关于部分变元的非常稳定性

本文利用极限方程的方法研究微分方程关于部分变元的多种非常稳定性,讨论了给定方程与其积限方程的非常稳定性的关系。     

同时顾及章动和极移的地球自转方程

通过引进章动坐标系相对惯性参照系的转动角速度随时间的变化 ,导出了一个可同时解出章动和极移的地球自转方程 ,用这个方程可同时研究地球的强迫和自由转动。与现行研究地球自转的惯用方法相比 ,该方法综合性强 ,易于理解。     

同时顾及章动和极移的地球自转方程

通过引进章动坐标系相对惯性参照系的转动角速度随时间的变化,导出了一个可同时解出章动和极移的地球自转方程,用这个方程可同时研究地球的强迫和自由转动,与现行研究地球自转的惯用方法相比,该方法综合性强,易于理解。     

Poisson重力边值问题

提出了Poisson重力边值问题,即关于扰动位的Poisson方程的Stokes问题和Neumann问题。作为导引,先研究Poisson方程的Dirichlet问题．再分别引入一种辅助函数,将Stokes问题和Neumann问题改化为Dirichlet问题,从而立即得到它们的积分解。最终解式表现为两部分叠加：一部分仅与边界观测相关,另一部分为对地形测量的响应,为研究地形测量对外部重力场和大地水准面的精化提供新的途径。     

正定矩阵的三角分解与线性对称方程组的解算

讨论用正定矩阵三角分解法解线性对称方程组的问题,将具有正定系数阵的线性方程组中的正定矩阵分解为两个互为转置的上、下三角阵之积,用比较法导出下三角阵诸元素与原矩阵诸元素之间的关系式,再将分解式代入原方程,从而导出用三角分解法解线性对称方程组的计算公式,此法计算规律性强,既适用于手算又适用于电算,可在测量平差等科学计算中广泛应用。     

用抛物方程计算曲边面积的几种方法

曲边面积的计算，比较流行的方法是辛普生法。但它必须已知抛物方程才能计算。在广泛使用电算器的今天，至少还有二种方法可以使用。能取得抛物方程可计算更准确，无抛物方程，只要有图形也可计算。用二次曲线来拟合实际存在的（图上显示的）曲线，一般多采用抛物方程。     

罗德里格矩阵在空间后方交会直接解法中的应用

经典的空间后方交会直接解法是先解算出空间距离,求出各摄影光束的方向角,解算一个6阶方程,然后解算出外方位元素.6阶方程中有18个三角函数,计算工作量较大,对此法进行改进,避免了三角函数计算,方程由6阶降为3阶,计算方便快速.     

正定矩阵的三角分解与线性对称方程组的解算

讨论用正定矩阵三角分解法解线性对称方程组的问题,将具有正定系数阵的线性方程组中的正定矩阵分解为两个互为转置的上、下三角阵之积,用比较法导出三角阵诸元素与原矩阵诸元素之间的关系式,再将分解式代入原方程,从而导出用三角分解法解线性对称方程组的计算公式,此法计算规律中,既适用于手算又适用于电算,可在测量平差等科学计算中广泛应用。     

多极子的平面近似解法

本文从多极子理论出发，建立了Bjerhammar球面多极子模型，使其避开了多极子强奇异性，且保持了多极子衰减快的优点。利用代数理论中Kronecker积的概念，建立了一个B氏球面多极子的平面近似解法，此法可确定较大区域的多极子密度函数。     

不等分经纬线多圆锥投影的设计与解析计算方法

用多圆锥投影作为世界图的数学基础,可以获得较良好的面积和角度变形。但以往的多圆锥投影,多为等分纬线的,在改善变形方面又有其局限性。若采用不等分经纬线的多圆锥投影,则可克服这一局限性。文章中,作者提出了建立不等分经纬线多圆锥投影的方法和计算变形的解析式子。本法的主要特点是：经线方程用的参数方程表示：x_(ij)=a_(0i)_j+a_(1i)_j~3+a_(2i)_j~5,y_(ij)=b_(0i)+b_(1i)_j~2+b_(2i)_j~4+b_(3i)_j~6。赤道方程用λ的奇次冪方程表示：x_(i0)=0,y_(i0)=c_0λ_i+c_1λ_i~3+c_2λ_i~5+c_3λ_i~7。非零度的纬线方程则用多圆锥投影一般公式表示x_(ij)=q_i-ρ_jcosδ_(ij),y_(ij)=ρ_jsinδ_(ij),式中δ_(ij)则由相应的赤道坐标（已由赤道方程求到）乘上一个与纬度有关的常数求得。关于经线的圆滑性问题,文章作了专门的讨论。为了简化经线方程和赤道方程的解算工作,作者提出了“过渡引数”法作为补充。“过渡引数”法即是：解经线或赤道方程时,不直接用或λ的弧度数为引数,而用一个简单的数ψ或θ为过渡。而ψ与,λ与θ之间则以一个常数α和β相联系。文章中应用本法,设计了一个适用于世界政治交通图的投影。在该投影中,1.0的面积等变形线正好通过我国中部,因而使     

Calculation of strongly singular and hypersingular surface integrals

Efficient numerical computation of integrals defined on closed surfaces in ℝ³ with non-integrable point singularities that arise in physical geodesy is discussed. The method is based on the use of polar coordinates and the definition of integrals with non-integrable point singularities as Hadamard finite part integrals. First the behavior of singular integrals under smooth parameter transformations is studied, and then it is shown how they can be reduced to absolutely integrable functions over domains in ℝ². The correction terms that usually arise if the substitution rule is formally applied, in contrast to absolutely integrable functions, are calculated. It is shown how to compute the regularized integrals efficiently, and, numerical efforts for various orders of singularity are compared. Finally, efficient numerical integration methods are discussed for integrals of functions that are defined as singular integrals, a task that typically arises in Galerkin boundary element methods. Received: 15 April 1997 / Accepted: 7 May 1998     

Le theoreme de conservation de la courbure et de la torsion

Based on exterior calculus, the G. Frobenius integration theorem, holonomic and anholonomic Riemannian geometry, the typical geodetic problems are summarized in a unified manner. The E. Cartan pseudotorsion of natural orthogonal coordinates causes the misclosure of a closed three dimensional traverse. Natural coordinate differences are path dependent, anholonomic, nonintegrable, nonunique, therefore. The geodetic pseudotorsion form depends only on the components of the A. Marussi tensor of gravity gradients. A physically defined coordinate system can be found which is pseudotorsion free, whose coordinates are holonomic, integrable, unique. The G. Frobenius transformation matrix is of rank three, explaining the number of three dimensions of an intrinsic surface geometry. The matrix elements depend on either the second derivatives of the real gravity potential and the Euclidean norm of its gravity vector or the second derivatives of the standard gravity potential, the Euclidean norm of its standard gravity vector and the vertical deflections. Incomplete information of the earth's gravity field leads to the concept of boundary value problems and satellite geodesy.      

Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere

The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ (or ℝ²) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions. Received: 10 June 1998 / Accepted: 20 May 1999     

大坝变形分析与预报的有限元法

在阐述有限元法基本理论的基础上,研究了采用ANSYS有限元分析软件进行大坝有限元建模、网格划分、荷载及边界条件施加等大坝变形分析的方法,在用有限元法获得水位位移分量及温度位移分量后建立大坝位移确定性模型,从而对大坝的变形监测提供可靠的依据。     

Log-cumulants of the finite mixture model and their application to statistical analysis of fully polarimetric UAVSAR data

Since its first flight in 2007, the UAVSAR instrument of NASA has acquired a large number of fully Polarimetric SAR (PolSAR) data in very high spatial resolution. It is possible to observe small spatial features in this type of data, offering the opportunity to explore structures in the images. In general, the structured scenes would present multimodal or spiky histograms. The finite mixture model has great advantages in modeling data with irregular histograms. In this paper, a type of important statistics called log-cumulants, which could be used to design parameter estimator or goodness-of-fit tests, are derived for the finite mixture model. They are compared with log-cumulants of the texture models. The results are adopted to UAVSAR data analysis to determine which model is better for different land types.     

<Emphasis Type="Italic">Integrated Remote Sensing and</Emphasis> Structural Analysis Studies of Tayyib Al-Ism Area,Northwestern Arabian Shield,Saudi Arabia

Geological and structural mappings of Tayyib Al-Ism area were carried out using the rocks finite strain data, the Landsat-7 Enhanced Thematic Mapper Plus (ETM+) data and the field based observations. To analyze the finite strain in the studied rocks, the R_f /? and Fry methods are applied to feldspar porphyroclasts and mafic grains from nine metavolcano-sedimentary samples (Hegaf Formation), four diorite-gabbros suite samples (Sawawin Complex), two meta-granite samples (Ifal suite) and five Zuhd alkali granite samples. The obtained data indicate traces of high to moderate level of deformation in the meta-granite and metavolcano-sedimentary rocks. The axial ratios along the XZ section range from 1.70 to 4.80 for the R_f/? method and from 1.50 to 4.50 for the Fry method. A sub-vertical trend of short axes in association with sub-horizontal foliation is also observed. These informations allow us to conclude that a finite strain in the deformed granitic rocks is of the same order of magnitude as in the metavolcano-sedimentary rocks. The contacts between the metavolcano-sedimentary and granitic rocks in Tayyib al Ism area were formed during the granitic intrusions along some of the faults under brittle to semi-ductile deformation conditions. These faults have significantly influenced the geometry and style of rifting in the Red Sea during the Neogene. The finite strain was accumulated in the area during the process of deformation, which superimpose the already existed nappe structure. It indicates that the nappe contacts formed during the accumulation of finite strain. In addition to finite strain analysis, band ratio images (3/1, 5/3, 7/5) and Principal Component Analysis (PCA) technique have been used, which proved effective in mapping geological and structural features of various rock bodies exposed in the study area.     

GPS水准面拟合方法研究

研究用较多已测点的原始数据,分别采用GPS水准的六参数法、多面函数法、移动曲面拟合法、有限元法逼近GPS网中较少检核点的高程异常值;再用较少已测点的原始数据,逼近GPS水准网中较多检核点的高程异常值.通过对实测数据的计算分析可发现,具有分区拟合性质的移动曲面拟合法与有限元法较优,使用较少的拟合点时,实测三等水准联合GPS高程观测可取代四等水准测量.     

基于约束条件的地图目标移位

地图目标移位是地图综合和空间信息可视化研究中的一个重要问题,其难点是如何在移位过程中满足一定的约束条件以保持目标之间的空间关系。本文以城市道路扩张为例,借助带约束性Delaunay三角网,结合有限元和空间推理方法,重点探讨顾及空间关系的基于约束条件的地图目标移位问题,并给出满足一定约束条件下的节点移位算法和计算实例。     

Finite covariance functions

Because of the full covariance matrices and the computer storage limitations the number of measurements which can be handled by the collocation method simultaneously, is limited. This paper presents a method to compute covariance functions with a finite support yielding sparse covariance matrices. The theoretical background is pointed out and, for the one- and two-dimensional case, special functions are developed which can be combined with the usually used covariance functions to get a “finite covariance function”. Simulated examples to demonstrate the behaviour of different solution methods to solve these special, sparse covariance matrices supplement our investigations.     

地表位移场的有限变形分析

为了精确分析地表位移场的变形状态，把地表变形视作有限变形，把有奶变形非线性力学理论应用到地表变形分析中。模拟计算结果表明，该理论能更精确地描述地表变形。