Статті
http://hdl.handle.net/123456789/74
This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian and Russian mathematician, one of the founder of our journal Professor Rostislav Grigorchuk, who was 50 years of age on February 23, 2003.2024-03-29T01:02:28ZOn faithful actions of groups and semigroups by orientation-preserving plane isometries
http://hdl.handle.net/123456789/82
On faithful actions of groups and semigroups by orientation-preserving plane isometries
Vorobets, Yaroslav
Feitful representations of two generated free
groups and free semigroups by orientation-preserving plane isometries
constructed.
2003-01-01T00:00:00ZStructural properties of extremal asymmetric colorings
http://hdl.handle.net/123456789/81
Structural properties of extremal asymmetric colorings
Verbitsky, Oleg
Let be a space with probability measure μ
for which the notion of symmetry is defined. Given A µ , let
ms(A) denote the supremum of μ(B) over symmetric B µ A. An
r-coloring of is a measurable map  : ! {1, . . . , r} possi-
bly undefined on a set of measure 0. Given an r-coloring Â, let
ms(; Â) = max1·i·r ms(Â−1(i)). With each space we associate
a Ramsey type number ms(, r) = infÂms(; Â). We call a col-
oring  congruent if the monochromatic classes Â−1(1), . . . , Â−1(r)
are pairwise congruent, i.e., can be mapped onto each other by a
symmetry of . We define ms?(, r) to be the infimum of ms(; Â)
over congruent Â.
We prove that ms(S1, r) = ms?(S1, r) for the unitary circle S1
endowed with standard symmetries of a plane, estimate ms?([0, 1), r)
for the unitary interval of reals considered with central symmetry,
and explore some other regularity properties of extremal colorings
for various spaces.
2003-01-01T00:00:00ZDynamics of finite groups acting on the boundary of homogenous rooted tree
http://hdl.handle.net/123456789/80
Dynamics of finite groups acting on the boundary of homogenous rooted tree
Szaszkowski, Zbigniew
Criterion of embedding of finite groups into the
automorphism groups of a homogenous rooted tree of a spherical
index n is formulated. The sets of natural numbers which are the
lengths of all orbits of finite groups acting on the boundary of tree
are described.
2003-01-01T00:00:00ZOn 2-state Mealy automata of polynomial growth
http://hdl.handle.net/123456789/79
On 2-state Mealy automata of polynomial growth
Reznykov, I. I.
We consider the sequence of 2-state Mealy au-
tomata over the finite alphabets, that have polynomial growth or-
ders and define the infinitely presented automatic transformation
semigroups.
2003-01-01T00:00:00Z