A limit theorem for products of free unitary operators

This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle. The author would like to express his gratitude to Diana Bloom for her help with editing, and to Professor Raghu Varadhan for useful discussions.     

多项式的特征和与二项指数和的混合均值

本文主要利用解析方法以及二项指数和与Dirichlet特征的性质，研究多项式的特征和与二项三次指数和的混合均值的计算问题，并得到一个较强的渐近公式.     

Extension of statistical replacement to systems with time-correlated fluctuations

Nonlinear systems with correlated stochastic parameters are approximated by simpler systems. This method is an extension of an earlier version of statistical replacement and statistical linearization. The extended method is applicable to systems with correlated fluctuations. We show how this general method reduces to the earlier methods in special cases.     

混凝土中的声发射波速特性及其在源定位中的应用*

利用声发射技术监测受载混凝土裂缝发展特征的首要任务是对声发射源的准确定位。为了解混凝土中声发射波速特性,提高声发射源定位精度,该文开展了一系列室内试验,构建了考虑衰减现象的声发射波速修正模型,优化建立了基于修正波速的区域穷举定位法。结果表明:水灰比越小,基准波速越大,波速随距离的衰减越大。骨料粒径越大,基准波速越大,波速随距离的衰减越大。直线距离小于500 mm时,可采用对数函数描述声发射波速与距离的定量关系,以此构建的波速修正模型满足工程精度要求。采用修正波速的区域穷举定位法对单轴压缩试验产生的裂缝进行定位时,定位点比时差定位法更接近裂缝实际位置,有效提高了定位精度。     

DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRODINGER SYSTEM

The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument.     

落柱式高压粘度装置的研制与压粘试验结果

作者研制了一台可测试润滑油在高压下的粘度和密度的落柱式高压粘度装置。本装置采用了新型高压粘性动密封和新型高压流变平垫静密封,经1200MPa试压、1000MPa压力下48小时保压和使用试验证明均无泄漏。用本装置所获得的压粘数据的重现性好、灵敏度高、可比性强。     

含不同共轭桥的TCNQ开闭壳层体系NLO性质的DFT研究

采用密度泛函理论(DFT)结合有限场(FF)方法,对不同共轭桥连接的四氰代二甲基苯醌(TCNQ)开壳层和闭壳层电子态的非线性光学(NLO)系数进行计算,并以乙烯桥为例讨论共轭链长度与NLO性质的关系.结果表明:开壳层体系的极化率和二阶超极化率值都大于闭壳层体系,且共轭桥的共轭性越强,体系的极化率和二阶超极化率越大;在自由基体系中,单重态的二阶超极化率随双自由基成分y和自旋多重度的增加而增大.体系的共轭链增长,BLA(BondLength Alternation,共轭分子中相邻单、双键键长差的平均值)逐渐减小,双自由基成分y逐渐增大,体系的二阶超极化率也逐渐增大.     

Quantification of the push-pull character of azo dyes and a basis for their evaluation as potential nonlinear optical materials

The push-pull characters of a large series of donor-acceptor substituted azo dyes—71 structures in all—have been quantified by the NN double bond lengths, d_NN, the ¹⁵N NMR chemical shift differences, Δδ_15N, of the two nitrogen atoms and the quotient, π^∗/π, of the occupations of the antibonding π^∗, and bonding π orbitals of this partial NN double bond. The excellent correlation of the occupation quotients with the bond lengths strongly infers that both π^∗/π and d_NN are excellent parameters for quantifying charge alternation in the push-pull chromophore and the molecular hyperpolarizability, β₀, of these compounds. By this approach, selected compounds can be appropriately considered as viable candidates for nonlinear optical (NLO) applications.     

激光等离子体微推进技术的研究进展

为了加快激光等离子体微推进技术(μLPP)在航天领域的应用,介绍了该项技术近10年的发展状况。讨论了激光等离子体微推进技术发展过程中衍生出的各种工作模式,并简略分析了不同工作模式的优缺点。着重介绍了靶特性对激光微推进性能的影响,包括靶材的选择、靶的结构、靶材掺杂,以及靶物相特性等。针对该项技术的最终发展目标是研制微小卫星姿轨控的激光等离子体微推力器(μLPT),介绍并分析了美国Phipps小组开展的激光微推力器的研制工作。最后,指出了激光等离子体微推进技术目前存在的一些问题,并展望了它的发展前景。