四维地籍的建立与分析

目的 分析了四维地籍的概念与需求,提出了时空宗地的概念,探讨了时空宗地的演化过程,给出了土地的恒等、类型、收缩与扩展4种权益变换和产生、消亡、边界调整、划入、划出与复合分并6种空间演化。基于4种空间拓扑关系与13种时间拓扑关系,建立了时空宗地的时空拓扑关系。在此基础上,结合地籍相关理论与技术发展,构建了四维地籍概念模型,并依据实现策略不同,提出了标签式、混合式与完全式3种解决方案。     

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.     

A compact model for the planar rhomboidal 4-body problem

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.     

Some consequences of applying lognormal theory to pseudolognormal distributions

A logarithmic transformation may be used to improve the efficiency of estimates of the mean when observations follow the lognormal distribution. But if this transformation is applied to observations that follow another distribution, bias may be introduced. We consider some consequences of erroneously applying lognormal estimation theory and demonstrate that biased estimates may be obtained for certain classes of distributions. Illustrations of bias obtained in gold sampling are given.