Theory of Ordered Spaces¶II. The Local Differential Structure

In this paper we investigate the conditions under which the ordered spaces defined in [1] are locally diffeomorphic to ℝ ^N . In Sect.~1 we give an introduction and an overview of the results. In Sect. 2 we show that the axioms of [1] do not suffice to make light rays locally homeomorphic to ℝ. We introduce this structure via the new connectedness axiom 2.13, and work out some of its immediate consequences. In Sect. 3 we give the (somewhat involved) construction of timelike curves in a D-set, which are basic to everything that follows. They are used in Sect. 4 to prove (i) a nested interval theorem for ordered spaces; (ii) the contractibility of order intervals in D-sets; and (iii) that order intervals in D-sets are star-shaped. The notion of D-countability (meaning that a D-set has a countable base in the subspace topology) is introduced in Sect. 5. The Urysohn lemma shows that a D-countable ordered space is locally metrizable. If this space is also locally compact, then it has finite topological dimension N; these results are established in Sect. 6. The local differential structure now follows from known results: the embedding of such spaces in ℝ^{2 n +1}, and the result that an open star-shaped region in ℝ ⁿ is diffeomorphic to ℝ ⁿ . In conclusion, we exhibit these inclusions in Fig. 3, and suggest the possibility that Wigner's position on the “Unreasonable effectiveness of mathematics in the natural sciences” may be open to reasonable doubt. The axioms of [1] are given in the Appendix. Received: 26 November 1997 / Accepted: 10 February 1999     

Yb原子高激发态的斯塔克光谱

采用ππ偏振激光，通过两步激发和光电离方法，在０－１５４Ｖ／ｃｍ电场范围内，测定了Ｙｂ原子ｎ－１８附近ｍ＝０的斯塔克光谱，首次把包含斯塔克效应的能量矩阵对角化方法推广到Ｙｂ原子，所获得的理论斯塔克图与实验结果基本符合，观察到低场中斯塔克簇随电场增加呈现线性结构以及＾１Ｐ１态与斯塔克簇在抗交叉过程中振子强度发生转移的现象，讨论了结构与量子亏损的关系。     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.     

光纤Mach-Zehnder干涉仪系统

介绍了光纤Mach-Zehnder(MZ)干涉仪系统的结构.给出了光纤Mach-Zehnder干涉仪系统中信号光与参考光的干涉原理以及影响干涉光强的因素.同时也分析了光纤耦合器的交叉耦合,另外也给出了PZT的作用.阐述了光纤偏振控制器的结构、工作原理及其对光纤Mach-Zehnder干涉仪系统传感臂偏振态的控制,最后给出了光纤Mach-Zehnder干涉仪系统的应用.     

裂解温度对CVD法制备多壁碳纳米管的影响

用SEM、TEM、HRTEM及拉曼光谱方法研究了催化裂解乙炔制备多壁碳纳米管过程中裂解温度的影响,结果表明,在650℃～700℃裂解乙炔,可获得产量高、直径分布均匀、石墨程度高的多壁碳纳米管,并对裂解温度影响机制进行了分析和探讨。     

2-(2-喹啉偶氮)-1,5-苯二酚分光光度法测定烟草样品中的钙

在 p H为 8.0的柠檬酸钠 -氢氧化钠缓冲介质中 ,Triton X- 10 0存在下 ,2 - (2喹啉偶氮 ) - 1,5苯二酚(QADHB)与钙反应生成 1∶ 1稳定配合物 ,λmax=5 5 5 nm,ε=4 .18× 10 4L· mol-1· cm-1。钙含量在 0 .1—2 5μg/ 2 5 m L的范围内符合比耳定律 ,方法用于烟草中钙含量的测定 ,结果令人满意。     

Effect of electron inertia on large amplitude solitary waves in presence of kinematic viscosity in dusty plasma

Nonlinear dust acoustic solitary waves in a dusty plasma are studied for nonzero kinematic viscosity. Sagdeev’s potential can be obtain upto any order in ϕ. The existence of soliton solution is determined by pseudopotential approach. It is seen that the electron inertia has a significant effect on the existence of solitary waves in presence of kinematic viscosity.     

Carbide precipitates in solution-quenched PH13-8 Mo stainless steel: A small-angle neutron scattering investigation

This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.     

A straightforward method for wall impedance eduction in a flow duct

The development of the advanced liner technology for aeroengine noise control necessitates the impedance measurement method under realistic flow conditions. Currently, the methods for this need are mainly based on the inverse impedance eduction principle, confronting with the problems of initial guess, high computation cost, and low convergence. In view of this, a new strategy is developed that straightforwardly educes the impedance from the sound pressure information measured on the duct wall opposing to the test acoustic liner embedded in a flow duct. Here, the key insight is that the modal nature of the duct acoustic field renders a summed-exponential representation of the measured sound pressure; thus, the characterizing axial wave number can be readily extracted by means of Prony's method, and further the unknown impedance is calculated from the eigenvalue and dispersion relations based on the classical mode-decomposition analysis. This straightforward method is simple in its basic principle but remarkably has the advantages of ultimately overcoming the drawbacks inherent to the inverse methods, incorporating the realistic multimode nonprogressive wave effects, high computational efficiency, possibly reducing the measurement points, and even avoiding the necessity of the duct exit impedance that bothers perhaps all the existing waveguide methods.     

Fisher-Shannon plane and statistical complexity of atoms

Using the Hartree-Fock non-relativistic wave functions in the position and momentum spaces, the statistical measure of complexity C, due to López-Ruiz, Mancini, and Calbet for the neutral atoms as well as their monopositive and mononegative ions with atomic number Z=1-54 are reported. In C, given by the product of exponential power Shannon entropy and the average density, the latter is then replaced by the Fisher measure to obtain the Fisher-Shannon plane. Our numerical results suggest that in overall the Fisher-Shannon plane reproduces the trends given by C, with significantly enhanced sensitivity in the position, momentum and the product spaces in all neutral atoms and ions considered.