On vertex adjacencies in the polytope of pyramidal tours with step-backs

We consider the traveling salesperson problem in a directed graph. The pyramidal tours with step-backs are a special class of Hamiltonian cycles for which the traveling salesperson problem is solved by dynamic programming in polynomial time. The polytope of pyramidal tours with step-backs $PSB (n)$ is defined as the convex hull of the characteristic vectors of all possible pyramidal tours with step-backs in a complete directed graph. The skeleton of $PSB (n)$ is the graph whose vertex set is the vertex set of $PSB (n)$ and the edge set is the set of geometric edges or one-dimensional faces of $PSB (n)$. The main result of the paper is a necessary and sufficient condition for vertex adjacencies in the skeleton of the polytope $PSB (n)$ that can be verified in polynomial time.Comment: in Englis

On Sushchansky p-groups

We study Sushchansky p-groups. We recall the original definition and translate it into the language of automata groups. The original actions of Sushchansky groups on p-ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful level-transitive actions on the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with, so-called, G groups that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions.Comment: 14 pages, 3 figure

Peculiarities of geological and thermobaric conditions for the gas hydrate deposits occurence in the Black Sea and the prospects for their development

The actuality has been revealed of the necessity to attract the gas hydrate deposits of the Black Sea into industrial development as an alternative to traditional gas fields. This should be preceded by the identification and synthesis of geological and thermobaric peculiarities of their existence. It was noted that the gas hydrates formation occurs under certain thermobaric conditions, with the availability of a gas hydrate-forming agent, which is capable of hydrate formation, as well as a sufficient amount of water necessary to start the crystallization process. The gas hydrate accumulation typically does not occur in free space – in sea water, but in the massif of the sea bed rocks. The important role in the process of natural gas hydrates formation is assigned to thermobaric parameters, as well as to the properties and features of the geological environment, in which, actually, the process of hydrate formation and further hydrate accumulation occurs. It was noted that the source of formation and accumulation of the Black Sea gas hydrates is mainly catagenetic (deep) gas, but diagenetic gas also takes part in the process of gas hydrate deposits formation. The main component of natural gas hydrate deposits is methane and its homologs – ethane, propane, isobutane. The analysis has been made of geological and geophysical data and literature materials devoted to the study of the offshore area and the bottom of the Black Sea, as well as to the identification of gas hydrate deposits. It was established that in the offshore area the gas hydrate deposits with a heterogeneous structure dominate, that is, which comprises a certain proportion of aluminosilicate inclusions. It was noted that the Black Sea bottom sediments, beginning with the depths of 500 – 600 m, are gassy with methane, and a large sea part is favourable for hydrate formation at temperatures of +8...+9ºC and pressures from 7 to 20 MPa at different depths. The characteristics of gas hydrate deposits are provided, as well as requirements and aspects with regard to their industrialization and development. It is recommended to use the method of thermal influence on gas hydrate deposits, since, from an ecological point of view, it is the safest method which does not require additional water resources for its implementation, because water intake is carried out directly from the upper sea layers. A new classification of gas hydrate deposits with a heterogeneous structure has been developed, which is based on the content of rocks inclusions in gas hydrate, the classification feature of which is the amount of heat spent on the dissociation process

Space colonization. Mars One

The colonization of Space is the process of creating human settlements beyond the Earth. Theoretically, the colony can be placed: оn the planets, their moons, asteroids; оn the orbits of the celestial bodies; in the Lagrange‘s points. The most popular projects of colonization are the colonization of Moon and Mars, and the creation of orbital colonies

Space colonization. Mars One

The colonization of Space is the process of creating human settlements beyond the Earth. Theoretically, the colony can be placed: оn the planets, their moons, asteroids; оn the orbits of the celestial bodies; in the Lagrange‘s points. The most popular projects of colonization are the colonization of Moon and Mars, and the creation of orbital colonies

Systems of subspaces of a unitary space

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.Comment: 20 page