模的弱消去问题和Exchange环的弱稳定条件

本文研究模的弱消去问题和exchange环的弱稳定条件,给出了wsrl条件的新刻划,证明了对具有有限exchange性质的模,外弱消去等价于内弱消去并等价于自同态环满足wsrl条件.     

图的周长的一个度条件

本文用度和给出一个关于图的最长圈的存在性条件.这一结果是N.Dean和P.Fraisse的相应结论的推广.     

色多项式对图的刻画

By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class bi-cycle graph and a second class bicycle graph(the Theorem 2), respectively.     

条件中位数L_1－模核估计的逐点相合性

设（Ｘ，Ｙ）．（Ｘ１，Ｙ１），（Ｘ２，Ｙ２），…为Ｒｄ×Ｒ１上ｉ．ｉ．ｄ．随机向量序列。Ｙ对Ｘ的条件中位数θ（ｘ）定义为在Ｘ＝ｘ时Ｙ的条件分布函数的中位数．校函数Ｋ（·）是Ｒｄ上正实值函数，对ｘ∈Ｒｄ，θ（ｘ）的Ｌ１－模核估计θｎ（ｘ）定义由（１）给出．本文中，我们将文献［４］的均匀核法推广至一般核的情况，并在定义了θ的Ｌ１－模核估计基础之上，研究了其逐点相合性质．     

一类Caterpillars图的匹配刻画

利用匹配多项式的性质以及匹配根的信息研究了图的匹配刻画问题,给出了一类Caterpillars图F（2,m,3）及补图匹配刻画的充分必要条件是m=2,5,8.     

和图、整和图与模和图的几个结果

Let N denote the set of positive integers. The sum graph G^＋（S） of a finite subset S belong to N is the graph （S, E） with uv ∈ E if and only if u ＋ v ∈ S. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N. By using the set Z of all integers instead of N, we obtain the definition of the integral sum graph. A graph G = （V, E） is a mod sum graph if there exists a positive integer z and a labelling, λ, of the vertices of G with distinct elements from {0, 1, 2,..., z - 1} so that uv ∈ E if and only if the sum, modulo z, of the labels assigned to u and v is the label of a vertex of G. In this paper, we prove that flower tree is integral sum graph. We prove that Dutch m-wind-mill （Dm） is integral sum graph and mod sum graph, and give the sum number of Dm.     

关于含1—因子图幂中边不交1—因子

本文讨论一般含1-因子连通图的n次幂中边不交1-因子的个数.从而证明了L.Nebesky(1984)猜想对含1-因子图成立.     

几类多圈图的拉普拉斯谱刻画

设图G是一个简单连通图. 如果任何一个与图G同拉普拉斯谱的图都与图G同构,则称图G是由其拉普拉斯谱确定的. 定义了双圈图theta_{n}(p_1,p_2,cdots,p_t) 和m 圈图H_n(mcdot C_3;p_1,p_2,cdots,p_t). 证明了双圈图theta_{n}(p)和theta_{n}(p,q),三圈图H_n(3cdot C_3;p)和H_n(3cdot C_3;p,q)分别是由它们的拉普拉斯谱确定的.     

赋权图中重圈的Dirac型条件

In this paper we give a Dirac type condition for heavy cycles in a 3-connected weighted graph,reading that if d~w(v)≥d for all v∈V(G)\{x} and w(uz)=w(vz),when uz,vz∈E(G) and uv ■ E(G).Then G contains either an (x,y)-cycle of weight at least 2d or a Hamilton cycle.     

条件(Q)条件(PT)对推出图及Rees商的传递性

研究了条件(Q)、条件(PT)对推出图、Rees商的传递性,证明了在推出图(1)中P满足条件(Q)当且仅当Y满足条件(Q)并且f是酉的.     

Automorphisms of Tensor Completions of Algebras

In the classical representation of different groups, frequent use is made of a linear automorphism group of various algebras. Since the linear automorphism group is only part of a full automorphism group, such an approach might seem to be too restrictive. In this connection, we point out a natural, wide class of algebras whose automorphisms are standard and are reducible to linear. Thus, for algebras in this class, studying the full automorphism group reduces to treating the linear, a traditional approach in the class of such algebras being quite general.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 368–382, May–June, 2005.     

Comparison of MacNeille,Canonical, and Profinite Completions

Using duality theory, we give necessary and sufficient conditions for the MacNeille, canonical, and profinite completions of distributive lattices, Heyting algebras, and Boolean algebras to be isomorphic. The second author was supported by VICI grant 639.073.501 of the Netherlands Organization for Scientific Research (NWO).     

Discrete-Time Geo X /G/1 Queue with Preemptive Repeat Different Priority

This paper considers a discrete-time Geo ^X /G/1 queue accepting two classes of messages with preemptive repeat different priority. Service times of messages of each priority class are i.i.d. according to a general discrete distribution function that may differ between two classes. The completion time and the stability condition for our system are investigated. By using the supplementary variable method and the generating function technique, we derive the joint system contents distributions at various observation instants and also compute the probability distribution for the unfinished work.     

Formal completions and idempotent completions of triangulated categories of singularities

The main goal of this paper is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic. We also discuss Thomason's theorem on dense subcategories and a relation to the negative K-theory.     

Completion via Nearness for Metrically Generated Constructs

In this paper we will study completeness in symmetric metrically generated constructs via nearness spaces. Our approach consists in associating an appropriate regular nearness space with a given symmetric metered space. The completion theory known for regular nearness space has some convenient properties on which our completion of symmetric metered spaces will be based. This technique appears to be suitable for most symmetric metrically generated constructs and leads to a firm completion theory.      

On some algorithmic problems regarding the hairpin completion

We consider a few algorithmic problems regarding the hairpin completion. The first problem we consider is the membership problem of the hairpin and iterated hairpin completion of a language. We propose an O(nf(n)) and O(n²f(n)) time recognition algorithm for the hairpin completion and iterated hairpin completion, respectively, of a language recognizable in O(f(n)) time. We show that the n factor is not needed in the case of hairpin completion of regular and context-free languages. The n² factor is not needed in the case of iterated hairpin completion of context-free languages, but it is reduced to n in the case of iterated hairpin completion of regular languages. We then define the hairpin completion distance between two words and present a cubic time algorithm for computing this distance. A linear time algorithm for deciding whether or not the hairpin completion distance with respect to a given word is connected is also discussed. Finally, we give a short list of open problems which appear attractive to us.     

Completion of merotopic spaces and extension of uniformly continuous maps

A general Riesz merotopic space (X, ν) determines a not necessarily topological closure operator c_ν on X. The space (X, ν) is said to be complete if every cluster on (X, ν) is contained in an adherence grill on (X, c_ν). We discuss a method of obtaining a large class of completions of a given Riesz merotopic space with induced T₁ closure space. As special cases we get the simple completion, which induces a simple closure space extension, and the strict completion, which induces a strict closure space extension. We show that the category of complete separated T₁ Riesz merotopic spaces is epireflective in the category of separated T₁ Riesz merotopic spaces, the reflection of an object being the simple completion. Similarly the category of complete clan-covered quasi-regular T₁ Riesz merotopic spaces is epireflective in the category of clan-covered quasi-regular T₁ Riesz merotopic spaces, the reflection of an object being the strict completion.     

实（AF）—代数的理想

给出实（AF）－代数Bratteli图的理想的概念,讨论了这个理想与实（AF）－代数的理想的关系,是对实（AF）－代数结构理论的进一步完善。