evolution of Si 2p core-level photoemission during a structural conversion from the Si (1 1 1)– -Ag to the Si(1 1 1)– -Ag superstructures induced by Ag adatoms adsorption at 140 K was studied using synchrotron radiation. The component from the top-layer Si-trimer atoms on the former surface was found to split into two components in the latter surface. The result is discussed in terms of a relaxation in some of the Si trimers induced by Ag adatoms sitting on the nearby Ag triangles of the -Ag substrate. The intensity ratio between the split components is a key to exclude some structure models proposed so far for the phases.     

Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system

We study the enhanced Kerr-nonlinear coefficient in a three-level A-type atomic system for various coupling-beam powers. The Kerr-nonlinear coefficient behaves very differently in the strong and the weak coupling power regions and changes sign when the coupling or probe frequency detuning changes sign. Comparisons of Kerr-nonlinear coefficients as functions of probe frequency detuning, coupling power, and coupling frequency detuning are presented.     

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

射流式单重态氧发生器研究

单重态氧O2 (a1Δg)是迄今唯一能用纯化学反应高效产生的具有长寿命的亚稳激发态分子 .为了考察提出的用两个O2 (1Δ)能量汇集反应生成氧第二单重激发态O2 (b1Σ+ g)以实现近可见短波长化学激光方案的现实性 ,设计和实验了一个氯流量为 3～ 10mmol/s的射流式单重态氧发生器 (JSOG) .考察了三种具有不同孔径和孔数目的喷头、氯气流量和脱水冷阱温度等对JSOG出口的O2 (1Δ)浓度、O2 (1Δ)分压、氯利用率及水蒸气含量的影响 .发现用聚氯乙烯管作冷阱时 ,最佳冷阱介质温度为 - 140～ - 15 0℃ ,对此提出了O2 (1Δ)表面脱活与脱水互相竞争的解释 .在最佳条件下 ,可将O2 (1Δ)气中水分压降低至 4Pa ,这一结果是首次报导     

类钴氙离子入射Ni表面激发的红外光谱线和X射线谱

当高电荷态类钴氙离子（cobalt like -Xe, Xe²⁷⁺）入射金属Ni表面过程中,共振电子俘获释放势能完成中性化,形成多激发态的Xe原子,其外壳层电子退激辐射红外光谱线.入射离子特殊的势能释放方式、离子动能和金属表面引起离子增益的能量在极短的时间（飞秒量级）沉积靶平方纳米尺度的空间范围,引起靶表面原子激发和电离,形成复杂组态之间的跃迁,特别是偶极禁戒跃迁（电四极跃迁、磁偶极跃）和X射线发射.单离子X射线产额随入射离子的动能增加而增加. 关键词： 高电荷态离子 红外光谱线 X射线 禁戒跃迁     

含stubs量子波导系统的电子自旋极化输运性质

理论上研究了含stubs的Rashba自旋轨道耦合（spin-orbit coupling, SOC）量子波导系统的自旋极化输运性质. 利用晶格格林函数方法,发现由于stubs和SOC产生的势阱使系统中出现束缚态,这些束缚态与传播态之间相互干涉导致电导中出现Fano共振结构,同时在对应的自旋极化率中也出现Fano共振或反共振结构. 此外,由于系统结构的突变使电子被反向散射和量子干涉效应,电导中出现一系列的共振峰. 但是,当系统加上外磁场后,所有这些效应都被抑制, 系统重新出现量子化电导, 同时自旋电导也出 关键词： 量子波导 自旋极化输运 自旋轨道耦合     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.     

Investigation of odd-parity Rydberg states of Eu I with autoionization detection

Isolated-core-excitation (ICE) scheme and autoionization detection are employed to study the bound Rydberg states of europium atom. The high-lying states with odd parity have been measured using the autoionization detection method with three different excitation paths via 4f⁷6s6p[ ⁸P_5/2], 4f⁷6s6p[ ⁸P_7/2] and 4f⁷6s6p[ ⁸P_9/2] intermediate states, respectively. In this paper the spectra of bound Rydberg states of Eu atom are reported, which cover the energy regions from 36000~cm^-1 to 38250~cm^-1 and from 38900~cm^-1 to 39500 cm^-1. The study provides the information about level energy, the possible J values and relative line intensity as well as the effective principal quantum number n^* for these states. This work not only confirms the previous results of many states, but also discovers 11 new Rydberg states of Eu atom.