Presentations for Two Extensions of the Monoid of Order-Preserving Mappings on a Finite Chain

The purpose of this paper is to give presentations for the monoids of orientation-preserving mappings on a finite chain of order n, and orientation-preserving or reversing mappings on such a chain. Both these monoids are natural extensions of the monoid of order-preserving mappings. The obtained presentations are on two and three generators, respectively, and have n + 2 and n + 6 relations, respectively.AMS Subject Classification (1991): 20M05 20M20 06A05     

$${\text{IA}}$$ -Automorphisms of Free Products of Two Abelian Torsion-Free Groups

Let be the free product of two Abelian torsion-free groups, let and , where is the Cartesian subgroup of the group , and let F contain no zero divisors. In the paper it is proved that, in this case, any automorphism of the group is inner. This result generalized the well-known result of Bachmuth, Formanek, and Mochizuki on the automorphisms of groups of the form , , , where is a free group of rank two.     

The Normal Zeta Function of the Free Class Two Nilpotent Group on Four Generators

We calculate explicitly the normal zeta function of the free group of class two on four generators, denoted by F_2,4. This has Hirsch length ten.     

基于GIS和禁忌搜索集成技术的农产品物流配送路径优化

分析农产品物流配送模式,对带时间窗的车辆路径问题进行描述,建立有时限的配送路径优化模型,应用GIS与禁忌搜索算法集成技术求解该模型,开发农产品物流配送路径优化系统,并以晋安区农产品物流配送基础数据为范例,进行系统的初步应用研究.