The Lattice of Completions of an Ordered Set

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind–MacNeille completion P. The lattice K(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closure operators on any complete lattice. In particular, if K(P) is finite, then it is an upper semimodular lattice and an upper bounded homomorphic image of a free lattice, and hence meet semidistributive.     

Linear programs with an additional rank two reverse convex constraint

An efficient algorithm is developed for solving linear programs with an additional reverse convex constraint having a special structure. Computational results are presented and discussed.     

变分方法与反向上下解

本文在非线性方程的下解不小于上解这一条件（即反向上下解条件）下研究了其解的存在性．我们证明了，如果非线性算子方程有变分结构，有一对反向上下解，对应的算子映某个锥入锥并且满足一定的辅助条件，那么这一方程在锥中至少有两个解．另外，本文还研究了反向上下解条件下非线性椭圆边值问题正解的存在性．     

给定压力下纯铁材料的冲击相变与层裂特性研究

采用VISAR测量样品自由面速度剖面和回收样品观测分析联合技术,开展等厚对称碰撞实验,结合文献中的实验结果,研究了冲击加载压力大于纯铁材料冲击相变阈值约2~5 GPa和大于冲击相变阈值约10 GPa两种压力状态下纯铁材料的加卸载历程及各相区的变化,并从应力波相互作用的角度,指出了冲击加载压力略大于纯铁材料相变阈值约2 GPa时,等厚对称碰撞样品"反常"二次层裂与冲击相变及逆相变的关联机制。     

Further results on several types of generalized inverses

Let R be an associative ring with unity 1 and let a,b,c∈R. In this paper, several characterizations for hybrid (b,c)-inverses of a are given. Also, the hybrid (b,c)-inverse of a is characterized by the group inverse of ab, under certain hypothesis. In particular, existence criteria for the the inverse along an element are obtained. Finally, we get the double commutant property and the reverse order law of annihilator (b,c)-inverses.     

基于前景理论的混合不确定情景下在线多属性反向拍卖的赢者确定方法

在线反向拍卖在当今的经济社会发展中扮演越来越重要的角色,其主要应用于采购招标领域。而在实际的采购拍卖中有关商品属性和供应商信息等方面常会存在一定程度的不确定性,且这些不确定性的刻画又存在着多种模糊表述形式,这些都将增加采购方的风险预期和竞标供应商赢者确定的难度。为此,本文基于前景理论及模糊集理论,研究了同时存在精确数、区间数、三角模糊数、梯形模糊数和语义模糊术语五种属性描述方式的在线多属性反向拍卖的赢者确定问题,提出了一种更具一般性的混合不确定情景下的在线多属性反向拍卖赢者(中标者)确定方法。最后,通过数值算例和比较分析验证了本文所提方法的合理性与有效性,并通过稳健性分析进一步说明方法的稳定性和适用性。     

联图$K_5+P_n$的交叉数

A join graph denoted by G + H,is illustrated by connecting each vertex of graph G to each vertex of graph H.In this paper,we prove the crossing number of join product of K_5 + P_n is Z(5,n) + 2 n + [n/2] + 4 for n ≥ 2.     

The anti‐Specker property,positivity, and total boundedness

Working within Bishop‐style constructive mathematics, we examine some of the consequences of the anti‐Specker property, known to be equivalent to a version of Brouwer's fan theorem. The work is a contribution to constructive reverse mathematics (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

圈的多重联图的邻点可区别E-全染色的一些结果

记χ_(at)~e(C_n_i)为n_i阶的圈C_n_i的邻点可区别E-全色数.若n_i≡0(mod 2)(i=1,2,3…,t),则χ_(at)~e(C_n_1+C_n_2+…+C_n_t)=2t;若n_i≡0(mod 2)(i=1,2,3…,r,l相似文献