独立渐进随机环境中随机行走

讨论了一类独立但不一定同分布随机环境中随机行走的常返性和非常返性，进而研究了常返性中的正常返，以及在它们基础上逃逸速度的极限性质，从而推广了Solmn的理论框架。     

国民经济的最优增长模型

本文利用 Cobb-Douglas生产函数建立了一类描述国民经济收入和积累率关系的数学模型 ,并利用该模型求出了国家预定经济增长目标下的计划投资量以及保持国民经济快速增长的合理的投资量和消费目标 .     

构筑思维创新能力基石——提高电容容量的设计

本通过设计两种提高电容容量的方法，从发现问题、研究问题和总结问题的三方面提高学生的创新思维能力。     

数学实验课程的教学与数学素质的培养

分析了现行工科数学教学中存在的主要问题 ,认为数学实验课程的教学是培养数学素质不可缺少的环节 ,并就如何更好地发挥数学实验课程教学的作用提出了一些具体的建议 .     

No directed fractal percolation in zero area

We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {p _k}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN ¹⁻ k is partitioned intoN ² congruent subsquares, and each of these is retained with probabilityp _k. independent of all others. We show that if Π_k p _k =0 (i.e., if the area of the limiting set vanishes a.s.), then a.s. the limiting set contains no directed crossings of the unit square (a directed crossing is a path that crosses the unit square from left to right, and moves only up, down, and to the right).     

Behaviour of Bu(CH2—CHCH2)SnCl2 in water and water-cosolvent media: An approach to understanding the chemical degradation of organotins in aquatic environments

The behaviour of allylbutyltin dichloride in water, water–ethanol and water–hexane media, under either homogeneous or heterogeneous conditions, has been studied. 1,3-Diallyl-1,3-dibutyl-1,3-dichlorodistannoxane, butyltin di(hydroxy)chloride and butyltin trichloride arise from the solvolytic, acid–base and degradation processes. The degradation process involving the cleavage of the tin–carbon allyl bond has been interpreted to occur via an intramolecular reaction at the expense of the cation [Bu(CH₂=CHCH₂)Sn(OH)(H₂O)_n]⁺. The mechanistic pathway is ascribable to an internal interaction of the electrophilic cation with a bonded water molecule. This mechanistic proposal may be of some help with understanding of the chemical degradation of diorganotin derivatives in aquatic environments.     

在线原麦汁浓度检测仪

原麦汁浓度是啤酒生产过程中的一项重要指标。溶液的折射率是其浓度的函数 ,全反射的临界角与其浓度之间有一一对应关系。利用线阵CCD做为高精度探测器件 ,检测全反射临界角的变化 ,可测量溶液的浓度。临界角的变化与电源的波动及光源的强度变化等因素无关 ,并且溶液中的固体颗粒、小气泡等不影响检测精度。研制了一种在线检测原麦汁浓度的测试仪器 ,介绍了仪器的光学结构及数据处理方法。现场测量精度为± 0 1(以浓度表示)     

Selective grafting of amine groups on polyethylene by means of NH3−H2 RF glow discharges

Plasma treatments in Radio Frequency Glow Discharges fed with NH₃−H₂ mixtures have been performed for modifying polyethylene surfaces. Treatment kinetics and the role of species present in the glow have been investigated. Actinometric Optical Emission Spectroscopy has been utilized as a plasma diagnostic technique. Electron Spectroscopy for Chemical Analysis has been utilized for studying surface composition of treated substrates, which have been examined both astreated and after derivatization of amine-functionalities with 4-trifluoromethylbenzaldehyde vapors. It has been found that experimental plasma parameters and plasma density of active species can be controlled to achieve selective grafting of-NH₂ among all other nitrogen-containing groups.     

Numerical computation of viscous profiles for hyperbolic conservation laws

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterization of the heteroclinic manifold which can be understood as a generalized phase condition; in the case of shock profiles, this phase condition has a natural interpretation regarding their stability. We prove that our method converges and present numerical results for several systems of conservation laws. These examples include traveling waves for the Navier-Stokes equations for compressible viscous, heat-conductive fluids and for the magnetohydrodynamics equations for viscous, heat-conductive, electrically resistive fluids that correspond to shock wave solutions of the associated ideal models, i.e., the Euler, resp. Lundquist, equations.

     

A multi-reference exponential expansion for the electronic wave function

The expansion structure of a CI vector as combination of excitations from a model-space reference determinant is investigated. It is shown that between the linear and the exponential expansions there is a relation which is similar to the single-reference case, if the internal excitations are adsorbed into the reference vector. Moreover, expansions with respect to different determinants are related by a set of linear equations. By using these two properties, a State-Specific Coupled-Cluster formalism is proposed. Received 2 November 2000 / Received in final form 1st March 2002 Published online 28 June 2002