A general timing condition for consecutive collision orbits in the limiting case µ = 0 of the elliptic restricted problem

Consecutive collision orbits in the limiting case µ = 0 of the elliptic restricted three-body problem are investigated. in particular those in which the infinitesimal mass collides twice with the smaller (massless) primary. A timing condition is presented that allows the extension of previous results to the case of arbitrary relative orientation of the orbits of the infinitesimal mass and the smaller primary. The timing condition is expressed in two general forms - in terms of orbit parameters and eccentric (or hyperbolic) anomalies at the times of collision - for the specific cases of elliptic. parabolic or hyperbolic orbits of the infinitesimal mass. Some families of solutions are presented.     

MOND—theoretical aspects

I discuss open theoretical questions pertaining to the modified dynamics (MOND)—a proposed alternative to dark matter, which posits a breakdown of Newtonian dynamics in the limit of small accelerations. In particular, I point the reasons for thinking that MOND is an effective theory—perhaps, despite appearance, not even in conflict with GR. I then contrast the two interpretations of MOND as modified gravity and as modified inertia. I describe two mechanical models that are described by potential theories similar to (non-relativistic) MOND: a potential-flow model, and a membrane model. These might shed some light on a possible origin of MOND. The possible involvement of vacuum effects is also speculated on.     

Theoretical investigation of the cavity expansion problem based on a hypoplasticity model

The problem of the symmetric quasi‐static large‐strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so‐called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Laplace method to investigate subsurface geologic structures and its application

The ages of layered strata show a particular spatial distribution, and the bedding plane is isopotential surface of a scalar T(x, y, z) correlative to the age of a given stratigraphic horizon. The scalar T is obtained as the solution of boundary value problem of Laplace equation in power series, and the solution describes the three-dimensional geologic structures within an analytical space bounded by faults or unconformities on which the value of T jumps. The solution is termed the horizon function and consists of the datum succession and the structural part. The datum succession defines the relationship between the relative age (time-scale; T) and the thickness of strata (spatial scale; z) for undeformed horizontal strata. Geologic structures are described by the structural part of the solution composed by Fourier series, and the coefficients included there are determined by the least-square method using the dip and strike defined by particular combinations of the derivatives of T or the horizon data obtained in the area. The undersampled nature of geologic data is overcome by the selection of solution type, Eigenvalues, and boundary condition. Geological map and cross-sections are composed quantitatively and automatically by combining the spatial distribution of investigated T with the digital map defining the landform of the area. Test results were examined from this point of view. Improvement of the structural part to have the result fit completely the measured data is possible by introduction of the multiplying polynomials, although this concerns mathematical nature of the potential T.     

四川省农业生态环境问题与对策

四川地处长江中上游地区，是全国三大林区之一和生态保护与建设的重点区域。搞好四川农业生态环境建设，对全国的生态保护与建设和长江中下游地区的经济发展有着十分重要的作用。该文全面分析评价了四川省农业生态环境的主要问题和演变趋势，提出了四川省农业生态环境恢复与重建的对策措施。     

Stability of periodic solutions for Hill’s averaged problem with allowance for planetary oblateness

We analyze the stability of periodic solutions for Hill’s double-averaged problem by taking into account a central planet’s oblateness. They are generated by steady-state solutions that are stable in the linear approximation. By numerically calculating the monodromy matrix of variational equations, we plot its trace against the integral of the problem—an averaged perturbing function, for two model systems, [(Sun + Moon)-Earth-satellite] and (Sun-Uranus-satellite). We roughly estimate the ranges of values for the parameters of satellite orbits corresponding to periodic solutions of the evolutionary system that are stable in the linear approximation.     

On the Hill stability in the general problem of three finite bodies

We construct zero-kinetic-energy surfaces and determine the regions where motion is possible. We show that for bodies with finite sizes, there are bounded regions of space within which a three-body system never breaks up. The Hill stability criterion is established.     

卫星重力梯度边值问题的点质量调和分析

研究并建立由全球重力梯度复组合分量及全张量解算全球点质量模型的基本方程,进一步推导得到基于卫星重力梯度的单定边值问题和超定边值问题的点质量调和分析解.通过采用分块循环矩阵分解大型线性方程组的方法,实现点质量调和分析解的稳定解算.最后运用EGM2008模型进行模拟数值计算,验证卫星重力梯度边值问题的点质量调和分析法的有效...     

卫星遥感影像有理函数模型优化方法

针对高分辨率遥感影像有理函数模型（RFM）在实际应用中存在过度参数化和定位精度不高的问题,提出基于离差阵和消去变换及残余系统误差补偿的高分辨率遥感影像RFM优化方法。试验结果表明,经过参数筛选后的RFM参数均为无偏估计值,拟合精度可以达到全部参数用于拟合时的精度,而且模型病态性基本消除,模型稳定性更高;残余系统误差补偿方法可以有效消除RFM拟合严格成像模型的残余误差,达到与严格成像模型一致的对地定位精度。     

地图自动着色算法研究与实践

从四色问题的抽象模型入手,通过对现有的搜索算法——遗传算法、模拟退火算法这两种算法的原理和流程进行了较为细致的分析,总结出它们在地图四色填充实现过程中的优点与不足之处,并进行比较,找出这两种算法的结合点进行算法的改进优化,将模拟退火算法引入遗传算法,使它们结合起来解决地图四色填充问题,从而形成相对优化的算法,以期达到更加优化的效果。