A numerical investigation of the one-dimensional Newtonian three-body problem

The one-dimensional Newtonian three-body problem is known to have stable (quasi-)periodic orbits when the masses are equal. The existence and size of the stable region is discussed here in the case where the three masses are arbitrary. We consider only the stability of the periodic (generalized) Schubart's (1956) orbit. If this orbit is linearly stable it is almost always surrounded by a region of stable quasi-periodic orbits and the size and shape of this stable region depends on the masses. The three-dimensional linear stability of the periodic orbits is also determined. Final results show that the region of stability has a complicated shape and some of the stable regions in the mass-plane are quite narrow. The non-linear three-dimensional stability is studied independently by extensive numerical integrations and the results are found to be in agreement with the linear stability analysis. The boundaries of stable region in the mass-plane are given in terms of polynomial approximations. The results are compared with a similar work by Héenon (1977).We thank the referee for pointing out this reference to us.     

A search for collision orbits in the free-fall three-body problem I. Numerical procedure

A numerical procedure is devised to find binary collision orbits in the free-fall three-body problem. Applying this procedure, families of binary collision orbits are found and a sequence of triple collision orbits are positioned. A property of sets of binary collision orbits which is convenient to search triple collision orbits is found. Important numerical results are formulated and summarized in the final section.     

Planar motions of a charged particle in a magnetic-binary system with spherical or oblate primaries

In this paper we present for the first time simple symmetric motions in the planar magnetic-binary problem where both primaries are spherical bodies or oblate spheroids. From the study of this case it follows that there is a dense and complicated distribution of the families of such motions in the phase space. Our results also show that the orbital characteristics of the particle and the configuration of the phase space are appreciably affected by the oblateness of the primaries only if these parameters become sufficiently large.     

地下水资源管理模型在应用中的问题

本文总结出地下水资源管理模型实际应用中存在的三大问题：第一，管理模型建立自身存在问题；第二，模型研制者和决策管理者合作不够；第三，地下水资源管理比较混乱。对三大问题进行了详细的论述，并提出了解决问题采取的措施。     

A computerized geologic mapping system based on logical models of geologic structures

In this article we describe the basic framework of the computerized geologic mapping system cigma. The system, whic is based on a mathematical formulation of geologic concepts, consists of the following six subsystems: (1) input of geologic data set; (2) inference of stratigraphic sequence; (3) construction of logical models of geologic structures; (4) determination of three-dimensional geologic boundary surfaces; (5) construction of three-dimensional solid model of geologic structures; and (6) graphical presentation. Geologic structures are summarized in several tables called logical models of geologic structures. Each model is constructed automatically from input data on structural relations between geologic bodies. The model interprets the data automatically to create data files necessary to determine the shapes of geologic boundaries; it also provides a threedimensional solid model of geologic structures referring to the shapes of boundaries. As a prototype, we introduce two types of contacts corresponding to conformity and unconformity into the logical model and show that it is possible to draw a geologic map automatically. More complex geologic structures can be introduced into the geologic mapping system through further formulation of geologic structures.     

The main mean motion commensurabilities in the planar circular and elliptic problem

We study the motion of asteroids in the main mean motion commensurabilities in the frame of the planar restricted three-body problem. No assumption is made about the size of the eccentricity of the asteroid. At small to moderate eccentricity, we recover existing results (shape of the phase space and location of secondary resonances). We also provide global pictures of the dynamics in the region of secondary resonances. At high eccentricity, the phase space portraits of the integrable part of the Hamiltonian show new families of stable orbits for the 3:2 and 2:1 cases and the secular resonances ₅ and ₆ are located.     

Compatible potentials and orbits in synodic systems

For a given family of orbits f(x,y) = c ^* which can be traced by a material point of unit in an inertial frame it is known that all potentials V(x,y) giving rise to this family satisfy a homogeneous, linear in V(x,y), second order partial differential equation (Bozis,1984). The present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity . The new equation, which relates the synodic potential function (x,y), = –V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780!\[\tfrac{1}{2}\]²(x ² + y ²) to the given family f(x,y) = c ^*, is again of the second order in (x,y) but nonlinear.As an application, some simple compatible pairs of functions (x,y) and f(x, y) are found, for appropriate values of , by adequately determining coefficients both in and f.     

About stability of libration points in the restricted photogravitational three body problem

Nonlinear stability of the triangular libration point in the photogravitational restricted three body problem was investigated in the whole range of the parameters. Some results obtained earlier are corrected. The method for proper determination of cases when stability cannot be determined by four order terms of the hamiltonian was proposed.     

几种修正的自适应神经网络学习算法及其应用

针对一般ＢＰ网络的拓扑结构和参数选择的随意性问题,讨论了几种自适应ＢＰ网络,即自适应调整网络的拓扑结构和自适应调节学习步长的改进ＢＰ算法,综合二者构造了一种修正的自适应ＢＰ算法．为了验证改进算法的有效性,将这几种算法与标准ＢＰ算法进行了比较．结果表明：对于ＸＯＲ问题,这几种算法的学习速度和计算精度都有不同程度的提高．将算法用于油气预测的实际中,也取得了满意的结果