Lattices on simplicial partitions

In this paper, (d+1)-pencil lattices on simplicial partitions in R^d are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of this fact leads to an efficient computer algorithm for the design of a lattice.     

Nonobtuse tetrahedral partitions

We show how to generate refinements of tetrahedral partitions, where no obtuse angles appear. Such partitions play an important role in deriving discrete maximum principles and maximum norm error estimates for the finite element method. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 327–334, 2000     

半连续格和半代数格的映射性质

研究了半连续格及半代数格的一些映射性质,讨论了强连续格的函数空间,给出了强连续格到方体的嵌入定理.     

单调概念格性质研究

概念格是知识表示和数据分析的重要工具,单调概念格是概念格的推广。本文就Deogun等提出的单调概念格进行了两方面的研究:一,指出Deogun等提出的单调概念格性质的错误并加以修正;二,证明单调概念格就是闭格,从而找到用拓扑闭包算子和拓扑交结构来表示单调概念格的两种格表示方法,并建立起单调概念格与有上界的拓扑交结构的范畴等价。本文所建立的单调概念格的拓扑表示方法将方便我们进一步研究单调概念格的构造算法、约简算法和实际应用,具有理论和实际的双重意义。     

Smooth格和强Smooth格

引入了强smooth格的概念,讨论了smooth格与强smooth格的一些基本性质,证明了强smooth格可用保任意交和Scott闭集之并的映射嵌入到某方体[0,1]X之中.     

广义半Smooth格

引入了广义半Smooth格和广义半Smooth代数格的概念,讨论了它们的一些基本性质,证明了完备格L是广义完全分配格当且仅当L是拟连续的广义半Smooth格。     

Strongly Pseudoalgebraic Lattices

In the recent twenty years,the generalizations of continuous lattices have attracted aconsiderable deal of attention (see [1 -6] ) .The so-called generalized continuous lat-tices(GCL) (see[2 ] ) is one of the most successful generalizations of continuous lat-tices.In 1 990 ,Venugopalan gave the definition of pseudoalgebraic lattice and provedthat a complete lattice is a compact totally order-disconnected(Preistley) space with re-spect to the Lawson topology if and only if it is a pseadoalgeb…     

Average adjacencies for tetrahedral skeleton-regular partitions

For any conforming mesh, the application of a skeleton-regular partition over each element in the mesh, produces a conforming mesh such that all the topological elements of the same dimension are subdivided into the same number of child-elements. Every skeleton-regular partition has associated special constitutive (recurrence) equations. In this paper the average adjacencies associated with the skeleton-regular partitions in 3D are studied. In three-dimensions different values for the asymptotic number of average adjacencies are obtained depending on the considered partition, in contrast with the two-dimensional case [J. Comput. Appl. Math. 140 (2002) 673]. In addition, a priori formulae for the average asymptotic adjacency relations for any skeleton-regular partition in 3D are provided.     

格上度量理论

通过对格上两种度量理论,即M．A．Erceg意义下的度量理论与史福贵意义下的度量理论的介绍与评述,展现出格上拓扑学中有关度量理论发展的概况,从这里可以看到,这一般拓扑学听度量理论比较,格上度量理论的研究有基本思想和研究方法上都有其独到之处。     

Fuzzy Ideals and Fuzzy Distributive Lattices

Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved.     

Dimension of -splines on type-6 tetrahedral partitions

We consider a linear space of piecewise polynomials in three variables which are globally smooth, i.e. trivariate C¹-splines of arbitrary polynomial degree. The splines are defined on type-6 tetrahedral partitions, which are natural generalizations of the four-directional mesh. By using Bernstein–Bézier techniques, we analyze the structure of the spaces and establish formulae for the dimension of the smooth splines on such uniform type partitions.     

幂等剩余格

研究一种特殊的刺余格--幂等刺余格,证明满足幂等性的一般刺余格必是可换剩余格,即不存在非可换的幂等剩余格.讨论幂等剩余格的基本性质以及与各类特殊剩余格之间的关系.在一般剩余格中引入psG-滤子的概念,给出其一组等价条件,并借助psG-滤子刻画幂等刺余格的特征.     

On a Characterization Theorem of Semimodular Lattices

In general lattice theory,there are two basic criterion theorems:　 (1 ) A lattice L is modular if and only if L does not contain a pentagon N5(seeFig. 1 a) .　 (2 ) A lattice L is distributive ifand only if L contains neither a pentagon N5nor a dia-mond M3(see Fig. 1 b) .　 Now,the problem is that if L is semimodular,whether L possesses the similar char-acteristic?In this regard,the following conclusion is obtained in this paper:　 A lattice L is semimodular if and only if L does not co…     

Local lagrange interpolation with cubic splines on tetrahedral partitions

We describe an algorithm for constructing a Lagrange interpolation pair based on C¹ cubic splines defined on tetrahedral partitions. In particular, given a set of points , we construct a set P containing and a spline space based on a tetrahedral partition whose set of vertices include such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets , and (2) the method provides optimal approximation order of smooth functions.     

Lattices on simplicial partitions which are not simply connected

In this paper, (d+1)-pencil lattices on simplicial partitions in R^d, which are not simply connected, are studied. It is shown, how the fact that a partition is not simply connected can be used to increase the flexibility of a lattice. A local modification algorithm is developed also to deal with slight partition topology changes that may appear afterwards a lattice has already been constructed.     

Fuzzy格上的KKM定理

讨论定义和Ｆｕｚｚｙ格上的某类映射的性质,主要结果是定理２．１。近几攫来,国内外许多专家、学者热心研究的ＫＫＭ定理,广义ＫＫＭ定理等冼多结果,都是定理２．１的一些简单和推论。由此说明,Ｆｕｚｚｙ格理论具有广泛的应用性。     

Laskerian Lattices

In this paper we investigate prime divisors, B _w-primes and zs-primes in C-lattices. Using them some new characterizations are given for compactly packed lattices. Next, we study Noetherian lattices and Laskerian lattices and characterize Laskerian lattices in terms of compactly packed lattices.     

拟连续格的逆极限

给出以保任意交和定向并为态射的拟连续格范畴的逆极限,讨论函子保广义拟连续格逆极限的条件。     

预线性与对合非结合剩余格

非结合剩余格是非结合格值逻辑系统的代数抽象,本文研究几类特殊非结合剩余格的代数性质。证明了满足预线性条件的非结合剩余格必是分配格,并给出预线性非结合剩余格的充分必要条件。同时,引入对合和强对合非结合剩余格的概念,研究了它们的基本性质,并分别给出对合和强对合非结合剩余格的等价条件。最后,通过反例说明强对合预线性非结合剩余格不一定是蕴涵格。     

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.