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     

泡沫的持液量研究

泡沫的持液量（ｈ，ｍｇ／ｃｍ３）是泡沫的基本特性之一．本文对形成泡沫的起泡剂浓度、增粘剂浓度、气体流量和温度等因素对Ｈ的影响及变化规律作了研究，并对Ｈ与泡沫表观粘度和泡沫半衰期的相互关系作了描述，对泡沫的实际应用具有一定的指导意义．     

昆明奶牛毛发中某些常量及微量元素含量初探

一些常量元素及微量元素对动植物体的健康成长有着明显影响。我们研究了高产奶牛与一般奶牛牛毛中某些常量及微量元素的含量,发现高产奶牛牛毛中许多常量及微量元素的平均含量均高于一般奶牛,而钴、砷、铜、硒、钾、铬及钼在高产奶牛和一般奶牛个体牛毛中的含量较少交错或者不交错。     

STABILITY CRITERIA FOR A CLASS OF UNCERTAINSYSTEMS WITH TIME—DELAY

Some stability criteria are obtained for a class of uncertain systems with time-delay usingLyapunov functional and analytic techniques. It is easy to check the criteria by making use of theboundedness of the uncertainties.     

Technical Notes ：STUDIES ON THE VALUE OF SECONDARY MARKET TO THE SUPPLY CHAIN

This paper investigates the impact of a secondary market, where retailers can buy and sell excessinventories, on the supply chain. We develop a two-period model with a single manufacturer and tworetailers. At the beginning of the first period the retailers order and receive products from themanufacturer, but at the beginning of the second period, they can trade surplus products betweenthemselves in the secondary market. We investigate the impact of the correlated dependence ofretailers' demand on both the quantity effect and the allocation effect under the secondary market.Lastly,we study potential strategies for the manufacturer to increase sales with the existence of thesecondary market.     

网的收敛与分离公理

用Ｍｏｏｒｅ－Ｓｍｉｔｈ收敛给出了一个拓扑空间分别是Ｔ０，Ｔ１，正则，正规空间的充要条件．     

FROM MANUFACTURING SCHEDULING TO SUPPLY CHAIN COORDINATION：THE CONTROL OF COMPLEXITY AND UNCERTAINTY

With time-based competition and rapid technology advancements, effective manufacturingscheduling and supply chain coordination are critical to quickly respond to changing marketconditions. These problems, however, are difficult in view of inherent complexity and variousuncertainties involved. Based on a series of results by the authors, decomposition and coordination byusing Lagrangian relaxation is identified in this paper as an effective way to control complexity anduncertainty.A manufacturing scheduling problem is first formulated within the job shop context withuncertain order arrivals, processing times, due dates, and part priorities as a separable optimizationproblem. A solution methodology that combines Lagrangian relaxation, stochastic dynamicprogramming, and heuristics is developed. Method improvements to effectively solve large problemsare also highlighted. To extend manufacturing scheduling within a factory to coordinate autonomicmembers across chains of suppliers, a decentralized supply chai     

可编程控制器调速器

本文以联合研制成功的水电站可编程控制调速器为对象，详细介绍其硬件与软件构成及工作原理。同时，对多种调节模式等方面也进行了一些探索。     

酵母原生质体形成中的电镜观察

用蜗牛酶处理对数期啤酒酵母和异常汉逊酵母细胞,可以有效地从中分离到原生质体透射电镜观察证明了细胞中周质体的存在,揭示了酵母原生质体的释放机理和蜗牛酶的作用位点。     

Au吸附在GaAs（110表面的研究

研究了Au吸附在GaAs(110)表面的吸附构型,并计算了表面态密度和表面能带结构.计算结果表明,可以认定Au与Ga的悬挂键杂化成键,从而引起2条附加的能带,一条位于禁带之中,距价带顶为0.9ev;另一条与价带共振,离价带顶为0.7ev,所得结果与实验结果相一致.