Vol 20, No 10 (2014)

In the work sufficient conditions for existence at least one positive solution of two-point boundary problem for one class of strongly nonlinear differential equations of the fourth order are received. The problem is considered on a segment [0,1] (more general case of segment[0, a] is reduced to considered). On the ends of a segment the solution of y and its second derivative of y′′ areequal to zero. Right part of an equation f (x, y) isn’t negative at x\geq 0 andat all y. Performance of sufficient conditions is easily checked. Performance ofthese conditions is easily checked. In the proof of existence the theory of conesin banach space is used. Also apriori estimates of positive solution, which ispossible to use further at numerical construction of the solution are obtained.

In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial differential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the final stage it is shown that the limit of subsequence is the required generalized solution.

In this paper the possibility of using the method of successive calculations to solve the transportation problem on the maximum profit is investigated. The feature of this problem is that a set of consumers isn’t defined and gets out from wider set of possible consumers by the criterion of a maximum of profit. Profit is calculated on the basis of consumer demand and prices, which are determined by the contract between the consumer and the company carrying out transportation. It is shown that this problem is reduced to maximization of the profit function defined on the set of all subsets of consumers. The submodularity of profit function is proved, that justified application of method of successive calculations to solve this problem.

One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.

This paper is devoted to the varieties of Leibnitz algebras over a field of zero characteristic. All information about the variety in case of zero characteristic of the base field is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with finite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sufficient condition for a finiteness of colength of variety of Leibnitz algebras.

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of finite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic finite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

Water-oil contact moving task has a high significance in a waterflooding the- ory: it’s possible to improve oil recovering characteristics due to prediction of flow features for both liquids - oil and water displaced it. There is the simplest mathematical pattern for conjoint oil-water flow presenting: it is called ”versi- color” liquids model and it suggests making oil and water physically identical to simplify solving process for water-oil contact moving task. However, another pattern was used in research described in this paper: it is called pistonlike dis- placement model and it supposes that oil and water physical characteristics, for example, viscosities, may be different. As for the oil-keeping reservoir pattern used in this research it was presented as homogeneous and infinity, with fixed thickness: furthermore its surface was covered by dual periodical lattice included production and injection wells in its cells.

The short description of scientific equipment of МРТ (multichannel recorder of temperatures) is resulted and experimental results about current temperatures in local zones of containers of the scientific equipment, received in 42 daily flight of a space vehicle ”FOTON-M” № 4 are presented. It is shown, that the most essential factors defining a thermal mode in containers of scientific equipment, their position on the external surface of the spacecraft, focused almost during all flight by panels of solar batteries on the Sun and conditions on coils or, that’s the same, current deviation of a normal to a plane of orbit spacecraft from a direction on the Sun. Thus time numbers of data about values of temperatures have strongly pronounced oscillatory character with the orbital period of movement of spacecraft and with high level of correlation between them, and also dependence values of temperatures from the position of a plane of orbit of a spacecraft concerning the Sun.

The article provides data on the distribution in the Kinelsky District of the Samara Region of some members of the Mustelidae family (American mink, pine marten, forest polecat and steppe polecat) in three biotopes (lime-oak deciduous forest, fallow lands and fields, riparian areas of the floodplain in Samara River valley). It is noted that the traces of American mink were found only in riparian areas near the thawed patches and fishing holes where animals foraging. European pine marten occurs in all biotopes avoiding unforested sites, but the greatest number of traces was observed in the forest. Polecat traces were mostly recorded in the open areas. In the forest, they were observed every year, but in smaller quantities. The work also presents data on the population dynamics of mustelids in the Kinelsky District of the Samara Region in the winter period of 2005-2011.