12 research outputs found
On the finite state automorphism group of a rooted tree
The normalizer of the finite state automorphism
group of a rooted homogeneous tree in the full automorphism group
of this tree was investigated. General form of elements in the normalizer was obtained and countability of the normalizer was proved
Classification of the local isometry groups of rooted tree boundaries
Classification of the groups of local isometries of
the rooted tree boundaries is established for transitive groups
Tarski monoids: Matui's spatial realization theorem
We introduce a class of inverse monoids, called Tarski monoids, that can be
regarded as non-commutative generalizations of the unique countable, atomless
Boolean algebra. These inverse monoids are related to a class of etale
topological groupoids under a non-commutative generalization of classical Stone
duality and, significantly, they arise naturally in the theory of dynamical
systems as developed by Matui. We are thereby able to reinterpret a theorem of
Matui on a class of \'etale groupoids as an equivalent theorem about a class of
Tarski monoids: two simple Tarski monoids are isomorphic if and only if their
groups of units are isomorphic. The inverse monoids in question may also be
viewed as countably infinite generalizations of finite symmetric inverse
monoids. Their groups of units therefore generalize the finite symmetric groups
and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147
Anisotropic Fermi Surface and Quantum Limit Transport in High Mobility Three-Dimensional Dirac Semimetal Cd
Dynamics of Findings of Non-specific Resistance in the Mouth Cavity in Children with Lesions of the Mucous Membrane Epithelium of the Mouth Cavity Against Acute Lymphoblastic Leukemia in the Treatment Process.
There was conducted study of dynamics of findings of non-specific resistance in the mouth cavity in children with lesions of the mucous membrane epithelium of the mouth cavity against acute lymphoblastic leukemia in the treatment process by authors-developed methods. It is known that in children with leukemia immunodeficiency states develop immunological disorders resulted from treatment with cytotoxic drugs. Moreover, not only general, but also the local immunity of the mouth cavity suffers, which is accompanied by development of infectious processes in the tissues that perform the barrier function, which include mucous membrane epithelium of the mouth cavity. A key role in the system of antimicrobial protection of the mouth cavity is performed by mucolytic enzyme lisocyme and α-defensins (HNP 1-3). 76 children with acute lymphoblastic leukemia aged from 2 to 18 years suffering from such dental diseases as generalized chronic Catarrhal gingivitis, erosive-ulcerative and candidal stomatitis took part in the clinical study. All children under clinical study were divided into 2 groups - the main and comparison. Standard protocol treatment was used in the comparison group. Developed treatment-and-prophylactic complex was used in the main group. The children of the main group were prescribed developed treatment-and-prophylactic complex depending on the period of the disease: the first version of local treatment was used in the acute period and the relapse of the disease, the second - in the period of remission. The results of research have shown a stimulating effect of therapeutic and prophylactic measures on the natural antimicrobial system of mouth cavity protection, both in children of the main groups under study and in the comparison groups. Such a phenomenon should be considered as a positive process that contributes to the increase of resistance in periodontal tissues and mucous membrane epithelium of the mouth cavity