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     

中学校园环境景观设计探讨

以某中学校园环境景观设计为例，对景观设计中如何挖掘校园文化内涵，如何体现人与自然高度和谐统一，如何走可持续发展道路，如何通过艺术化、人性化空间的塑造．来创造富有时代气息的中学校园环境作了探讨。     

也论中西精神--与张秀成先生商榷

本文认为，中学和西学各有优劣，应互相吸取，但在总体上是西学优于中学。首先，在思维方式上，西学的分析思维，使西方社会分工较细，促进了社会化大生产的产生；也使西学学科门类众多；西学在方法上崇尚专精深，对任何问题都穷追不舍，非要证明或证伪，促进了科学的进步。中学的综合思维则使中国社会分工不细，学科门类不多，在研究方法上则不究细节。其次在义利关系上，西方私有神圣，最后却私也有了公也有了；中国公有神圣，改革开放前却公也没有私也没有。再次，在男女关系上，西学以个体为本，正是为了自身的尊严不受侵犯，才不得侵犯他人的尊严，这就有了平等精神。相反，古代中国的根本大法是三纲五常，夫为妻纲、男尊女卑，被论述为符合阳主阴辅的天道法则，追求男女平等，就是违反天道，就会被天诛地灭，中国没有男女平等。     

坚持用好作风选人加强干部队伍建设

从几方面阐述了在干部选拔中,应坚持用好的作风选作风好的人,切实推进干部制度建设.     

杜仲氨基酸成份的研究

本文借助氨基酸自动分析仪对杜仲离体培养愈伤组织、树叶、树皮中氨基酸含量进行了系统研究，共检测出１６种氨基酸，其总含量为４１．４９～２０８．２２ｍｇ／ｇ，其中包括７种必需氨基酸。     

高频等离子体化学气相淀积法制备TiO2超细粒子

利用ＴｉＣｌ４＋Ｏ２体系，在高频等离子体化学气相淀积反应器中合成了纯度高、粒度细的ＴｉＯ２粒子。考察了工艺条件对ＴｉＯ２粒子物性的影响；探讨了ＴｉＯ２粒子晶型控制的方法，金红石型质量分数可通过工艺条件控制；探讨了ＴｉＯ２粒子晶型控制的方法。金红石型质量分数可通过工艺条件控制，减少ＴｉＯ２单体浓度可提高金红石型质量分数；也可通过在原料ＴｉＣｌ４中添加ＡｌＣｌ３等晶型转化剂，使可转化为单一金红石型Ｔｉ     

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.     

关于灰色系统基本方法的研究和评论

关于灰色系统基本方法的研究和评论朱宝璋（浙江经济高等专科学校嘉兴３１４００１）ＳｔｕｄｙａｎｄＲｅｖｉｅｗｓｏｎｔｈｅＥｓｓｅｎｔｉａｌＭｅｔｈｏｄｓｏｆＧｒｅｙＳｙｓｔｅｍＺｈｕＢａｏｚｈａｎｇ（ＺｈｅｊｉａｎｇＥｃｏｎｏｍｉｃｓＣｏｌｌｅｇｅ，Ｊ...     

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.     

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