Ideal Resonance Problem: the Post-Post-Pendulum Approximation

Explicit construction of the solutions of the Hamiltonian system given by H = H ₀(J) – A(J) cos (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order . The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed.     

考虑回水顶托影响的水位预报研究

将有回水顶托影响的河段视为多输入-单输出系统,把水位过程视为时间序列,用时间序列分析最优控制理论,建立了可考虑回水顶托影响的水位过程预报模型。提出了在棱柱形河道情况下,以时段水位涨差作变量时,模型中各参数应满足的物理性约束条件;较好地解决了长江荆江河段中受回水顶托影响的石首站的水位过程预报问题,为水位过程预报提供了一条不同于水文学途径和水力学途径的建模途径。     

基于遗传算法的优化搜索技术

遗传算法是借鉴生物界自然选择和自然遗传机制的随机化搜索算法,其主要特点是搜索不依赖于梯度信息,能自动获取和积累有关搜索空间的知识,并自适应地控制搜索过程,从而得到最优解或准最优解的通用搜索算法。它尤其适合于组合优化、机器学习、自适应控制、规划设计和人工智能等领域。     

Galactic and Stellar Dynamics: Limits and Perspectives

An elementary review about stellar and galactic dynamics is presented. Despite involving extremely classical Newtonian physics, stellar dynamics presents some fundamental difficulties rarely discussed in the literature, such as why the phase space distribution is assumed to be a smooth function of coordinates. Many systems are found to be unstable over intermediate time-scales, as more instabilities have been discovered over the years, so the old aim of describing equilibrium stable systems shifts presently toward understanding evolutive systems. From the linearized variational Boltzmann equation a distinction can be made between instabilities triggered by the chaotic part of phase space, and instabilities caused by steep gradients in the velocity part of the distribution function. The new challenges to include evolutive systems can presently only be studied efficiently with computer techniques. Future studies are likely to involve orders of magnitude more advanced computers in which parallelism will play a major role. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem

In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five. This revised version was published online in August 2006 with corrections to the Cover Date.     

应用水资源管理模拟模型研究2000年乌鲁木齐河流域供水方案

乌鲁木齐河流域包括乌鲁木齐市区及其南、北郊区,是全国着名的缺水流域。据分析1990年已经超采地下水资源1.2×10⁸m³,到2000年,流域及城市缺水将十分严重。乌鲁木齐河流域属于内陆河流域,在水资源开发利用过程中,地表水与地下水多次转换,目前该流域水资源的重复利用率已达167%.建立有效的地表水和地下水联合利用模拟模型,可了解地下水资源的动态变化及分析地表水和地下水的相互转换对可利用水资源总量的影响。通过分析得出,节流措施大大地提高了地表水的可利用量,而减少的地下水的可利用量却不多。在开源措施方面,对规划工程进行了方案组合,分析了其实施的必要性。通过大量运算提出该流域2000年六种供水方案,为解决乌鲁木齐市城市发展缺水问题及供水措施规划提供决策参考。     

Studies on the application of combining models for vertical crustal movements

There are several kinds of analyzing models for vertical crustal movements, every one of them has different advantages and disadvantages, and adapts to different situations. This paper deals with the theory of the optimizing combining models for vertical crustal movements. The purpose for this optimization is to improve the fitting ability of models. This research was supported in part by the National Science Foundation of China.     

区域地下水资源优化管理模型研究

在分析晋、陕、蒙接壤地区水文地质条件的基础上，建立了区域地下水运动的数学模型；采用有限元法与非线性规划相结合，识别了模型的水文地质参数；根据能源基地内的工业布局及用水需求，建立了区域地下水最优分配模型；利用响应矩阵法求得了本区地下水最优方案。最后对最优化模型进行了灵敏度分析，证实了最优化方案的合理性     

广义共轭梯度算法

在地球物理反问题的求解过程中,共轭梯度(CG)法是一种经典的、很有价值的主要算法之一。本文在经典的共轭梯度标准基础上,将进一步发展,推导出了求解阻尼最小二乘(LS)解和最小绝对值偏差(LAD)意义下的迭代再加权最小平方(IRLS)解的标准算法形式,从而使得CG法的应用更具一般性。为了更好地理解GCG法的性能,文中还给出了两个例子,并将计算结果与公认的、好的求解病态问题的奇异值分解(SVD)算法的计算结果进行了比较,结果表明:GCG法亦具有很强的求解病态问题的能力,精度高,且运算速度快。此外,GCG法还具有两个显着的特点:①算法简单、编程灵活;②可以保持系数矩阵的稀疏特征。     

大量数据排序算法的优化设计

本文结合工作实际需要，对大量数据的排序问题设计了优化算法，并给出了排序优化算法程序。