Shifting operations were first considered by erd ( ? ) s , ko and rado , it is an important tool to study simplicial complexes ) s , ko和rado提出，它是研究单纯复形的一个很有力的工具
2.
Algorithms based upon the delaunay triangulation are discussed . we also briefly survey some of the previous research on simplicial mesh generation 我们考察了一些基于delaunay三角剖分的算法，同时也简短地回顾先前的一些简单形网格生成算法。
3.
We have derived sufficient conditions which ensure the existence of solutions of nonlinear complementarity problems , a simplicial homtopy algorithm for nonlinear complementarity problems is established 摘要在更弱的情况下，我们首先给出了非线性互补问题存在解的几个充分条件，然后给出一个求解的单纯同伦方法。
4.
Spatial data model is formalized according to partial order relationship , equivalence relationship and simplicial complex theory . a formalizing two - tuple ( m , f ) multi - resolution spatial data model is presented . based on the jarno peschie algorithms , an improved algorithm of road network map generalization is developed 应用偏序关系、等价关系和单纯复形理论，初步研究了多分辨率空间数据模型形式化表达方法，提出了一个二元组形式化多分辨率空间数据模型。
5.
Aimed at the current problem of pipeline layout optimization technique , the research of irrigation pipeline layout and pipe diameter optimization has been done , the gis ( geography information system ) and graph theory were first put forwarded to applyed to the design of low pressure pipeline irrigation project in the paper . with the support of gis , the minimal spanning tree theory of graph theory and 120 project theory can be applied to irrigation pipeline ' s layout optimization . at the aspect of pipe diameter optimization , simplicial method and interior - point method are been used in solve liner optimization model of pipe diameter to reach minimum project cost or a nnual working cost of low pressure pipeline irrigation 本文主要针对当前南方地区低压管道输水灌溉规划设计中存在的技术难点，开发研究先进实用的树状低压输水灌溉管网计算机辅助设计系统。首次提出了将gis (地理信息系统)和图论技术应用于低压管道输水灌溉规划设计及灌溉管网优化中，在gis支持环境下，应用图论中的最小生成树法和120规划进行管道的最优化布置。建立以管道输水灌溉系统的年折算费用最小为目标函数的管径优化线性规划模型，并将内点法应用于线性优化模型的求解。
6.
In section 3 , we show that when i is a squarefree stable ideal , shiftij ( i ) and i have the same graded betti numbers , projective dimension and regularity , then ic and i have the same graded betti numbers , projective dimension and regularity . at last we apply the results we obtained to simplicial complexes 在第三节中证明了当i为无平方稳定理想时， shiftij ( i )与i的分次betti数、投射维数和正则度相同，从而i ~ c与i的分次betti数、投射维数和正则度相同，最后将所得结论推广到单纯复形上。
