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

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