适用于一般提法的埃尔米特插值多项式的差商构造公式

利用差商的非构造性定义建立了适用于一般提法的埃尔米特(Henmite)插值多项式的差商构造公式,并给出了插值余项估计。     

利福平菌丝体厌氧生化处理的研究

制药厂生产利福平过程中产生大量的利福平菌丝体,可严重污染环境。用厌氧消化法处理利福平菌丝体,消化温度40℃,反应器容积负荷2KgCOD/m~3·d,液料滞留期(SRT)14～20天,取得了良好的处理效果。COD去除率稳定在90％左右,BOD_5去除率达到95％以上,产气率达到0.49m~3/去除KgCOD。     

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method.     

现代信息技术及其对生产力的影响

“现代信息技术及其对生产力的影响”是太原市党政领导科技顾问清华大学吴建平教授于2004年3月29日在中共太原市委、太原市政府主办的“计算机网络技术的现状与发展趋势”科技讲座的演讲内容,上期已刊登第一部分,本期刊登第二、第三部分摘编。     

Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

论虚概念

把虚概念理解为“所指称的对象不存在于客观世界的概念”，是不对的，将导致把“理想模型”等本该是实概念的概念纳入其中，也把本该是虚概念的如“地心说”中的概念却排除在外。实际上，对象有虚实，属性也有虚实。实对象、实属性，属于实概念；虚对象、实属性，也属于实概念；实对象、虚属性，属于虚概念；虚对象、虚属性，是虚概念。可见，无论对象虚实，只要所指称的对象的主要特征所反映的属性不是客观的概念就是虚概念。     

苯乙烯和甲基丙烯酸丁酯无乳化剂的乳液共聚

本文研究了在18-冠(醚)-6存在下,苯乙烯和甲基丙烯酸丁酯无乳化剂乳液共聚。发现18-冠(醚)-6能起到相转移催化作用,加速共聚反应。对实验结果提出两相成核的解释。     

四硫代钼酸铵与四硫代钨酸铵合成方法改进的研究

对钼酸铵与硫化氢反应合成四硫代钼酸铵、钨酸与硫化氢反应合成四硫代钨酸铵的方法进行了改进。结果表明，采用改进后的方法，反应时间分别为７小时和１１小时。比文献值￣［１１］缩短了许多。产率分别为９１．１％和５２．１％，均高于文献值￣［１］。     

关于高维系统中Poincαre—Bendixson定理的反例

本文给出了在n(n≥4)维系统中,Poincare-Bendixson定理不成立的多项式系统的反例。