| 1. | Theorem in the models of the hexagonal lattice , ep is the expect with p
的开路即qx ）中点的个数得于无穷的开路。厂。 |
| 2. | The effect of coordination number on phase transition point from the study of renormalization group calculation for hexagonal lattice
从六角格子的实空间重整化群计算看配位数对相变点的影响 |
| 3. | In previous papers the triangular and the hexagonal lattices are often the study objects , but benzenoid lattice is the study object in this paper
在前人的文章中平移对称晶格都是选三角或六角格子作为研究对象，本文采用苯型烃晶格作为研究对象。 |
| 4. | The results of benzenoid lattice by site - block based on ising model are closer to the exact values of ising model than the triangular an d hexagonal lattices
本文在计算过程中仍采用重整化群的自旋?元块法，并采用ising模型，计算出的结果比三角和六角格子更接近ising模型的严格解。 |
| 5. | If ( p ) > 0 , then theorem in the models of the hexagonal lattice , let lr ( n ) be is an open path in rectangle [ 0 , n + l ] x [ 0 , n ] joining some vertex on its left side to some vertex on its right side
定理在正六边形渗流模型中，设r … ）表示在矩形pn刊1xp刀中存在一条连接它的左边界和它的右边界的开路。假设尸a叫二二，则18pp队r … ）广lo对充分大的n成立。 |
| 6. | If this paper also studies the band percolation of the models of the triangle lattice and the hexagonal lattice when p = pc and p > pc . such as the estimation of power of , x and xf and their upper and lower bound
本文还研究了正三角形和正六边形渗流在临界点处（ p pc ）和上临界状态（尸尸的渗流。特别考虑关于0 ， x和幂指数的估计，并且给出了估计的上下界。 |
| 7. | This paper studies the band percolation of the models of the triangle lattice and the hexagonal lattice . before we study the models of the triangle lattice and the hexagonal lattice , we will introduce period . let g = ( vc , ec ) be a connected graph , we write vg for the set of vertices of g and egfor the set of its edges , u e vc is a vertex , and v is the coordinate vector
在介绍平面正三角形和正六边形点格的边渗流模型之前我们先引入周期的概念：设g = ( v _ g , e _ g )为连通图其中v _ g , e _ g分别为图g的顶点集和边集， u v _ g为的顶点， v为平面的坐标向量。 |
| 8. | Its vertices are located at all points of the form ( i1 , i2 ) or each vertex has six neighbors . the six neighbors of the vertex v are the set of vertices the set of edges e the model of the hexagonal lattice the usual way to imbed the hexagonal lattice is such that its face are regular hexagons . the vertices are the points . the origin is in the center of one of the hexagons and the periods are ( , 0 ) and ( 0 , 3 )
顶点集合为为整数边的集合为相邻}正六边形点格模型为：平面是由正六边形点格组成，它的顶点坐标为其中，原点在一个正六边形的中心，周期为( 3 ~ ( 1 / 2 ) ， 0 )和( 0 ， 3 )我们可以把它在竖直方向压缩1 3 ~ ( 1 / 2 )倍使它成为周期图。 |
| 9. | Lr ( n ) is that there is an open path in rectangle [ 0 , n ] x [ 0 , n ] joining some vertex on its left side to some vertex on its right side when p > pc in the models of the triangle lattice and the hexagonal lattice , o theorem in the models of the hexagonal lattice , let lr ( n ) be is an open path in rectangle [ 0 , n ] x [ 0 , n ] joining some vertex on its left side to some vertex on its right side
定理在正六边形边渗流模型中，设lr … ）表示在边长为n正方形阻n沁xo ， n中存在一条连接它的左边界和它的右边界的开路，如果0 （ p ）叩，那么当n 。时p尸（ lr （ n ） ） l 。 |
| 10. | Chapter one percolation and the main inequality in percolation , chapter two main results of this paper , chapter three proof of the main results chapter four the general property and proposition about the band percolation of the models of the triangle lattice , the rectangle lattice and the hexagonal lattice
（ p pc ） “ ’若p pchix （ p三（一尸c广，若p pc这里p叫2一18本文的最后还提出了关于平面内正三角形，正四边形和正六边形的边渗流的一些共有的性质和猜想。 |
