Dynamics of implicit operations and tameness of pseudovarieties of groups

This work gives a new approach to the construction of implicit operations. By considering ``higher-dimensional' spaces of implicit operations and implicit operators between them, the projection of idempotents back to one-dimensional spaces produces implicit operations with interesting properties. Besides providing a wealth of examples of implicit operations which can be obtained by these means, it is shown how they can be used to deduce from results of Ribes and Zalesski, Margolis, Sapir and Weil, and Steinberg that the pseudovariety of -groups is tame. More generally, for a recursively enumerable extension closed pseudovariety of groups , if it can be decided whether a finitely generated subgroup of the free group with the pro- topology is dense, then is tame.

     

The structure of linear codes of constant weight

In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.

     

Łukasiewicz Tribes are Absolutely Sequentially Closed Bold Algebras

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets.     

Sturm-liouville operators with singular potentials

This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y ^" +q(x)y, whereq(x) is a distribution of first order, such that . The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by smooth potentialsq _n , provided that the condition holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results are obtained in the case of the whole axis. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 897–912, December, 1999.     

综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

Extensions of perfect GO-spaces and -discrete dense sets

In this paper, we prove that if a perfect GO-space has a -discrete dense set, then has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer.

     

Strong type estimate and Carleson measures for Lipschitz spaces

We establish a capacitary strong type estimate for Lipschitz space and characterize the related Carleson measures.

     

Elliptic problems with discontinuities

In this paper we prove two existence theorems for elliptic problems with discontinuities. The first one is a noncoercive Dirichlet problem and the second one is a Neumann problem. We do not use the method of upper and lower solutions. For Neumann problems we assume that f is nondecreasing. We use the critical point theory for locally Lipschitz functionals.     

包含轻子结构的夸克模型

对标准模型作手征性扩充后,模型中平行地存在手征性相反的夸克态.相应于构成强子的f代普通夸克,新加的同样代数、手征性相反的夸克可能构成轻子.对扩充后的模型超对称化之后,使得渐近自由性质的破坏所要求的代的数目从大于33/8减少到大于9/4,从而有可能解释手征相反的夸克构成的轻子为什么比普通夸克构成的强子大小要小得多等特点.