非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

具有拟理想正则*-断面的正则半群

本文提出了具有正则*-断面正则半群的概念，所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类；最后刻画了具有拟理想正则*-断面的正则半群的结构．     

非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

P-完全正则半群

求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P.     

加权正则函数的一些性质

正则函数是Clifford分析中的一类重要函数,加权正则函数是正则函数的进一步发展,也是一类重要的函数,因此具有一定的研究意义.在正则函数的研究基础上,并利用加权正则函数自身的性质,讨论了加权正则函数的平均值定理,最大模原理,Weierstrass定理以及一些其它推论.     

关于Locale范畴反射子范畴的注解

利用Locale中的完全正则元和零维元构造性地给出了任意Locale的完全正则反射以及零维反射的描述,并且对于满足‘(?)’关系插入性的Locale,特别地,对正规Locale,证明了全体正则元构成的Locale是其正则反射.进而,利用平稳(flat)子Locale的扩张引理给出了Locale的紧完全正则反射,紧零维反射以及紧正则反射的构造性描述.     

Embedding in R-closed spaces

Some problems in the theory of R-closed spaces are solved by showing that every regular space can be embedded in a minimal regular space and there is an R-closed space with no coarser minimal regular topology. A class of spaces is found so that when fed into the Jone's machinery for producing non-Tychonoff, regular spaces, the output is non-tychonoff R-closed and minimal regular spaces. Also, an example of a strongly minimal regular space that is not locally R-closed is given.     

Periodic billiard trajectories in regular polygons and closed geodesics on regular polyhedra

We consider the relations between the lengths of periodic billiard trajectories in regular triangles, squares, and regular pentagons and those of closed geodesics on the surfaces of regular polyhedra. The cases of regular tetrahedra and octahedra are fully resolved in [3]. The cases of cubes and regular icosahedra are treated below. In the case of regular dodecahedra we can present only preliminary partial results.     

Weakly Strict Regular Semigroups

Weakly strict regular semigroups WS represent a generalization of strict regular semigroups. For the intersection of WS with some usual e-varieties of regular semigroups, such as left regular orthodox semigroups and similar e-varieties V, we provide WS ⋂ V with a basis of identities and forbidden semigroups. The latter, by exclusion, characterize the given e-variety. We do this also for WS. Coupled with some results of Hall, Churchill and Trotter, we characterize in this way also the e-varieties of completely regular semigroups as well as regular semigroups which are locally completely regular. The e-varieties studied are depicted in a diagram.     

模糊正则文法的逼近性

为了扩大现有研究的应用范围,基于max-min型模糊正则文法引入了max-*型模糊正则文法(其中*为特定t-模)的概念,讨论了max-*型模糊正则文法可以通过max-min型模糊正则文法在任意给定的逼近精度来逼近.研究表明,当t-模*满足一定的条件时,max-*型模糊正则文法与max-min型模糊正则文法在生成模糊语言能力方面是等价的.     

L-fuzzy拓扑空间中的包含式正则分离性

本文首先在一般L-fuzzy拓扑空间中引入了包含式正则分离性的概念.其次将包含式正则分离性与点式正则分离性及正则分离性作了比较,讨论了它们之间的相互蕴含关系.最后说明了包含式正则分离性与包含式正规分离性及包含式完全正则分离性之间的协调性.     

Regular Component Splittable Languages

Every infinite regular language contains a regular subset of the formuv+w for some words u, v, w, where v is not the empty word. The regularsubsets of the above form are called regular components. Some well-knowncontext-free languages, such as the Dyck language and the balanced language(over an alphabet X with |X| = 2), are decomposed as disjointunions of disjunctive languages. In this paper, we investigate thedecompositions of some of the regular languages and the context-freelanguages as disjoint unions of regular components. An infinite language iscalled regular component splittable if it can be expressed as a disjointunion of regular components and a finite set. We show that the Dycklanguage, the balanced language and some disjunctive context-free splittablelanguages are regular component splittable. We also present an example toshow that there is a disjunctive context-free language which is not regularcomponent splittable.     

Tolerance relations on eventually regular semigroups

A semigroup is called eventually regular if a power of each element is regular. Regular and group-bound semigroups are each eventually regular. A tolerance relation on an eventually regular semigroup is introduced, and Lallement's result for regular semigroups is generalized to eventually regular semigroups. Weakly compatible tolerances on semigroups are studied. This research was partially supported by the National Science Foundation of Qufu Normal University. The author wishes to thank T. E. Hall for his comments and help in preparing this paper for publication.     

Semilattice transversals of regular bands I

Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties.     

正多边形对称群的子群

利用Lagrange定理和正多边形对称群的性质,首先对正多边形对称群的子群的性质进行了研究,其次讨论了正多边形对称群的子群的结构,由此完全确定了正多边形对称群的子群,最后应用所得结论求出了正六边形对称群的所有子群.     

全正则子半群构成链的正则半群(英文)

本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全0-单半群的结构.     

On quasi-strongly regular graphs

We study the quasi-strongly regular graphs, which are a combinatorial generalization of the strongly regular and the distance regular graphs. Our main focus is on quasi-strongly regular graphs of grade 2. We prove a “spectral gap”-type result for them which generalizes Seidel's well-known formula for the eigenvalues of a strongly regular graph. We also obtain a number of necessary conditions for the feasibility of parameter sets and some structural results. We propose the heuristic principle that the quasi-strongly regular graphs can be viewed as a “lower-order approximation” to the distance regular graphs. This idea is illustrated by extending a known result from the distance-regular case to the quasi-strongly regular case. Along these lines, we propose a number of conjectures and open problems. Finally, we list the all the proper connected quasi-strongly graphs of grade 2 with up to 12 vertices.     

On quasi-strongly regular graphs

We study the quasi-strongly regular graphs, which are a combinatorial generalization of the strongly regular and the distance regular graphs. Our main focus is on quasi-strongly regular graphs of grade 2. We prove a “spectral gap”-type result for them which generalizes Seidel's well-known formula for the eigenvalues of a strongly regular graph. We also obtain a number of necessary conditions for the feasibility of parameter sets and some structural results. We propose the heuristic principle that the quasi-strongly regular graphs can be viewed as a “lower-order approximation” to the distance regular graphs. This idea is illustrated by extending a known result from the distance-regular case to the quasi-strongly regular case. Along these lines, we propose a number of conjectures and open problems. Finally, we list the all the proper connected quasi-strongly graphs of grade 2 with up to 12 vertices.     

Quotient Maps of Locales

We consider regular epimorphisms in the category Loc of locales. Closed surjections with subfit domain are regular epimorphisms. However, there exists a closed surjection which is the composite of two regular epimorphisms without being regular epic itself. This example answers both of the following questions in the negative: Y. Li"s question of whether weak quotient maps are necessarily regular epimorphisms, and P. Johnstone"s related question of whether regular epimorphisms compose. It follows that not all extremal epimorphisms in Loc are regular. The weak quotient maps of Y. Li and the equationally closed subframes of A. Pultr and A. Tozzi are shown to be dual notions. We also give a new characterization of regular epimorphisms in Loc.