利用GPS高求取正常高的几种拟合方法

全面系统地研究了GPS点正常高的拟合方法,对平面拟合、二次多项式拟合、移动曲面拟合、多曲面拟合的GPS水准拟合方法,采用不同参数进行了论述。并结合实际测区,对GPS水准点进行了计算分析。提出了不同测区、不同地形、不同大地水准面的拟合方法,部分拟合方法已用于实际生产中,结果表明,这些方法是切实可行的。通过计算分析,得出结论：不同地形、不同面积的测区需要采用不同的拟合模型,并且拟合时采用的参数也不同。利用GPS高求定正常高,能够降低劳动强度和作业成本,提高作业效率。     

涉及微分多项式及例外函数的正规定则

设φ(z)≠0为区域D(c)C上的亚纯函数,a0(z),a1(z),…ak-1(z)为区域D上的全纯函数,k∈N.F为区域D上一族亚纯函数.对于任意的f(z)∈F,所有零点之级≥k 1,极点之级≥2.并且L(f)(z)=,k((z) ak-1(z)f(k-1)(z) …a1(z)f'(z) a0(z)f(z)≠φ(z),z∈D则F在D上正规.     

Integrated 3D density modelling and segmentation of the Dead Sea Transform

A 3D interpretation of the newly compiled Bouguer anomaly in the area of the “Dead Sea Rift” is presented. A high-resolution 3D model constrained with the seismic results reveals the crustal thickness and density distribution beneath the Arava/Araba Valley (AV), the region between the Dead Sea and the Gulf of Aqaba/Elat. The Bouguer anomalies along the axial portion of the AV, as deduced from the modelling results, are mainly caused by deep-seated sedimentary basins (D > 10 km). An inferred zone of intrusion coincides with the maximum gravity anomaly on the eastern flank of the AV. The intrusion is displaced at different sectors along the NNW–SSE direction. The zone of maximum crustal thinning (depth 30 km) is attained in the western sector at the Mediterranean. The southeastern plateau, on the other hand, shows by far the largest crustal thickness of the region (38–42 km). Linked to the left lateral movement of approx. 105 km at the boundary between the African and Arabian plate, and constrained with recent seismic data, a small asymmetric topography of the Moho beneath the Dead Sea Transform (DST) was modelled. The thickness and density of the crust suggest that the AV is underlain by continental crust. The deep basins, the relatively large intrusion and the asymmetric topography of the Moho lead to the conclusion that a small-scale asthenospheric upwelling could be responsible for the thinning of the crust and subsequent creation of the Dead Sea basin during the left lateral movement. A clear segmentation along the strike of the DST was obtained by curvature analysis: the northern part in the neighbourhood of the Dead Sea is characterised by high curvature of the residual gravity field. Flexural rigidity calculations result in very low values of effective elastic lithospheric thickness (t _e < 5 km). This points to decoupling of crust in the Dead Sea area. In the central, AV the curvature is less pronounced and t _e increases to approximately 10 km. Curvature is high again in the southernmost part near the Aqaba region. Solutions of Euler deconvolution were visualised together with modelled density bodies and fit very well into the density model structures. An erratum to this article can be found at     

自同构群的次单性分析及计算机实现

分析了几类特殊有限群的自同构群的次单性，得到了以下结论：（1）若n〉3且n≠6，Aut（An）均含有一个子群是次单群；（2）按照循环群Zn的阶的几种不同情况讨论了Aut（Zn）在哪些情况下包含一个子群是次单群，并给出了判定阶为P^i，2p^i（p为素数）的循环群的自同构群是否含有子群是次单群的计算机实现。     

一种基于三函数多项式的GPS轨道标准化方法

本文提出了一种基于三角函数多项式的GPS轨道标准化方法。该方法考虑了卫星运动的坐标的周期性特点，所以能获得很好的内插和外推精度。文中的算例分析得出了一些有益的结论。     

Rotating Stratified Heterogeneous Oblate Spheroid in Newtonian Physics

By solving the Euler hydrodynamical equations we have obtained closed form solutions for the angular velocities and pressures of a three stratified non-confocal heterogeneous oblate spheroid. Limiting and particular solutions cases, such as a spheroid with N layers, a stratified spheroid with the same eccentricities, as well as confocal layered spheroids are also explicitly written down. As an application, we have numerically estimated planet Earth's outer and inner cores' ellipticities to be _o=1/413.318 and _i=1/424.616, respectively. These Earth's ellipticities values are in good agreement with those found in the literature.     

青藏高原地磁场模型的研究

根据青藏高原地磁三分量绝对测量资料,使用泰勒多项式方法和冠谐分析方法,计 算了青藏高原地磁场（Ｘ, Ｙ,Ｚ ）的泰勒多项式模型和青藏高原地磁剩余场（△Ｘ,△Ｙ,△Ｚ）的冠谐 模型,并绘制了相应的理论地磁图．分析了磁异常点对地磁场模型的影响,对比分析了地磁 场的多项式模型和冠谐模型,讨论了地磁场模型的边界效应问题．     

软土路基沉降实时建模动态预测

在路基填筑施工过程中,用多项式与时间序列AR组合模型预测其沉降变形发展。根据沉降观测值,采用统计分析方法识别和建立多项式预测模型,预测在某时期沉降趋势值;用平稳时间序列分析方法建立随机部分模型,并预测沉降随机部分值,二者之和即为某时期沉降预测值。随着新观测数据的不断加入,及时修改预测模型参数值,达到实时预测之目的。工程实例研究表明：组合模型预测值明显优于单一趋势模型预测值。组合模型一步预测误差绝对值大多数情况下小于5 mm。预测步数越多,预测误差则越大。     

北斗三号卫星位置插值研究

针对北斗精密星历只能提供离散的三维坐标,而无法提供任意时刻卫星位置的问题,本文提出插值法计算任意时刻的卫星位置,即分别采用拉格朗日插值法、多项式拟合法、分段线性插值法及径向基函数拟合法对北斗三号卫星精密星历进行内插。试验结果表明,拉格朗日插值法和多项式拟合法能够较好地内插BDS-3的位置坐标。搭载CZ-3A运载火箭的卫星X方向位置和搭载CZ-3C运载火箭的卫星Z方向位置均采用拉格朗日插值法解算效果最优;其余位置方向采用多项式拟合法解算效果最优。     

Use of evolutionary computing for modelling some complex problems in geotechnical engineering

In this paper, the feasibility of using evolutionary computing for solving some complex problems in geotechnical engineering is investigated. The paper presents a relatively new technique, i.e. evolutionary polynomial regression (EPR), for modelling three practical applications in geotechnical engineering including the settlement of shallow foundations on cohesionless soils, pullout capacity of small ground anchors and ultimate bearing capacity of pile foundations. The prediction results from the proposed EPR models are compared with those obtained from artificial neural network (ANN) models previously developed by the author, as well as some of the most commonly available methods. The results indicate that the proposed EPR models agree well with (or better than) the ANN models and significantly outperform the other existing methods. The advantage of EPR technique over ANNs is that EPR generates transparent and well-structured models in the form of simple and easy-to-use hand calculation formulae that can be readily used by practising engineers.