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     

Sound communication inNezara viridula (L.) (Heteroptera: Pentatomidae): Further evidence that signal transmission is substrate-borne

We investigated the sound communication associated with mating inNezara viridula (L.) to clarify conflicting reports on the medium through which acoustic signals are borne. Recordings made from virgin pairs ofN. viridula during precopulatory and compulatory behaviour have revealed that signals transmitted as vibrations through the substrate are a more likely means of communication than signals transmitted by a radiation of sound pressure waves through the air (at least in Australian populations). We present evidence (additional to that already in the literature) that air-borne acoustics are an unlikely mechanism of sexual communication in this species. Specifically, the recorded pulse train patterns showed no consistency or repeatability in relation to different stages of mating behaviour. In contrast, frequency spectrograms of substrate-borne signals reveal repeatable patterns that do correspond with the stage of mating behaviour.     

MeV Pb离子在非晶Si中的射程离散──离子束混合和增强扩散的影响

１．０ＭｅＶ２０８Ｐｂ离子在非晶Ｓｉ中的投影射程ＲＰ和射程偏差ΔＲＰ作为注量和温度二者的函数用背散射法进行测定．注量的变化范围为５×１０１３～７×１０１４ｃｍ－２．注入是在室温和ｔ＝－１２０℃下完成的．由由实验所确定的投影射程，射程偏差与注量或温度无关，并且分别等于２９５和７２．２ｎｍ．与ＴＲＩＭ８６的计算结果相比较，发现ＲＰ的偏离为１８％，而ΔＲＰ的偏离为３６％．ＲＰ和ΔＲＰ二者与注量及温度的无关性，排除了所观察到的与ＴＲＩＭ的矛盾是由于注入期间辐射增强扩散或离子束混合效应而引起的解释。     

氧化物半导瓷中晶界势垒的起源

提出了一个关于氧化物半导瓷晶界势垒起源的新观点，认为晶界势垒起源于烧结过程中外界氧在晶界中的扩散，与材料的结构、化学缺陷、掺杂、外界气氛、烧结工艺、组成状态等有密切关系，并用此理论解释了许多实验现象。     

交织扩展Golay码编译码器实现方案的研究

论述了交织编码的工作原理，给出了一种交织扩展Ｇｏｌａｙ码的改进型软件设计方案，用ＴＭＳ３２０Ｃ２５实现了其编译码器并给出了模拟实验结果。实验结果表明，它能准确地纠正不大于７２比特位的差错；处理１２８×１２８×８比特位的一幅图像数据的运行时间为０．４１２ｓ．     

激光开槽、埋槽电极硅太阳电池

报道一种新颖的激光开槽、埋槽电极硅太阳电池的结构、工艺流程及其研制结果。在ＡＭ１．５，２５℃，１００ｍＷ／ｃｍ２的条件下，以面积为４５ｃｍ３的３６片硅片研制的硅太阳电池的输出参数的平均值为ＪＳＣ＝３６．１ｍＡ／ｃｍ２，Ｖ∞＝６３３ｍＶ，Ｆ．Ｆ．＝０．７９８，η＝１８．２３％，最后分析了种高性能硅太阳电池的设计特点。     

Development and function of T cells in mice rendered interleukin-2 deficient by gene targeting.

Interleukin-2 (IL-2) is a lymphocytotropic hormone which is thought to have a key role in the immune response of mammalian cells. It is produced by a subpopulation of activated T-lymphocytes and acts in vitro as the principal auto- and paracrine T-cell growth factor (for reviews see refs 1-3). IL-2 is, however, not the sole T-cell growth factor, nor does it act exclusively on T cells, also promoting growth of NK cells and differentiation of B cells. A role for IL-2 in T-cell development has been postulated but remains controversial. Here we test the requirement for IL-2 in vivo using IL-2-deficient mice generated by targeted recombination. We find that mice homozygous for the IL-2 gene mutation are normal with regard to thymocyte and peripheral T-cell subset composition, but that a dysregulation of the immune system is manifested by reduced polyclonal in vitro T-cell responses and by dramatic changes in the isotype levels of serum immunoglobulins.     

Purealidin A,a new cytotoxic bromotyrosine-derived alkaloid from the Okinawan marine spongePsammaplysilla purea

Summary A new bromotyrosine-derived alkaloid with antileukemic activity, purealidin A (5), has been isolated from the Okinawan marine spongePsammaplysilla purea and its chemical structure elucidated on the basis of the spectroscopic data.     

Aeromonas caviae: ecologic adaptation in the intestinal tract of infants coupled to adherence and enterotoxin production as factors in enteropathogenicity

Aeromonas caviae isolated from stools of diarrheic formula-fed infants and environmental sources produce acetic acid when grown in glucose broth, which is bactericidal (suicide phenomenon). A. caviae grows anaerobically in a minimal medium or under permissive conditions such as the intestinal tract of formula-fed infants. These isolates adhered to HEp-2 cells and produced a cytotoxic and a cytotonic enterotoxin which underscore their enteropathogenicity.     

在UBBE框架下考虑不肯定的上界的估计方法

对目前的ＵＢＢＥ模型进行了适当的推广，使在解决估计问题时可以考虑那些可能是误差上界的数值，并在此基础上提出了一种方法，能够通过对估计精度和可靠性进行合理的权衡确定所需估计值，实际案例研究结果表明所提方法能够较好地解决估计精度和可靠性之间的矛盾。