Inverse Spectra with Two and Three Maps

It is shown that, for any 1 n < , there exist four maps of the n-dimensional cube to itself such that the limit of any inverse sequence of n-cubes is the limit of some sequence with only these four bonding maps. A universal continuum in the class of all limits of sequences of n-cubes is constructed as the limit of an inverse sequence of n-cubes with one bonding map. All compact sets of trivial shape are represented by using only three maps of the Hilbert cube to itself. Two maps of the closed interval to itself such that any Knaster continuum can be obtained as the limit of an inverse sequence with only these two bonding maps are constructed.     

余Frame范畴中余积的构造

首先,在并半格中引入了上覆盖关系的概念,并以此为基础引入强并半格以及强并半格中上覆盖和C-滤子的概念,证明了强并半格S中全体C-滤子之族C Fil(S)是余Frame,讨论了简单上集值映射u:S→C Fil(S)的相关并半格同态性质;其次,证明了由一族余Frame{A_λ|λ∈Γ}的直积Π_(λ∈Γ)A_λ中只有有限个坐标非零的元素构成的子集A是强并半格,还证明了A是余Frame族{A_λ|λ∈Γ}在并半格范畴中的余积对象;最后,通过各个坐标集中的上覆盖关系在A中定义了上覆盖C~*,再结合简单上集值映射u:A→C~*Fil(A)和标准入射qλ:Aλ→Π_(λ∈Γ)A_λ(λ∈Γ),证明了强并半格A中由上覆盖C~*诱导的余Frame C~*Fil(A)是余Frame族{A_λ|λ∈Γ}在余Frame范畴中的余积对象.     

Design of cellular manufacturing systems using Latent Semantic Indexing and Self Organizing Maps

A new, efficient clustering method for solving the cellular manufacturing problem is presented in this paper. The method uses the part-machine incidence matrix of the manufacturing system to form machine cells, each of which processes a family of parts. By doing so, the system is decomposed into smaller semi-independent subsystems that are managed more effectively improving overall performance. The proposed method uses Self Organizing Maps (SOMs), a class of unsupervised learning neural networks, to perform direct clustering of machines into cells, without first resorting to grouping parts into families as done by previous approaches. In addition, Latent Semantic Indexing (LSI) is employed to significantly reduce the complexity of the problem resulting in more effective training of the network, significantly improved computational efficiency, and, in many cases, improved solution quality. The robustness of the method and its computational efficiency has been investigated with respect to the dimension of the problem and the degree of dimensionality reduction. The effectiveness of grouping has been evaluated by comparing the results obtained with those of the k-means classical clustering algorithm.AMS classification: 62H30     

The Killing vector and the generalised Killing equation in Finsler space

Rendiconti del Circolo Matematico di Palermo Series 2 - Recently we have studied the infinitesimal deformation in Finsler space [8] (1). Here we have obtained the necessary and sufficient condition...     

到复Grassmann流形的多重调和映照的构造

本文给出了一些到复Ｇｒａｓｓｍａｎｎ流形的多重调和映照的构造定理,从而推广了莫小欢,Ｂｕｒｓｔａｌｌ　Ｆ． Ｅ．,Ｗｏｏｄ Ｊ． Ｃ．和 Ｕｄａｇａｗａ Ｓ．的结果．     

On the Construction of K-Operators in Field Theories as Sections Along Legendre Maps

The time-evolution K-operator (or relative Hamiltonian vector field) in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the nonregular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we use sections along maps, in particular multivector fields (skew-symmetric contravariant tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a relevant result, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for nonregular field theories).     

Free Monoids over Semigroups in a Monoidal Category: Construction and Applications

The adjunction of a unit to an algebraic structure with a given binary associative operation is discussed by interpreting such structures as semigroups and monoids respectively in a monoidal category. This approach then allows for results on the adjunction of counits to coalgebraic structures with a binary co-associative co-operation as well. Special attention is paid to situations where a given coalgebraic structure induces a “dual" algebraic one; here the compatibility of adjoining (co)units and dualization is examined. The extension of this process to starred algebraic structures and to monoid actions is discussed as well. Particular emphasis is given to examples from many areas of mathematics.     

Category of G-Groups and its Spectral Category

Let G be a group. We analyse some aspects of the category G-Grp of G-groups. In particular, we show that a construction similar to the construction of the spectral category, due to Gabriel and Oberst, and its dual, due to the second author, is possible for the category G-Grp.     

拓扑空间范畴、拓扑FUZZ范畴与拓扑分子格范畴间的反射与余反射

从整体角度出发，证明了拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚ是ＴＭＬ的反射与余反射（非满）子范畴．     

The Category of Directed Systems in a Category

We present two related categorical constructions. Given a category C, we construct a category C^[d], the category of directed systems in C. C embeds into C^[d], and if C has enough colimits, then C is monadic over C^[d]. Also, if E,M is a factorization structure for C, then C^[d] has a related factorization structure E_d M_d such that if E consists entirely of monic arrows, then so does E_d and the E_d-quotient poset of an object A is naturally the poset of directed downsets of the E-quotient poset of A. Similarly, if M consists entirely of monicarrows, then so does M_d and the M_d-subobject poset of an object A is naturally the poset of directed downsets of the M-subobject poset. C^[d] has completeness and cocompleteness properties at least as good as those of C, and it is abelian if C is. Dualization gives the other construction: a category C^[i], the category of inverse systems in C, into which C also embeds and which satisfies similar properties, except that directed downsets in the E-quotient and M-subobject posets are replaced by directed upsets.     

On a Construction of Infinite Families of Regular Cayley Maps

Received: February 28, 1995     

A Model Category Structure on the Category of Simplicial Multicategories

We establish a Quillen model category structure on the category of symmetric simplicial multicategories. This model structure extends the model structure on simplicial categories due to J. Bergner.     

T-Radicals and E-Radicals in the Category of Modules

We introduce two classes of radicals by means of tensor product of modules and module homomorphisms and prove some properties of these radicals and their connection with attracting modules.     

Isocompactness in the Category of Locales

We study isocompactness in Loc defined, exactly as in Top, by requiring that every countably compact closed sublocale be compact. This is a genuine extension of the same-named topological concept since every Boolean (or, even more emphatically, every paracompact) locale is isocompact. A slightly stronger variant is defined by decreeing that the closure of every complemented countably compact sublocale be compact. Dropping the adjective “complemented” yields a formally even stronger property, which we show to be preserved by finite products. Metrizable locales (or, more generally, perfectly normal locales) do not distinguish between the three variants of isocompactness. Each of the stronger variants of isocompactness travels across a proper map of locales, and in the opposite direction if the map is a surjection in Loc.     

T-Radicals in the Category of Modules

This paper deals with the class of idempotent radicals defined by means of a tensor product. Their effect on Abelian groups is described. We also establish their connection with attracting modules. Mathematics Subject Classification (2000) 18E40.     

Making the Category of Doi-Hopf Modules into a Braided Monoidal Category

We investigate how the category of Doi-Hopf modules can be made into a monoidal category. It suffices that the algebra and coalgebra in question are both bialgebras with some extra compatibility relation. We study tensor identies for monoidal categories of Doi-Hopf modules. Finally, we construct braidings on a monoidal category of Doi-Hopf modules. Our construction unifies quasitriangular and coquasitriangular Hopf algebras, and Yetter-Drinfel'd modules.     

基于群范畴的L-fuzzy结构提升范畴及其表示

引入群范畴上L-fuzzy结构提升范畴与格值结构提升范畴概念,L-fuzz结构是在逻辑层面表达群理论多值语义的有点化描述,也是Zermelo-Fr(a)nkel公理集合理论和各种代数形式理论的格值模型的语义赋值,而格值结构是在范畴层面表达群理论多值语义的无点化描述,本文建立了L-fuzzy结构与格值结构这两种不同数学结构之间的联系,证明了在范畴层面上述两种结构是同构的.给出了基于群范畴的L-fuzzy结构的格值结构表示.     

Contact and Conformal Maps in

When the action of the conformal group O(1, n+1) on may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C⁴ map between domains and in whose differential is a (variable) multiple of a (variable) isometry at each point of is the restriction to of a transformation x g·x, for some g in O(1,n+1). In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group G on the space G/P, where P is a minimal parabolic subgroup.     

Killing and the Coxeter transformation of Kac-Moody algebras

Inventiones mathematicae -