凸子格与幂格

本文研究了分配格上的幂格.利用格的相对凸子格,建立了分配格上的幂格与凸子格之间的联系,获得了分配格上的幂格的刻划.     

相对凸子格的一类相对理想与相对滤子

文中给出了相对凸子格的一类相对理想、相对滤子以及相对最小理想的具体表达式,证明了相对凸子格可表示为相对理想与相对滤子的交,讨论了相对理想成为相对素理想的充要条件,阐述了格的素理想与相对凸子格的相对素理想的关系。     

格的凸子格格与幂格

研究格的凸子格的性质,建立格的非空凸子格组成的幂格与幂格的联系,证明在同构意义下,分配格的幂格都是它的非空凸子格组成的幂格的子格。     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

直觉模糊格及其同态

在K.Atanassov引进直觉模糊集的基础上,定义了直觉模糊格,并讨论了它的简单性质,给出了直觉模糊集截集与直觉模糊格的关系,证明了A是格L的一个直觉模糊子格的充要条件是A的截集是L的一个子格,然后在格同态与同构意义下,研究了直觉模糊格的像与原像。最后给出了直觉模糊凸子格的概念,并得到了它的一些基本性质。     

(∈,∈∨_q)-区间值模糊子格

将区间值模糊集的概念和运算应用于子格概念的研究,引入(∈,∈∨q)-区间值模糊子格的概念并考察它们的基本性质。给出了格L上区间值模糊集成为L的(∈,∈∨q)-区间值模糊子格的若干等价条件;讨论(∈,∈∨q)-区间值模糊子格与子格及(∈,∈∨q)-模糊子格间的相互关系;获得了(∈,∈∨q)-区间值模糊子格的像与原像成为(∈,∈∨q)-区间值模糊子格的条件。     

L-fuzzy子格群乘积的刻画

借助L-fuzzy集的水平截集,给出L-fuzzy子格群乘积的若干等价刻画。     

L-Fuzzy子格群的同态

证明了双诱导映射下L-Fuzzy子格群的像与逆像仍为L-Fuzzy子格群,基于L-Fuzzy集的层次结构特征,研究L-Fuzzy子格群的同态,给出了它们的性质.     

(∈,∈∨q(λ,μ))-模糊子格

给出(∈,∈∨q(λ,μ))-模糊子格的概念,得到了它的一些等价刻画,另外,还研究(∈,∈∨q(λ,μ))-模糊子格的同态像与同态原像的基本性质。其中值得指出的是,当λ=0,μ=1时可以得到R osen feld定义下的模糊子格的相应结果;当λ=0,μ=0.5时可以得到(∈,∈∨q(λ,μ))-模糊子格的相应结果;当λ=0.5,μ=1时则得到(∨,q-)-模糊子格的相应结果。     

格群的L—Fuzzy子格群的等价刻画及应用

给出L-Fuzzy子格群的几种等价刻画,利用它们得到一些结果。     

格群的T—Fuzzy子格群

引入格群L关于t-norm T的Fuzzy子格群、Fuzzy正则子格群（简称T-Fuzzy子格群、T-Fuzzy正规子格群）等概念,研究它们的性质,给出T-Fuzzy子格群的刻画。     

L-Fuzzy子格群的若干刻画

在L是完全分配格时，讨论L-Fuzzy子格群的一些特征性质。特别地，借助L—Fuzzy集的几种水平截集给出它的若干刻画。最后给出这些刻画的一个应用。     

On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

The 3-ball is a local pessimum for packing

It was conjectured by Ulam that the ball has the lowest optimal packing fraction out of all convex, three-dimensional solids. Here we prove that any origin-symmetric convex solid of sufficiently small asphericity can be packed at a higher efficiency than balls. We also show that in dimensions 4, 5, 6, 7, 8, and 24 there are origin-symmetric convex bodies of arbitrarily small asphericity that cannot be packed using a lattice as efficiently as balls can be.     

On finite lattice coverings

We consider finite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the finite arrangements C _n such that conv , where C _n is a subset of a covering lattice for K (which satisfies some natural conditions). We prove that for a fixed lattice the optimal arrangement (measured with the parametric density) is either a sausage, a so-called double sausage or tends to a Wulff-shape, depending on the parameter. This shows that the Wulff-shape plays an important role for packings as well as for coverings. Further we give a version of this result for variable lattices. For the Euclidean d-ball we characterize the lattices, for which the optimal arrangement is a sausage, for large parameter. Received 19 May 1999.     

Convex lattice polygons with all lattice points visible

Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the polygon are visible from it. We completely classify such polygons, show that there are finitely many of lattice width greater than 2, and computationally enumerate them. As an application of this classification, we prove new obstructions to graphs arising as skeleta of tropical plane curves.     

格蕴涵代数的左幂等元

为了研究命题真值取于格上的逻辑系统,文献[1]给出了格蕴涵供数的概念,文献[2-6]给出了格蕴涵代数的滤子,同态和性质（P）的概念,并讨论了它们的一些性质。本文在格蕴函代数中引入左幂等元的概念,讨论格蕴函代数中左幂等元的性质及由全体左幂等元所构成集合的代数结构,得到格蕴涵代数的分解定理：格蕴涵代数可以分解为由左幂等元构成左映射的像集合与对偶核的直和。     

L-可定义集与L-粗糙概念格

对基于剩余格L的L-广形式背景引入了L-可定义集概念,研究L-可定义集的性质及其与L-粗糙概念之间的关系.培出L-广可定义集的刻画;得到常值L-案均为L-可定义集的若干等价条件;证明全体L-可定义集在L-集包含序下是相应L-幂集格及L-粗糙概念格的子完备格;给出全体L-可定义集恰为全体L-粗糙概念外延的一个充要条件.