等面积纬度函数和等量纬度变换的直接解算公式

为实现等面积投影和等角投影间的直接变换,借助计算机代数系统Mathematica,推导出了等面积纬度函数和等量纬度变换的直接解算公式,并将式中系数统一表示为椭球第一偏心率的幂级数形式,可解决不同参考椭球下的变换问题。算例分析表明,本导出公式的计算误差分别小于10 m2和10-4(″),可供实际使用。     

关于有限群超可解性的一种新判定方法

利用子群的弱s-置换性质研究超可解子群的积的问题,并给出群的超可解性的一些判别方法。设群G可以表示为2个子群A和B的积,A在G中拟正规且B为超可解,如果A的Sylow子群的所有极大子群在G中弱s-置换,则G为超可解群。从而得到1个群为超可解群的这样的一种新判别法。     

基于MapReduce的地图代数并行计算方法

针对大规模栅格数据的空间分析,设计并实现了一种基于MapReduce架构的通用地图代数并行计算方法。该方法能将栅格像素矩阵按数据行分割为多个独立的子矩阵,并在并行节点上使用地图代数的四种算子对来自不同矩阵的像素进行分析计算。栅格数据叠加实验结果表明,该方法具备有效性和可靠性,能降低计算对硬件设备的要求,并提升了计算效率。     

Cartographic support for locational problem‐solving by groups

Collaborative spatial decision‐making environments in which group members individually and collectively pursue solutions to semi‐structured problems have a unique set of geographic visualization requirements. Group members often pursue diverse strategies as they attempt to solve such problems. As a consequence, numerous mapped representations of alternative solutions are generated. It is difficult to compare and synthesize these results, especially when decision‐makers have little or no previous cartographic training. In this paper, we derive several map types that synthesize representations of alternative solutions to location‐selection problems. These synthetic maps, designed to be accessible to group members, are created by decomposing solutions into a collection of atomic elements that are then placed into an accounting framework. Network map algebra operations are performed within this framework, and the results are accumulated and displayed as maps. Group members can use these maps to identify similar and dissimilar elements of alternative solutions to a problem. Such maps are intended to promote discussion and support group consensus‐building activities.     

多维统一GIS构建与实现的几何代数方法

针对时空GIS发展所面临的时空表达不统一,高维扩展困难等问题,基于以多维统一和坐标无关为特征的几何代数理论,建立多维统一GIS构建的层次体系与方法。利用几何代数对象构造中几何维度与Grassmann维度的一致性,实现整合维度结构与几何关系的多维地理对象自适应表达。利用几何代数算子的特征内蕴与结构明晰特性,构建多维统一计算模型以及可支撑复杂地理计算的多维统一分析框架,进而建立基于几何代数的多维统一GIS系统架构与实现方案。对上述关键技术加以实现并进行了相关应用案例分析。结果显示,基于几何代数构建的多维统一GIS有望突破现有时空GIS的不足,可为以多维统一表达与运算为特征GIS的发展提供新的数学工具与实现途径。     

Efficiently implementable algebra for distributed in-network spatial analysis

Existing sensor network query processors (SNQPs) have demonstrated that in-network processing is an effective and efficient means of interacting with wireless sensor networks (WSNs) for data collection tasks. Inspired by these findings, this article investigates the question as to whether spatial analysis over WSNs can be built upon established distributed query processing techniques, but, here, emphasis is on the spatial aspects of sensed data, which are not adequately addressed in the existing SNQPs. By spatial analysis, we mean the ability to detect topological relationships between spatially referenced entities (e.g. whether mist intersects a vineyard or is disjoint from it) and to derive representations grounded on such relationships (e.g. the geometrical extent of that part of a vineyard that is covered by mist). To support the efficient representation, querying and manipulation of spatial data, we use an algebraic approach. We revisit a previously proposed centralized spatial algebra comprising a set of spatial data types and a comprehensive collection of operations. We have redefined and re-conceptualized the algebra for distributed evaluation and shown that it can be efficiently implemented for in-network execution. This article provides rigorous, formal definitions of the spatial data types, points, lines and regions, together with spatial-valued and topological operations over them. The article shows how the algebra can be used to characterize complex and expressive topological relationships between spatial entities and spatial phenomena that, due to their dynamic, evolving nature, cannot be represented a priori.     

基于波前重建和李代数积分的地震波走时计算

地震波走时计算在数值模拟、层析反演和偏移成像中均有重要意义。将波前重建与李代数积分相结合,提出了一种新的适应横向变速介质的非对称走时算法,称之为wave-front construction-Lie algebra integral(WFC-LAI)算法。本算法利用一次波前重建计算成像射线走时进行坐标变换,将深度域单平方根算子透镜项转化为常数,在射线坐标系下计算李代数积分和指数映射,得到地震波走时的解析表达式。数值试验表明,该方法计算结果与线性横向变速介质中走时的理论值吻合。通过与波前重建结果对比,WFC-LAI算法对于求取横向变速介质中地震波走时是可行的,节省了存储空间,易于并行,有利于提高Kirchhoff积分叠前深度偏移的精度和效率。     

基于地图代数的山脊线和山谷线提取方法

将地图代数的思想和方法引入地形结构线的提取,先利用地图代数距离变换得到等高线各自的权属范围,再在等高线各自的影响区域内进行地形特征的提取,后采用区域互补的方法进行特征线段的连接,为特征线段合理连接提供了新思路。     

一阶Weyl代数上Stafford定理的Groebner基底实现

J.T.Stafford证明了 n阶 Weyl代数的每一左理想都是由 2个元素生成的。本文对一阶Weyl代数 A1 进行研究 ,在 J.Dixmier结果的基础上 ,利用 Groebner基知识 ,根据原有生成元 ,能算法性的构造出 A1 的每一左理想的 2个生成元 ,从而在一阶 Weyl代数上实现了 Stafford定理     

自然图形间的中间线和比例线方法

依据国际海洋法公约对海洋划界的＂中间＂线要求和定义,剖析了中间线（中轴）和比例线法的原理,相应剖析并讨论了中间线法缺点所在,指出严密实现地球椭球面上自然图形比例线方法是海上划界技术的新的趋势,介绍了地图代数在中间线法、比例线法上的基础性工作。