http://dspace.nbuv.gov.ua:80/handle/123456789/150340 2026-04-18T10:23:14Z 2026-04-18T10:23:14Z http://dspace.nbuv.gov.ua:80/handle/123456789/157397 2019-06-20T22:28:25Z 2006-01-01T00:00:00Z

Nilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted tree This paper deals with a semigroup of orderdecreasing transformations of a rooted tree. Such are the transformations α of some rooted tree G satisfying following condition: for any x from G α(x) belongs to a simple path from x to the root vertex of G. We describe all subsemigroups of the mentioned semigroup, which are maximal among nilpotent subsemigroups of nilpotency class k in our semigroup. In the event when rooted tree is a ray we prove that all these maximal subsemigroups are pairwise nonisomorphic.

2006-01-01T00:00:00Z Reznykov, I.I. http://dspace.nbuv.gov.ua:80/handle/123456789/157396 2019-06-20T22:28:18Z 2006-01-01T00:00:00Z

On sequences of Mealy automata and their limits Reznykov, I.I. We introduce the notions of n-state Mealy automaton sequence and limit of this sequence. These notions are illustrated by the 2-state Mealy automaton sequences that have the set of finite limit automata.

2006-01-01T00:00:00Z Protasova, O.I. http://dspace.nbuv.gov.ua:80/handle/123456789/157395 2019-06-20T22:28:02Z 2006-01-01T00:00:00Z

Pseudodiscrete balleans Protasova, O.I. A ballean B is a set X endowed with some family of subsets of X which are called the balls. The properties of the balls are postulated in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. A ballean is called pseudodiscrete if "almost all" balls of every pregiven radius are singletons. We give a filter characterization of pseudodiscrete balleans and their classification up to quasi-asymorphisms. It is proved that a ballean is pseudodiscrete if and only if every real function defined on its support is slowly oscillating. We show that the class of irresolvable balleans are tightly connected with the class of pseudodiscrete balleans.

2006-01-01T00:00:00Z Spalinski, J. http://dspace.nbuv.gov.ua:80/handle/123456789/157394 2019-06-20T22:27:48Z 2006-01-01T00:00:00Z

Fibrations and cofibrations in a stratified model category Spalinski, J. We introduce n-acyclic cofibrations and n-acyclic fibrations in a stratified model category and show that they have the key properties of (acyclic) cofibrations and (acyclic) fibrations in a model category. We analyse their action on sets of homotopy classes and give an application to homotopy colimits and limits.

2006-01-01T00:00:00Z