EJECTION–COLLISION ORBITS AND INVARIANT PUNCTURED TORI IN A RESTRICTED FOUR‐BODY PROBLEM

We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1–2μ and μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses form at any time a collinear central configuration. The body of mass 1–2μ is located at the center of mass. The paper has two main goals. First, to prove the existence of four transversal ejection–collision orbits, and second to show the existence of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and for an arbitrary value of the mass parameter 0<μ≤1/2. This revised version was published online in July 2006 with corrections to the Cover Date.     

An integrated wavelet concept of physical geodesy

For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking and gradiometry. Received: 28 February 1997 / Accepted: 17 November 1997     

A VARIATIONAL METHOD FOR COMPUTING POTENTIAL COEFFICIENTS USING DIFFERENT TYPES OF GRAVIMETRIC DATA

In this paper,a variational method is presented for solving theclassical gravimetric,satellite gravimetric and satellite altimetric mixed typeboudary value problem to obtain the potential coefficients.According to thisprinciple,classical gravimetric data（height measured by geometric levelling orheight triangulation）,satellite gravimetric data（height measured by satellitegeodesy technique）and satellite altimetric data can be used jointly to calculate thepotential coefficients.     

扩散波的时空反演与洪水实时预报技术

以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Ｑ（ｘ,ｔ）的同时反演计算扩散波波速Ｃ（ｘ,ｔ）和扩散系数Ｄ（ｘ,ｔ）,根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。     

Seismic frame design via inverse mode design of frame-ground systems

A two-step stiffness design procedure is developed for a moment-resisting planar frame supported by a prescribed two-dimensional finite-element ground-pile system. In the first step, a hybrid inverse eigenmode problem is formulated and its solution is derived in an analytical form. A difficulty resulting from the existence of multiple interface nodes is overcome by incorporating a deformation constraint into a set of linear equations for finding the lowest-mode displacements at the interface nodes and in the ground. In the second step, the fundamental natural frequency of the combined system and the lowest mode-strain ratios in the frame specified in the first step are regarded as the parameters for adjusting the mean peak seismic member-end strains to their specified values. If the fundamental natural frequency of the frame with a fixed-base happens to be close to that of the ground, a difficulty arises in the two-step stiffness design procedure because of an irregular response amplification and of the non-predominance of the lowest-mode components. A new practical design procedure of rapid convergence is proposed such that an initial design is found for a stiff ground and that a sequence of stiffness designs is generated with respect to a ground stiffness parameter without any differential coefficient of series expansion. The accuracy of the model utilized in this paper and the validity of the present stiffness design procedure are verified through time-history response analysis.     

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.     

二华平原区环境地质问题与地下水资源开发

本文从二华平原区地下水动态特征以及与地下水开采有关的环境地质问题入手,研究人类工程活动与地质环境之间的相互作用和相互制约关系,预测地下水资源开发过程中可能出现的环境地质问题,提出合理开发利用地下水资源的意见。     

福建数字地震台网试运行期间编目工作的若干问题

本文对福建数字地震台网试运行期间在测定地震参数、编辑地震目录和台网观测报告等方面存在的问题及其解决过程作简短回顾。     

Irregular Satellites of Jupiter: a study of the capture direction

The irregular satellites of Jupiter are believed to be captured asteroids or planetesimals. In the present work is studied the direction of capture of these objects as a function of their orbital inclination. We performed numerical simulations of the restricted three-body problem, Sun-Jupiter-particle, taking into account the growth of Jupiter. The integration was made backward in time. Initially, the particles have orbits as satellites of Jupiter, which has its present mass. Then, the system evolved with Jupiter losing mass and the satellites escaping from the planet. The reverse of the escape direction corresponds to the capture direction. The results show that the Lagrangian points L1 and L2 mainly guide the direction of capture. Prograde satellites are captured through these two gates with very narrow amplitude angles. In the case of retrograde satellites, these two gates are wider. The capture region increases as the orbital inclination increases. In the case of planar retrograde satellites the directions of capture cover the whole 360° around Jupiter. We also verified that prograde satellites are captured earlier in actual time than retrograde ones. This paper was presented at the Asteriods, Comets and Meteors meeting held at Búzios, Rio de Janeiro, Brazil in August 2005 and could not be included in the special issue related to that conference.