一个组合数学问题

讨论展开式（η＿１＋ｂη＿０）（η＿２＋ｂη＿０＋ｂη＿０）…（η＿ｎ＋ｂη＿（ｎ－１）…＋ｂ￣ｎη＿０）．引入个迅速求得Ａｆ（ｎ）的计算规则，以及系数的计算公式，这公式是牛顿二项式展开系数公式的推广。     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

第二类Fredholm积分方程的泰勒展开解法

本进一步发展了用Taylor公式求解第二类Fredholm积分方程的方法，并给出了近似解的误差精度分析．     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Monte Carlo Simulation of Electron Transport and X-Ray Generation. II. Radiative Processes and Examples in Electron Probe Microanalysis

Theoretical models for Monte Carlo simulation of radiative processes, i.e. bremsstrahlung and characteristic x-ray emission, are presented. Possible strategies for simulating electron transport are briefly described. For mechanisms involving energy loss and angular deflections, difficulties for strict implementation of accurate numerical differential cross sections still remain due to the strong correlations between these variables. Practical solutions for the case of inelastic collisions and bremsstrahlung emission are described. Comparisons of simulation results with experimental data for several problems of interest in electron probe microanalysis are presented.     

逻辑函数最大项展开式和CRM展开式的转换

在逻辑函数的CRM展开式和两种新运算基础上，对函数量大项展开系数和CRM展开系统(dj系数)之间的关系作了较详细的讨论，并提出了两者的矩阵转换法，快速转换法和直接代入转换法，具备较好的实用性．     

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.     

逻辑函数在布尔减-异或、布尔除-符合代数系统中的规范展开式

证明了布尔减、异或运算以及布尔除、符合运算的完备性,并从与-异或及或-符合代数系统中的RM、CRM展开式出发,分别推导了任意逻辑函数在布尔减-异或及布尔除-符合代数系统中的规范展开式.举例说明了与-或-非代数系统中规范展开式与布尔减-异或、布尔除-符合代数系统中的规范展开式之间的转换.     

应用无衍射贝塞尔光束的固体线膨胀系数测量系统

测量固体线膨胀系数是工程设计中的一项重要工作。这套非接触固体线膨胀系数测量系统利用激光三角法进行了设计。通过采用线阵CCD作为信号传感器来实现自动化测量。通过采用无衍射贝塞尔光束来提高测量精度和增大测量范围。