线有向图的幂敛指数

设G是有向图，LG表示c的线有向图，本文得到了它们的幂敛指数及周期之间的关系：k（G）－1≤（LG）≤k（G）＋1,p（LG）=p（G）特别地，当G为本原图时有：k（LG）＝k（G）＋1     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

Polarisation interferometry flying height testing

The in-depth analyses of polarisation interferometry flying height testing are presented. The drawbacks of the oblique incidence polarisation interferometry method are discussed. The application of the dual-beam normal incidence polarisation interferometry method is illustrated. It is shown that with this normal incidence polarisation interferometer, not only the flying height can be measured down to contact without losing accuracy, but the optical parameters of the head-slider can also be determined.     

涂有半导体气敏薄膜的长周期光纤光栅气敏传感特性理论分析

首先利用耦合模理论研究了长周期光纤光栅LPFG折射率敏感特性,数值计算了长周期光纤光栅透射谱谐振波长与环境介质折射率的关系。其次分析了半导体氧化物气敏膜光学特性机理,当气体与薄膜接触时,气体会使敏感膜的消光系数、吸收系数和相应的折射率发生变化。基于上述两点,提出可将气敏膜涂于光栅表面,利用气敏膜的折射率随环境气体成分和浓度变化而变化的特性,从而影响LPFG透射谱谐振波长的变化,通过检测波长的变化达到探测气体成分和浓度的目的。由于长周期光纤光栅对环境介质折射率的灵敏度高于光纤,且其传感信号属于波长调制,测量信号不受光强波动及光纤损耗的影响,因此其灵敏度比强度型光纤气体传感器高。     

A subfringe integration method for multiple-beam Fizeau fringe analysis

Some aspects concerning the subfringe integration method in interferogram analysis have been investigated and modified. The modified algorithm, introduced in this paper, is capable of reconstructing the phase in the presence of noise or errors in carrier frequency. The subfringe integration method was applied to analyze two computer simulated patterns of equispaced Fizeau fringes using N bucket integration. Also, it is used to analyze the multiple-beam Fizeau fringe. The refractive index profile of polyethylene fiber is obtained by using two methods, subfringe integration method, and Fourier transform method. A comparison between the obtained results using the maintained methods is presented.     

Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves

We study the relationship between the growth and decrease of the sum of the entire Dirichlet series of finite order (in the sense of Ritt) on arbitrary curves going to infinity. For a class of exponents having a regular distribution (in a certain sense), we obtain a test for the logarithm of the maximal term to be equivalent to the logarithm of the absolute value of the sum of the Dirichlet series on at least one unbounded sequence of points of the curve.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 37–51.Original Russian Text Copyright © 2005 by A. M. Gaisin, I. D. Latypov.     

Application of refractive index mixing rules in binary systems of hexadecane and heptadecane with n -alkanols at different temperatures

Density and refractive index have been experimentally determined for binary liquid mixtures of hexadecane and heptadecane with 1-butanol, 1-pentanol, 1-hexanol and 1-heptanol at 298.15, 308.15 and 318.15 K. A comparative study of Lorentz—Lorenz (L-L), Weiner (W) and Heller (H), and Gladstone-Dale (G-D) relations for predicting the refractive index of a liquid has been carried out to test their validity for the eight binaries over the entire mole fraction range of hexadecane and heptadecane at the three temperatures. Comparison of various mixing rules has been expressed in terms of average percentage deviation. The performance of the Lorentz-Lorenz and Heller relations is relatively better than that of the Weiner and Gladstone-Dale relations.     

PROPAGATION CHARACTERISTICS OF GAUSSIAN BEAMS WITH ASTIGAMATISM

Transformation of Gaussian beams propagating through an axially asym-metric optical system is studied in detail by means of the complex curvature tensor andthe tensor ABCD law.Some important propagation characteristics of Gaussian beamswith simple or general astigmatism are demonstrated by typical numerical examples.     

K-theory for rickart C*-algebras

We give an explicit index map for any properly infinite closed ideal of a Rickart C ^*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K ₁-groups of any quotient algebra of a Rickart C ^*-algebra.     

Measuring the thickness and refractive index of a thick transparent plate by an unexpanded laser beam

The thickness and refractive index of a thick transparent plate are measured by using an unexpanded HeNe laser beam. The laser beam is incident at different angles onto the plate; and then two reflected beams; from the front and back surfaces; are received on a distant screen: the corresponding separations between them are measured. A theoretical relation between the refractive index; thickness; angle of incidence and separation is derived. This relation is experimentally verified and shows good agreement. The errors in the measured thickness and refractive index are analysed. The method is non-contact; non-destructive and low cost.