石窟的地学基础及其分类

石窟是一种佛教建筑，以往均从宗教、文化和艺术等方面加以研究，但开凿石窟离不开一定的地质地貌，尤其是岩石条件，因此，石窟与地学，特别是岩石有着密切的关系。着重岩石与石窟的关系探讨石窟的地学基础及其分类，从地学的角度探讨有关石窟的保护问题。     

广东河台云西金矿床石英的拉曼光谱特征及其对含金性的评价

本文对广东河台云西金矿的石英进行了拉曼光谱研究。结果表明,含金石英与不含金石英的拉曼光谱有着本质的差异。作者通过量子理论的研究,对其差异进行了剖析,发现这种差异与它们之间成分、组构、形成温度的差异紧密联系。因此,作者得出结论:石英的拉曼光谱可以用于评价其含金性。     

Asymptotic analysis of the interaction between linear long waves and a submerged floating breakwater of wavy surfaces

In this work, we carried out an asymptotic analysis, up to the second order in a regular expansion, of the interaction of linear long waves with an impermeable, fixed, submerged breakwater composed of wavy surfaces. Below the floating breakwater, there is also a step with a wavy surface. The undulating surfaces are described by sinusoidal profiles. The effects of three different geometric parameters — the amplitude of the wavy surfaces and the submerged length and width of the structure — on the reflection and transmission coefficients are analyzed. The hydrodynamic forces are also determined. The governing equations are expressed in dimensionless form. Using the domain perturbation method, the small wavy surfaces of the breakwater are linearized. The wavy surfaces of the breakwater generate larger values of the reflection coefficient than those obtained for breakwaters with flat surfaces, and the largest values of this coefficient are obtained when the length of the breakwater is of the same order of magnitude as the wavelength. The asymptotic solution is compared with the theoretical solutions that have been reported in the specialized literature and with a numerical solution. The present mathematical model can be used as a practical reference for the selection of the geometric configuration of a submerged floating breakwater under shallow flow conditions.     

GPS/BDS卫星摄动力数值分析

由精密星历利用拉格朗日插值公式求二次导数的方法计算了卫星在J2000.0惯性坐标系下的总加速度;利用现有的力模型计算了地球中心引力,地球非球形摄动力,太阳、月球和其他行星的摄动力,地球固体潮摄动力,相对论效应摄动力对GPS/BDS卫星所产生的加速度数值大小;利用G-file里的BERNE太阳光压模型参数计算了GPS卫星太阳光压摄动加速度大小;对GPS/BDS卫星所受的不同摄动力进行了数值分析,对同一摄动力对不同类型卫星的影响进行了数值分析比较。结果表明,现有力模型与GPS/BDS卫星所受的实际作用力仍有一定的差距,不同类型卫星所受摄动力有明显差异,在精密定轨的实际应用中应根据不同类型卫星建立合适的力学模型。     

GNSS卫星地影的一体化建模方法和星蚀参数计算

基于日地关系建立地影模型,利用数值法可以高精度计算单个卫星的地影参数,但是难以快速而全面地分析某一类卫星的地影参数变化和分布规律。本文从日、地和卫星三者的几何关系出发,提出了一种基于空间视场的卫星地影直接建模方法。首先,分别利用轨道半长轴和太阳的周年视运动确定卫星地影的大小和位置变化;其次,基于球面几何分析法推导了卫星地影参数的计算公式以及扁率摄动等对长期预报的影响改正公式。对北斗混合星座中3类卫星的地影参数分析试验表明,卫星地影模型和地影参数解析法能够快速获得中高轨近圆轨道类型的星蚀规律信息。     

Acoustic plane-wave reflection from a rough surface over a random fluid half-space

Plane-wave reflection from a rough surface overlying a fluid half-space, with a sound speed distribution subject to a small and random perturbation, is considered. A theory based upon a boundary perturbation method in conjunction with a formulation derived from Green's function for the coherent field in the random medium have been applied to a typical oceanic environment to study their effects on the plane-wave reflection. By considering the coherent field itself, the plane-wave reflection may be obtained straightforwardly through a procedure consistent with the formalisms currently employed in rough surface scattering. The results show that both the rough surface and medium inhomogenieties may reduce the plane-wave reflection, however, the characteristics of the curves representing their effects are different, enabling us to identify the dominant scattering mechanism. The results for the coherent reflection due to the individual scattering mechanism are compatible with those found in the existing literature.     

线性最小二乘问题解流形的逼近性

研究两个线性最小二乘问题解流形之间的逼近性。所得结果可看作普通最小二乘问题扰动理论的继续。推广了若干已有结论。     

关于矩阵方程A~TX+X~TA=B的极小范数解

作者讨论矩阵方程 ATX+ XTA=B。该方程在 Hamilton力学研究中有用。首先利用L yapunov方程证明了极小 Frobenius范数解的存在性和惟一性。然后用奇异值分解给出了求解最小范数解的一种方法。最后讨论极小范数解的向前扰动分析和最佳向后扰动分析