Realizations of Topological Categories

There are functor-preordering-structured categories S(F,P), defined by the Prague School, in which every concrete category over a concretizable basecategory is realizable. Over nice basecategories there are realizations of all topological categories in some topological S(F,L). This gives rise for a new characterization of those concrete categories having a topological hull.     

Domain理论与拓扑

Ｄｏｍａｉｎ理论作为计算机程序设计语言研究的数学基础,序和拓扑的相互结合在这一领域中起着基本而重要的作用,本文力图从Ｄｏｍａｉｎ理论产生的背景,它在几个方面的发展,反映Ｄｏｍａｉｎ理论与拓扑的紧密联系,使我们看到序和拓扑的结合怎样应用于程序设计语言研究。     

Localization of Universal Problems. Local Colimits

The notion of the root of the category, which is a minimal (in a precise sense) weakly coreflective subcategory, is introduced in view of defining local solutions of universal problems: If U is a functor from C to C and c an object of C, the root of the comma-category c|U is called a U-universal root generated by c; when it exists, it is unique (up to isomorphism) and determines a particular form of the locally free diagrams defined by Guitart and Lair. In this case, the analogue of an adjoint functor is an adjoint-root functor of U, taking its values in the category of pro-objects of C. Local colimits are obtained if U is the insertion from a category into its category of ind-objects; they generalize Diers' multicolimits. Applications to posets and Galois theory are given.     

On the Generalization of the Courant Nodal Domain Theorem

In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if u_λn is an eigenfunction associated with the nth variational eigenvalue, λ_n, then u_λn has at most 2n−2 nodal domains. Also, if u_λn has n+k nodal domains, then there is another eigenfunction with at most n−k nodal domains.     

泛灰线性方程组的泛灰矩阵求解方法

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .根据泛灰数的性质 ,定义了泛灰矩阵 ,提出了泛灰线性方程组的泛灰矩阵解法 ,并给出了算例 .     

FS-相容Domain的定向完备化及相关范畴性质

引入FS-相容Domain概念,研究FS-相容Domain的性质,主要结果有：（1）FS-相容Domain的收缩核与连续函数空间还是FS-相容Domain;（2）FS-相容Domain是有限生成上集,从而是Scott紧的;（3）FS-相容Domain的定向完备化是FS-Domaln;（4）有最大元的FS-Domain去掉最大元后是FS-相容Domain;（5）证明了以Scott连续映射为态射,FS-相容Domain为对象的范畴FS-CDOM是笛卡儿闭范畴并以FS-Domain范畴FS-DOM作为满的反射子范畴。     

Universal Induction and True Universal Arithmetic

We prove that every finitely generated (as a ring) model for induction for universal formulas without parameters satisfies also all true universal sentences. Mathematics Subject Classification: 03C62.     

L-Fuzzy Domain上的广义Scott拓扑

本文研究了L-fuzzy domain上的广义Scott拓扑,利用[1]中引入的L-fuzzy domain.获得了其上的广义Scott拓扑,它是Domain上Scott拓扑的推广,证明了一个L-fuzzy单调映射是L-fuzzy Scott连续映射当且仅当它关于L-fuzzy domain上的广义Scott拓扑连续.     

Universal Coefficient Theorem in Triangulated Categories

We consider a homology theory on a triangulated category with values in an abelian category. If the functor h reflects isomorphisms, is full and is such that for any object x in there is an object X in with an isomorphism between h(X) and x, we prove that is a hereditary abelian category, all idempotents in split and the kernel of h is a square zero ideal which as a bifunctor on is isomorphic to. The second author is a researcher from CONICET, Argentina.     

Homotopy Classification of Categorical Torsors

The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G,) over a small category . We show a natural bijection between the set of equivalence classes of such torsors and [B({}),B(G,)], the set of homotopy classes of continuous maps between the corresponding classifying spaces. These results are applied to algebraically interpret the set of homotopy classes of maps from a CW-complex X to a path-connected CW-complex Y with _i (Y)=0 for all i1,2.     

Finite Paths are Universal

We prove that any countable (finite or infinite) partially ordered set may be represented by finite oriented paths ordered by the existence of homomorphism between them. This (what we believe a surprising result) solves several open problems. Such path-representations were previously known only for finite and infinite partial orders of dimension 2. Path-representation implies the universality of other classes of graphs (such as connected cubic planar graphs). It also implies that finite partially ordered sets are on-line representable by paths and their homomorphisms. This leads to new on-line dimensions. Mathematics Subject Classifications (2000) 06A06, 06A07, 05E99, 05C99.J. Nešetřil: Supported by a Grant LN00A56 of the Czech Ministry of Education. The first author was partially supported by EU network COMBSTRU at UPC Barcelona.     

Some Categorical Algebraic Properties: Counter-Examples for Functor Categories

This work is a complement to the authors earlier papers, where it is shown that a functor category inherits from such properties as amalgamation, transferability and congruence extension if has either products or certain pushouts. A general scheme is given for constructing counter-examples which show that the latter condition on is essential. In particular, it is shown that the functor categories , , ( resp.) do not satisfy the amalgamation (congruence extension resp.) property in general. Moreover, one class of categories is described, where the condition of the existence of certain pushouts is not only sufficient, but also necessary for to preserve the considered properties of .Mathematics Subject Classifications (2000) 18A25, 18A32, 18B99, 08B26.Dali Zangurashvili: The support rendered by INTAS Grant 97 31961 is gratefully acknowledged.     

Domain理论中的映射

Domain理论的目的是为程序设计语言提供数学语义的模型,信息状态域的指标称为Domain,而程序的指称是Domain间的映射。本文主要介绍Domain理论中的三类重要映射－Scott连续映射,Berry的稳定映射以及CM映射的定义以及等价刻画和表示。     

On the Cohomology of Categories, Universal Toda Brackets and Homotopy Pairs

A category of homotopy pairs is characterised by a cohomology class which generalizes the notion of Toda bracket. Explicit computations of such cohomology classes are described.     

A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues

In this paper, we derive “universal” inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin–Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain.     

Characterizations of Stable Functions on L—domains

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆＤｏｍａｉｎｓｔｈｅｏｒｙ（ｉｎｔｒｏｄｕｃｅｄｂｙＤ．Ｓｃｏｔｔ）ｉｓｔｏｍｏｄｅｌｔｈｅｄｅｎｏｔａｔｉｏｎａｌｓｅ－ｍａｎｔｉｃｓｏｆｃｏｍｐｕｔｅｒｐｒｏｇｒａｍｍｏｎｇｌａｎｇｕａｇｅｓ［１］．Ａｎｉｍｐｏｒｔａｎｔｆｒａｍｅ－ｗｏｒｋｆｏｒｔｈｅｄｅｎｏｔａ－ｔｉｏｎａｌｓｅｍａｎｔｉｃｓｏｆｐｒｏｇｒａｍｍｉｎｇｌａｎｇｕａｇｅｓｉｓｔｈｅｃａｔｅｇｏｒｙｏｆＬ－ｄｏｍａｉｎｓｗｉｔｈｓｔａｂｌｅｆｕｎｃｔｉｏｎｓ．Ｌ－ｄｏｍ…     

Universal consistency of delta estimators

This paper considers delta estimators of the Radon-Nikodym derivative of a probability function with respect to a σ-finite measure. We provide sufficient conditions for universal consistency, which are checked for some wide classes of nonparametric estimators.     

泛灰线性方程组的白化求解方法与应用

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .由于泛灰行列式运算复杂 ,根据泛灰的性质 ,提出了泛灰线性方程组的白化解法 .理论证明这种求解方法的正确性 .并给出了算例 .     

On a Property of Urysohn's Universal Metric Space

Mathematical Notes -