粘性／非粘性方程有限元和谱方法混合逼近

讨论有粘性和无粘性Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程有限元和谱方法混合逼近问题，弱交面匹配关系被应用。收敛估计显示有限元精度和谱精度可在各自的子区域中得到。     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

煤与瓦斯突出预报的模糊聚类关联分析法

首先采用模糊聚类分析对煤与瓦斯突出的样本集合进行分类，建立不同突出程度的模糊模式。然后用关联分析确定待预报样本与模式的关联程度，以此预测预报样本的煤与瓦斯突出危险程度。这种预报方法相对于模糊聚类分类后，将模式与待预报样本组成新的样本集合，再进行聚类分析，以此分类结果进行预报法。不仅可靠程度高，而且能定量描述待报样本与模式的亲和程度。     

Routh—Hurwitz条件的若干应用方法

本文介绍Routh—Hurwitz条件的若干应用方法,特别是给出了判别矩阵谱半径小于1的方法,这些方法有实用价值。     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

The k-means range algorithm for personalized data clustering in e-commerce

This paper describes the k-means range algorithm, a combination of the partitional k-means clustering algorithm with a well known spatial data structure, namely the range tree, which allows fast range searches. It offers a real-time solution for the development of distributed interactive decision aids in e-commerce since it allows the consumer to model his preferences along multiple dimensions, search for product information, and then produce the data clusters of the products retrieved to enhance his purchase decisions. This paper also discusses the implications and advantages of this approach in the development of on-line shopping environments and consumer decision aids in traditional and mobile e-commerce applications.     

On the evolution of two-dimensional patterns in an inviscid liquid sheet

We perform an analysis of the pattern formation for a moving sheet of inviscid fluid. The sheet, which is assumed to have an infinite horizontal extent, moves at some prescribed velocity into a passive surrounding gas. The sheet’s thickness is assumed much smaller than the horizontal scale of the fluid motion. By considering a system that is symmetric with respect to the horizontal planes, long scale asymptotics are used to reduce the full governing equations in three dimensions to a set of three coupled nonlinear partial differential equations for the horizontal components of the velocity field and the height of the interface profile. The interfacial conditions consisting of the kinematic and normal stress balance are incorporated into these evolution equations. Investigations are carried out as function of the sole dimensionless parameter, namely the Weber number. A small amplitude stability analysis around the planar gas–liquid interface reveals that wave patterns in the form of traveling plane waves occur subcritically, and are therefore unstable. The reduced evolution equations are solved numerically for fixed values of the Weber number. Since the reduced system of equations is homogeneous, the wave motion is generated by initial conditions. Five initial conditions have been imposed: one-dimensional rolls, two-dimensional squares, two-dimensional hexagons, two-dimensional ridges, and smooth peaks. The ensuing evolution of the liquid sheet’s shape and corresponding flow fields are described by illustrations of the changes in the sheet’s morphology with time.     

高纯金属镨中痕量稀土杂质的电感耦合等离子体原子发射光谱分析及光谱干扰的校正

本文提出了PGS-2型平面光栅光谱仪(色散率0.18纳米,二级光谱)与PlasmaTherm ICP-5000D射频发生器联用,乙醇预去溶方式进样,同时直接测定高纯金属镨中5个痕量稀土杂质元素的方法。并讨论了基体浓度对检出限的影响以及光谱干扰及其校正方法。当样品溶液中镨的浓度为5毫克/毫升时,测定下限分别为镧、钕和钐0.002%,铈0.003%和钇0.0005%。获得了良好的实验结果,其相对标准偏差为1.2-6.2%。     

关于Fuzzy聚类分析及其在脊髓灰质炎中的应用

本文用Fuzzy数学的观点探讨了Fuzzy聚类分析，并通过对脊髓灰质炎病毒抗体水平的Fuzzy聚类分析，获得了良好的聚类效果，为该项问题的研究提供了科学依据。     

泥浆传送涡轮转速信号的分析处理

本文对传送涡轮钻转速信号的泥浆信道的干扰与噪声特性作了分析,从理论上阐述了从强的周期性干扰与噪声中实时检测出转速信号频率的谱分析法。提出了干扰带的概念,并详细分析了不同窗函数在已定干扰带的条件下所需的数据时宽。根据噪声强度推导了用平均法降低噪声功率谱方差所需的分段数以及总的数据时宽。