长春市地下水开发环境问题研究

本文根据近期地下水动态监测资料，结合地下水赋存的环境水文地质条件，分析论述了长春市由于不合理开发地下水资源而产生地下水水位下降，水量削减、水质污染、地面沉降等环境地质问题，提出了防治对策及建议。     

Karst Collapse Mechanism and Criterion for Its Stability

Karst collapse, caused by natural or artificial abstraction of groundwater, has been a focus of environmentalgeological problems for its ever-increasing hazardousness. The potential erosion theory and vacuum suction erosion theory, which reveal the origin of karst collapse macroscopically, are popularly accepted. However, a mathematic prediction criterion for karst collapse cannot be established only by these two theories. From a new perspective, this paper attempts to explain the microcosmic mechanism of karst collapse on the basis of these two theories. When the shear stress surpasses the shear strength of soil, a certain point or a certain plane in the unconsolidated soil covering karst caves will fail under the mechanical effects of water and air as well as its load-pressure, and with the increase of damaged points, a breaking plane appears and the soil on karst caves is completely damaged; as a result, the karst ground collapses. On the basis of the Mohr-Coulomb failure theory and previous studies,     

前馈神经网络隐性单调与泛化能力

应用前馈人工神经网络对广域单调的两组样本进行了模拟反演，引入单调前馈网络的概念对其权值和阈值定解问题和泛化能力进行了较诉研究。表明前馈人工神经网络是一个表达形式简单的复杂系统，其单调特征是隐性的，而且训练网络的成熟性对样本数量和样本内在规律性有一定依赖。强调了前馈人工神经网络的应用效果，指出单调与复合问题还需进一步深入研究。     

重力学反问题中零外部位密度的研究

对重力学反问题研究中零外部位密度的数学性质及物理意义进行了系统研究和分析．首先从基本定义及条件的描述入手，推演出其数学表示和限制，由此揭示重力学反问题的非适定性形态，进而论及其与非零外部位密度之间的数学关系．由此证明对应于给定外部位的场源函数可以分解成零外部位密度与调和密度的直和．通过对其物理意义的讨论，为地球物理反演非零外部位场源及物理大地测量学构制等效场源提供理论依据．     

反演二维弹性波动方程组多参数的渐近展开法

采用摄动法对二维弹性波动方程组的系数反问题进行渐近近似,给出了反演系数的具体计算方法。用摄动法解微分方程组的系数反问题还是首次。此外,还采用了地球物理分层模型,这种分层模型便于更精细地反映地球不同圈层的物理特征,更接近于实际情况。同时对进一步提高反演分辨率、增加反演参数、对病态方程组如何克服不适定性等问题,作了具体阐述,具有重要的理论意义与应用价值。     

Impulsive time-free transfers between halo orbits

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L ₁ libration point of the Sun-Earth/Moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristic velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.An earlier version was presented as Paper AIAA 92-4580 at the AIAA/AAS Astrodynamics Conference, Hilton Head Island, SC, U.S.A., August 10–12, 1992.     

Adiabatic invariants for the nonconservative Kepler's problem

This paper considers adiabatic invariants for the classical Kepler problem with resisting forces. The analysis is based on the theory of integrating factors and theory of adiabatic invariants in the Krylov-Bogoliubov-Mitropolski variables. The adiabatic invariants are series with respect to a small parameter. Also, for every particular case of nonconservative forces, it is shown that, with a complete set of adiabatic invariants, an approximate solution of the problem can be obtained. Four problems are analyzed in detail where approximate solutions are compared with numerical.