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.     

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.     

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.     

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.     

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.     

The structure of regular disjoint groups of real homeomorphisms

The structure of disjoint iteration groups of real homeomorphisms has been determined by M. C. Zdun without any regularity condition. In this paper we turn to the regular case and describe the structure of regular disjoint groups of real homeomorphisms which are generalizations of regular disjoint iteration groups. It is shown that such a group is either embedded in a regular iteration group, or it is homeomorphically conjugate to a regular piecewise linear disjoint group.     

A concept of variety for regular biordered sets

We define a bivariety of regular biordered sets to be a nonempty class of regular biordered sets which is closed under taking direct products, regular bimorphic images and relatively regular biordered subsets. It is then shown that there is a complete lattice morphism mapping the complete lattice of all e-varieties of regular semigroups onto the complete lattice of all bivarieties of regular biordered sets; as a corollary we prove that there is a complete lattice morphism mapping the complete lattice of all e-varieties of E-solid regular semigroups onto the complete lattice of all varieties of solid binary algebras. Examples of bivarieties include the class of all solid regular biordered sets and the class of all local semilattices. For each setX with at least two elements, we show that a bivariety contains a free object onX if and only if it consists entirely of solid regular biordered sets or it consists entirely of local semilattices. The author gratefully acknowledges the financial support of an Australian Postgraduate Research Award.     

On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups

We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general.     

PMS-代数中的正则理想

本文提出伪补 Ｍ Ｓ 代数（简称 Ｐ Ｍ Ｓ 代数）中正则理想、正则同余关系的概念,研究正则理想与核理想、０ 理想之间的关系,讨论正则同余关系的性质,得到若干结果     

Strongly Regular Decompositions of the Complete Graph

We study several questions about amorphic association schemes and other strongly regular decompositions of the complete graph. We investigate how two commuting edge-disjoint strongly regular graphs interact. We show that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise we show that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. We study strongly regular decompositions of the complete graph consisting of four graphs, and find a primitive counterexample to A.V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic.     

A Note of Regularity on Completely Distributive Lattices

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Model-theoretic properties of regular polygons

This work is devoted to results obtained in the model theory of regular polygons. We give a characterization of monoids with axiomatizable and model-complete class of regular polygons. We describe monoids with complete class of regular polygons that satisfy some additional conditions. We study monoids whose regular core is represented as a union of finitely many principal right ideals and all regular polygons over which have a stable and superstable theory. We prove the stability of the class of all regular polygons over a monoid provided this class is axiomatizable and model-complete. We also describe monoids for which the class of all regular polygons is superstable and ω-stable provided this class is axiomatizable and model-complete. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 107–157, 2004.     

正则环的投射根

研究了正则环上投射根的性质.证明了正则环的投射根左右对称,且模去投射根的正则环只有零投射根.给出了矩阵环及角落环投射根的计算式,并得到了投射根为零的正则环的一些刻画。最后讨论了投射根为零的正则环在各种环运算下的封闭性和正则环的MP-维数.     

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．     

Regular reduction of controlled Hamiltonian system with symplectic structure and symmetry

In this paper, our goal is to study the regular reduction theory of regular controlled Hamiltonian (RCH) systems with symplectic structure and symmetry, and this reduction is an extension of regular symplectic reduction theory of Hamiltonian systems under regular controlled Hamiltonian equivalence conditions. Thus, in order to describe uniformly RCH systems defined on a cotangent bundle and on the regular reduced spaces, we first define a kind of RCH systems on a symplectic fiber bundle. Then we introduce regular point and regular orbit reducible RCH systems with symmetry by using momentum map and the associated reduced symplectic forms. Moreover, we give regular point and regular orbit reduction theorems for RCH systems to explain the relationships between RpCH-equivalence, RoCH-equivalence for reducible RCH systems with symmetry and RCH-equivalence for associated reduced RCH systems. Finally, as an application we regard rigid body and heavy top as well as them with internal rotors as the regular point reducible RCH systems on the rotation group SO(3) and on the Euclidean group SE(3), as well as on their generalizations, respectively, and discuss their RCH-equivalence. We also describe the RCH system and RCH-equivalence from the viewpoint of port Hamiltonian system with a symplectic structure.     

The cycle structure of regular multipartite tournaments

A multipartite tournament is an orientation of a complete multipartite graph. A tournament is a multipartite tournament, each partite set of which contains exactly one vertex. Alspach (Canad. Math. Bull. 10 (1967) 283) proved that every regular tournament is arc-pancyclic. Although all partite sets of a regular multipartite tournament have the same cardinality, Alspach's theorem is not valid for regular multipartite tournaments. In this paper, we prove that if the cardinality common to all partite sets of a regular n-partite (n3) tournament T is odd, then every arc of T is in a cycle that contains vertices from exactly m partite sets for all m{3,4,…,n}. This result extends Alspach's theorem for regular tournaments to regular multipartite tournaments. We also examine the structure of cycles through arcs in regular multipartite tournaments.     

Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets

In this paper, we give a new lifting construction of “hyperbolic” type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters.     

Regular polytopes of type {4,4,3} and {4,4,4}

Abstract regular polytopes generalize the classical concept of a regular polytope and regular tessellation to more complicated combinatorial structures with a distinctive geometrical and topological flavour. In this paper the authors give an almost complete classification of the (universal) locally toroidal regular 4-polytopes of Schläfli types {4,4,3} and {4,4,4}.     

Existence varieties with lattices of regular subsemigroups

A class of regular semigroups is called an existence variety, ore-variety, if it is closed under taking homomorphic images, regular subsemigroups, and direct products. For a regular semigroupS, the set of all regular subsemigroups ofS forms a partially ordered set under set inclusion. We determine for whiche-varietiesV the set of regular subsemigroups of members ofV forms a lattice. This includes the known result that the regular subsemigroups of an orthodox semigroup form a lattice.Presented by R. Freese.