Computation of the eigenvalues of Sturm-Liouville problems with parameter dependent boundary conditions using the regularized sampling method

The purpose in this paper is to compute the eigenvalues of Sturm-Liouville problems with quite general separated boundary conditions nonlinear in the eigenvalue parameter using the regularized sampling method, an improvement on the method based on Shannon sampling theory, which does not involve any multiple integration and provides higher order estimates of the eigenvalues at a very low cost. A few examples shall be presented to illustrate the power of the method and a comparison made with the the exact eigenvalues obtained as squares of the zeros of the exact characteristic functions.

     

Apparatus for High-Resolution Solid Hydrogen Matrix Isolation Spectroscopy and Its Application

Apparatus integrating a Fourier transform-infrared (FT-IR) spectrometer and a mid-infrared difference frequency generation (DFG) laser spectrometer was built for the study of the matrix isolation spectrum in solid molecular hydrogen. A 3-cm-long molecular hydrogen crystal was grown in a liquid-helium Dewar, and its infrared absorption spectrum in the 1-5 μm region was recorded to test the system. The W₀(0) (ν=0←0, J=6←0) line around 2410 cm⁻¹ of solid hydrogen was investigated with the DFG laser spectroscopy. High-resolution matrix isolation spectrum of CO² co-deposited with hydrogen on a BaF₂ cold plate at liquid-helium temperature was studied.     

Sequential Estimation of the Parameters in a Trigonometric Regression Model with the Gaussian Coloured Noise

This paper considers the estimation problem for a trigonometric regression model with the noise specified by the Ornstein–Uhlenbeck process with unknown parameter. We propose a sequential procedure which ensures a prescribed mean square precision uniformly in the nuisance parameter. The asymptotic behaviour of the procedure duration mean has been studied. This revised version was published online in August 2006 with corrections to the Cover Date.     

Novel optical film sensor design based on p-polarized reflectance

A new scheme of optical film sensor is presented. The sensor is based on p-polarized reflectance, consisting of a sensing coated substrate, is easily optimized for maximum sensitivity in different applications. The resolutions of refractive index n_f, extinction coefficient k_f and thickness h_f of the sensitive films are predicted to be 10⁻⁷, 10⁻⁵ and 10⁻³ nm, respectively. Experimentally, we selected the sol–gel derived SnO₂ films as gas-sensitive films and conducted preliminary gas-sensing test. The results indicate that novel optical film sensor scheme has higher sensitivity, and the detection sensitivity is available to 10⁻¹ ppm on the condition of optimum optical parameters and incident angle.     

理想流体一维绝热稳定流动能量方程推导

对理想流体一维绝热稳定流动作了讨论．对一般理想流体(可压缩或不可压缩)，用两种方法推出了能量方程．在此基础上，讨论了流动可逆性及不同流体性质对流动参数的影响．     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

关于三维Minkowski空间中直线汇的一些注记

本文研究了三维Minkowski空间中直线汇的一些性质,特别是关于类时线汇的性质．讨论了线汇基本元素的存在性,并证明了关于三维Minkowski空间中类时线汇的配分参数的一个结果,推广了苏步青1927年的—个成果．     

Collective bounce-off phenomenon in139La+Ag(Br) reaction at 1.1 A GeV energy

Out of a total statistics of 896¹³⁹La+Ag(Br) interactions, 128 interactions having multiplicity of target fragments (Z⩾1)⩾8 and projectile fragments (Z⩾2)⩾4 have been selected. They correspond to quasi-peripheral interactions. Azimuthal angle correlation between sources of target fragments (TFs) and projectile fragments (PFs) shows the existence of bounce-off effect. Using data of La+Ag(Br) and⁸⁴Kr+Ag(Br) reactions it is shown that individual helium [Z=2, PFs] and heavier fragment [Z⩾3, PFs] show different emission characteristics. Further, a two prong correlation functionT(Φ _ij ) plotted for heavier fragments and helium fragments separately, indicates the possibility of existence of different physical conditions. This observation is supported by the different momentum widths of helium fragments and heavier fragments. From the momentum width data of Kr+Ag(Br) reactions normalized density comes out to be ≈4.7. Using quasi-elastic kinematics for the bounce-off nuclei, the excitation energy has been computed from the experimental data of flow angles. The strength of bounce-off seems to decrease with the increase of excitation energy or temperature.     

物理实验中最佳参量值的选取

许多物理实验中，一些参量要靠实验者本身去选择，参量的选取应以由此而产生的误差最小为标准，本文从误差分析入手，通过典型的实例，给出了选取最佳参量的一种方法。     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.