Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.     

Virial oscillations of celestial bodies: V. The structure of the potential and kinetic energies of a celestial body as a record of its creation history

The physical meaning of the terms of the potential and kinetic energy expressions, expanded by means of the density variation function for a nonuniform self-gravitating sphere, is discussed. The terms of the expansions represent the energy and the moment of inertia of the uniform sphere, the energy and the moment of inertia of the nonuniformities interacting with the uniform sphere, and the energy of the nonuniformities interacting with each other. It follows from the physical meaning of the above components of the energy structure, and also from the observational fact of the expansion of the Universe that the phase transition, notably, fusion of particles and nuclei and condensation of liquid and solid phases of the expanded matter accompanied by release of energy, must be the physical cause of initial thermal and gravitational instability of the matter. The released kinetic energy being constrained by the general motion of the expansion, develops regional and local turbulent (cyclonic) motion of the matter, which should be the second physical effect responsible for the creation of celestial bodies and their rotation.     

Diffuse radiation,twilight, and photochemistry — I

A photochemical scheme which includes a detailed treatment of multiple scattering up to solar zenith angles of 96° (developed for use in a GCM) has been used to study partitioning within chemical families. Attention is drawn to the different zenith angle dependence of diffuse radiation for the two spectral regions <310 nm and >310 nm. The effect that this has on the so-called 40 km ozone problem is discussed. The importance of correctly including multiple scattering for polar ozone studies is emphasised.     

Combined mine tremors source location and error evaluation in the Lubin Copper Mine (Poland)

A modified method of mine tremors location used in Lubin Copper Mine is presented in the paper. In mines where an intensive exploration is carried out a high accuracy source location technique is usually required. The effect of the flatness of the geophones array, complex geological structure of the rock mass and intense exploitation make the location results ambiguous in such mines. In the present paper an effective method of source location and location's error evaluations are presented, combining data from two different arrays of geophones. The first consists of uniaxial geophones spaced in the whole mine area. The second is installed in one of the mining panels and consists of triaxial geophones. The usage of the data obtained from triaxial geophones allows to increase the hypocenter vertical coordinate precision. The presented two-step location procedure combines standard location methods: P-waves directions and P-waves arrival times. Using computer simulations the efficiency of the created algorithm was tested. The designed algorithm is fully non-linear and was tested on the multilayered rock mass model of the Lubin Copper Mine, showing a computational better efficiency than the traditional P-wave arrival times location algorithm. In this paper we present the complete procedure that effectively solves the non-linear location problems, i.e. the mine tremor location and measurement of the error propagation.     

PSO-RBFNN模型及其在岩土工程非线性时间序列预测中的应用

岩土工程受力变形演化是一个典型的非线性问题,其演化的高度非线性和复杂性,很难用简单的力学、数学模型描述,但可用粒子群优化径向基神经网络对岩土工程应力、位移非线性时间序列进行动态实时预测。网络径向基层的单元数通过均值聚类法确定后,所有其它参数：中心位置、形状参数、网络权值,均通过粒子群优化算法在全局空间优化确定。工程实例应用表明,该模型预测结果准确、精度高,有良好的应用前景。     

Solution of an unstable axisymmetric Cauchy–Poisson problem of dispersive water waves for a spectrum with compact support

 It has been known that the axisymmetric Cauchy–Poisson problem for dispersive water waves is well posed in the sense of stability. Thereby time evolution solutions of wave propagation depend continuously on initial conditions. However, in this paper, it is demonstrated that the axisymmetric Cauchy–Poisson problem is ill posed in the sense of stability for a certain class of initial conditions, so that the propagating solutions do not depend continuously on the initial conditions. In order to overcome the difficulty of the discontinuity, Landweber–Fridman's regularization, famous and well known in applied mathematics, are introduced and investigated to learn whether it is applicable to the present axisymmetric wave propagation problem. From the numerical experiments, it is shown that stable and accurate solutions are realized by the regularization, so that it can be applicable to the determination of the ill-posed Cauchy–Poisson problem.     

关于具二次约束最小二乘问题的敏度分析

本文系统地研究具二次约束最小二乘问题的敏度分析。首先给出长期方程唯一正根的上界和下界；然后证明割线法用于计算拉格朗日乘子时全局收敛；最后给出解的扰动界。     

分潮波模型多资料数值计算方法研究 Ⅱ.有限差分最小二乘方法

对含多资料的分潮波模型的超定问题进行探讨，建立一种有限差分—最小二乘方法，该方法使得岸边资料直接进入了计算方程，并保证岸界法向流速为零条件。通过对渤海的四大分潮的试算，证实本方法可行。     

四阶奇异边值问题无穷多个正解存在性的一个注记

本文考虑四阶奇异边值问题x( 4 ) =λa(t) f (t,x(t) ) ,0 相似文献   

Fuzzy Optimum Model of Semi-Structural Decision for Lectotype Optimization of Offshore Platforms

In the process of concept design of offshore platforms, it is necessary to select the best from feasible alternatives through comparison and filter. The criterion set, used to evaluate and select the satisfying alternative, consists of many qualitative and quantitative factors. Therefore, the selection is a problem of multicriteria and semi- structural decision- making. Different from traditional methods in semi- structural decision- making, a new framework and methodology is presented in this paper for evaluation of offshore platform alternatives. First, the criterion set is established for the evaluation of alternatives. Next, the approach is studied to construct the relative membership degree matrix, in which both qualitative and quantitative factors are consistent with the uniform calculating standard. And then a new weight-assessing method is developed for calculation of the weights based on the relative membership degree matrix. Finally, a multi-hierarchy fuzzy optimum model is adopted to select t