Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

SH波对无限介质土中衬砌结构的动应力集中

运用复变函数法和保角映射法对无限介质土中的衬砌结构进行分析.通过引入两个势函数将弹性介质的控制方程解耦成两个Helmholtz方程.利用所得势函数的通解,得到无限土介质和衬砌结构的位移和应力的表达式,利用无限介质与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,可确定波函数展开式中的末知系数,并给出动应力集中系数的数值结果.     

等角投影理论和方法综述

等角投影比其它性质投影之研究更为深刻，应用也最为广泛。本文对等角投影的历史发展作了简单回顾，重点对等角投影的数学基础、等角投影的一般公式、等角投影变形量度［８］、具有极值特性的等角投影和探求等角投影的方法等进行了综述。最后提出需要继续研究的若干问题作为等角投影研究展望。     

The Relegation Algorithm

The relegation algorithm extends the method of normalization by Lie transformations. Given a Hamiltonian that is a power series = ₀+ ₁+ ... of a small parameter , normalization constructs a map which converts the principal part ₀into an integral of the transformed system — relegation does the same for an arbitrary function [G]. If the Lie derivative induced by [G] is semi-simple, a double recursion produces the generator of the relegating transformation. The relegation algorithm is illustrated with an elementary example borrowed from galactic dynamics; the exercise serves as a standard against which to test software implementations. Relegation is also applied to the more substantial example of a Keplerian system perturbed by radiation pressure emanating from a rotating source.This revised version was published online in October 2005 with corrections to the Cover Date.     

Possibilities of GPS Kinematic Measurements for Geological Survey in East Slovakia

This paper deals with transformation procedures for observed GPS data from the world geodetic system WGS-84 into the national geodetic grid datum S-UTCN(system of united trigonometric cadaster network) and Baa(the Baltic Sea after adjustment).Transformation from WGS-84 into SUTCN is performed most frequently by means of the 7-element Helmert transformation with three identical points.Geodetic network was adjusted by two ways.     

三维坐标转换的通用整体最小二乘算法

三维坐标转换模型属于非线性EIV（errors-in-variables）模型,现有整体最小二乘算法均设定了某些特殊假设条件,如仅适用于小角度或者属于非统计意义上的数值解,并且不能用于结构性的系数矩阵等,算法适用性受到极大限制。本文提出了三维坐标转换模型的通用加权整体最小二乘算法,该算法适用于任意旋转角度以及一般性的权矩阵情况下的三维坐标转换模型,并且将结构性系数矩阵、同时包含随机和非随机元素的系数矩阵等情况纳入到了统一的坐标转换模型算法。实例计算表明,本文提出的算法具有通用性,适用于实际应用中的各类三维坐标转换模型。     

Comparison between Deprit and Dragt-Finn perturbation methods

In this paper, the relationship between the Dragt-Finn transform and the classical Lie transform introduced by Deprit is discussed. The relative performance of the algorithms used for the computations of the transformed functions is compared, and the relation between their generators is given. These generators produce the same transform which insures the construction of the same invariants.     

Perturbed Gylden Systems and Time-Dependent Delaunay-Like Transformations

We study the possibilities and limitations of the application of generalized Delaunay-like transformations (in the 6-dimensional phase space) and TR-like mappings (in the 8-dimensional, extended phase space) to perturbed two-body problems with a time-varying Keplerian parameter μ(t), that is, to Gylden-type systems. For the sake of theoretical completeness, both negative- and positive-energy motion (with nonstationary coupling parameter) are, in principle, considered. Our developments are intended to introduce canonical variables parallelling the classical ones of Delaunay and the Delaunay-Similar variables of Scheifele. This revised version was published online in August 2006 with corrections to the Cover Date.     

Groundwater flow in anisotropic aquifers reduced to the isotropic case

By applying the technique of conformal transformation of the metric, widely used in general relativity and cosmology, the analysis of groundwater flow in an anisotropic aquifer (in which the hydraulic conductivity is a tensor) is reduced to the case of an isotropic one. This reduction is achieved for a particular conformal factor of the transformation. Examples of application of this technique are given. Copyright © 2004 John Wiley & Sons, Ltd.     

A Time-Transformed Leapfrog Scheme

We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in N-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct N-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included.