Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

氢化物发生-原子荧光光谱法直接测定地球化学样品中痕量碲

采用硝酸-氢氟酸-高氯酸溶解样品,以Fe3+作减缓剂,不需分离富集,用氢化物发生-原子荧光光谱法直接测定地球化学样品中痕量碲。对测定介质、KBH4浓度、铁盐的作用等条件进行试验。方法检出限为0.0031μg/g,精密度(RSD,n=11)<6.10%。方法用于国家一级地球化学标准物质中痕量碲的测定,结果与标准值一致。     

碱消解-高效液相色谱-电感耦合等离子体质谱法测定生物样品中的甲基汞和乙基汞

建立了碱消解-高效液相色谱-电感耦合等离子体质谱联用系统测定生物样品中甲基汞(MeHg)与乙基汞(EtHg)的分析方法。为提高灵敏度,选用微流量的PFA雾化器,在优化的检测条件下,MeHg及EtHg检出限可达到0.036μg/L和0.03μg/L;线性范围达到4个数量级,两条工作曲线线性相关系数为1。对1.78μg/L MeHg、1.65μg/L EtHg的混合标准溶液重复测定7次,色谱峰面积的相对标准偏差(RSD)分别为1.79%和1.44%。对标准物质BCR 464(金枪鱼)的分析结果表明,测定值与标准值基本吻合,但略低于标准值;甲基汞和乙基汞的加标回收率分别为85.9%和84.5%。高效液相色谱与质谱联用技术的高灵敏度和低检出限能够满足生物样品中汞形态定量分析的要求。     

Geochronology of Pliocene volcanism in the Dzhavakheti Highland (the Lesser Caucasus). Part 1: Western part of the Dzhavakheti Highland

Isotopic-geochronological study of the Pliocene magmatic activity in western part of the Dzhavakheti Highland (northwestern region of the Lesser Caucasus) is carried out. The results obtained imply that the Pliocene magmatic activity lasted in this part of the highland approximately 2 million years from 3.75 to 1.75–1.55 Ma. As is established, the studied volcanic rocks correspond in composition mostly to K-Na subalkaline and more abundant normal basalts. Time constraints of main phases in development of basic volcanism within the study region are figured out. We assume that individual pulses of silicic to moderately silicic volcanism presumably took place in the Dzhavakheti Highland about 3.2 and 2.5 Ma ago.     

基于Poulos弹性理论的被动桩改进算法

传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。     

Modelling of periodic wave transformation in the inner surf zone

In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement.     

水溶液中聚合物在粘土上的吸附

水溶液中聚合物在粘土上的吸附对于聚合物污染防治和污水处理等都有重要意义。Scheutjens-Fleer理论是应用范围最广的聚合物吸附理论,适应于从单体到长链高聚物,从链无相互作用的稀溶液到纯聚合物的吸附研究。本文简要介绍了有关聚合物吸附的重要参数,包括吸附量、耦合分数或直接表面覆盖、平均层厚度和链段密度,以及相应的测定方法。文中分析了影响聚合物吸附研究发展的主要问题,指出水溶液中聚合物在粘土上的吸附研究的发展方向是综合研究吸附等温线和A/V效应、耦合分数、吸附层厚度、吸附分级现象和对粘土层间的影响,并与Scheutjens-Fleer理论计算结果进行比较。     

某船坞南翼墙基岩水下控制爆破技术

本文介绍的基岩水下爆破属临近重要建筑物的水下控制爆破。当岩石裂隙发育，且岩面有较厚的石碴覆盖层，其技术难度大，采取的诸如搭钢平台钻孔。塑料套管护孔，以及孔间、排间塑料导爆管雷管接力式微差起爆网路等措施，都是成功之经验，值得今后类似工程推广应用。     

A community-wide intercomparison exercise for the determination of dissolved iron in seawater

The first large-scale international intercomparison of analytical methods for the determination of dissolved iron in seawater was carried out between October 2000 and December 2002. The exercise was conducted as a rigorously “blind” comparison of 7 analytical techniques by 24 international laboratories. The comparison was based on a large volume (700 L), filtered surface seawater sample collected from the South Atlantic Ocean (the “IRONAGES” sample), which was acidified, mixed and bottled at sea. Two 1-L sample bottles were sent to each participant. Integrity and blindness were achieved by having the experiment designed and carried out by a small team, and overseen by an independent data manager. Storage, homogeneity and time-series stability experiments conducted over 2.5 years showed that inter-bottle variability of the IRONAGES sample was good (< 7%), although there was a decrease in iron concentration in the bottles over time (0.8–0.5 nM) before a stable value was observed. This raises questions over the suitability of sample acidification and storage.