Algebra and Discrete Mathematics, 2006, № 4http://dspace.nbuv.gov.ua:80/handle/123456789/1503442024-03-29T02:08:15Z2024-03-29T02:08:15ZNilpotent subsemigroups of a semigroup of order-decreasing transformations of a rooted treehttp://dspace.nbuv.gov.ua:80/handle/123456789/1573972019-06-20T22:28:25Z2006-01-01T00:00:00ZNilpotent 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.
2006-01-01T00:00:00ZOn sequences of Mealy automata and their limitsReznykov, I.I.http://dspace.nbuv.gov.ua:80/handle/123456789/1573962019-06-20T22:28:18Z2006-01-01T00:00:00ZOn 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.
2006-01-01T00:00:00ZPseudodiscrete balleansProtasova, O.I.http://dspace.nbuv.gov.ua:80/handle/123456789/1573952019-06-20T22:28:02Z2006-01-01T00:00:00ZPseudodiscrete 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.
2006-01-01T00:00:00ZFibrations and cofibrations in a stratified model categorySpalinski, J.http://dspace.nbuv.gov.ua:80/handle/123456789/1573942019-06-20T22:27:48Z2006-01-01T00:00:00ZFibrations 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