REMARKS ON SOME CLASSES OF POSITIVE CONTINUOUS FUNCTIONS IN C^n

Here we prove two propositions providing sufficient conditions of belonging positive continuous functions in to classes and These auxiliary classes plays important role in theory of entire functions of bounded L-index in direction and bounded L-index in joint variables, where are continuous functions. They help to constuct general theory of bounded index for very wide class of entire functions, because for every entire functions with bounded multiplicities of zero points there exists a corresponding function or providing boundedness of L-index in direction or boundedness L–index in joint variables respectively. Our result requires uniform boundedness of logarithmic derivative in all variables and for belonging the function to class Q^n. Another result requires uniform boundedness of logarithmic derivative in directions and for belonging the function to class Q^n_b where is the complex conjugate vector to b.

EVALUATION OF CHARACTERISTICS OF RESISTANCE OF PROPAGATION OF CORROSION- FATIGUE CRACKS OF LONG-TERM OPERATED DRILL PIPES

The aim of the proposed article is to determine the patterns of the corrosion-fatigue cracks in long-term operational metal elements of drill strings (steel 45, 36G2S, 40HN) when drilling wells in corrosive environments (drilling fluid "Biocar", potassium polymer mud and on the air). Based on the obtained results of experimental studies, diagrams of cyclic corrosion crack resistance for the studied systems "metal - medium" were drawn. The cyclic crack resistance characteristics of long-used metals of drill string elements are determined - the values of constants (C and n) in power dependence of Paris, as well as the values of threshold and critical stress intensity factory. The influence of drilling mud of the corrosion crack resistance of the investigated metals of drill string elements was estimated quantitatively. In particular, in the environment of drilling mud "Biocar" the process of corrosion-fatigue crack development in the studied metals of the elements of drill strings is not significantly, in the range of 1-5%, differs from the development of fatigue crack on the air. Whereas in the potassium polymer drilling mud media, the rate of corrosion-fatigue cracks development in the investigated metals of the drill strings elements significantly, in the range of 15-35%, differs from the development of fatigue cracks on the air. It is established that under the influence of working loads the process of the corrosion-fatigue crack development in long-operated elements of drilling string is accelerated by more than 10% in the media of the potassium polymeric drilling mud than in the environment of drilling mud "Biocar".

STATIC STRAINING AND LONGITUDINAL OSCILLATIONS OF UNDERGROUND PIPELINE BUILT ON BLOCK FOUNDATION

The article considers the issues of forecasting the strength of underground pipelines, which are operated on seismically active sections of the route, composed of relatively rigid mobile blocks. According to the literature, the problems of the influence of the interaction of base faults on the stress state of the pipeline have not been studied to date. The aim of the work is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged basis caused by static or time-harmonious mutual movement of its blocks along the axis of the pipe in the presence of several faults. Boundary value problems for differential equations of static tensile-compression and steady-state longitudinal oscillations of a tubular rod with discontinuous right-hand sides are formulated. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetric displacement of the foundation blocks, the distributions of axial displacement and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations, are investigated.

ON LOCAL TWO-POINT PROBLEM FOR THE EQUATION WITH THE OPERATOR OF GENERALIZED DIFFERENTIATION

A local two-point problem with the oprator of Gelfond-Leontiev generalized differentiation with a complex argument is investigated. The conditions of unity and existence of the solution of the problem are obtained. It is proved that such conditions are satisfied for almost all (relative to Lebesgue measure) node of interpolation.

MODEL REPRESENTATIONS OF THE MELTS STRUCTURE DESCRIPTION BY THE MODEL OF HARD SPHERES

In the article the optimization of the oil and gas enterprise, a complex process both from the technological and from the economic point of view is investigated. It is noted that today the development of methods of mathematical modeling of physical processes, for example, in oil fields on the basis of theoretical research and modern computer technology is absolutely relevant One of the ways is to create new or improve existing mathematical models of processes occurring in oil and gas reservoirs, and calculate on their basis the characteristics of the process that optimize production. From this perspective, the study appears particularly relevant liquids in a narrow, purely physical and chemical aspects – namely melt. Various fluid models have been proposed to describe the equilibrium and kinetic properties of liquids (melts), as well as to interpret experimental results. Model representations are also used in solving integrodifferential equations that relate distribution functions to interaction potentials. It is noted that integrodifferential equations are a powerful mathematical algorithm for describing inhomogeneous dynamic models, but they depend directly on the efficiency of software that implements the proposed models. The model of hard spheres as simple fluid model proposed use. The reasons that allow you to choose this model as optimal were defined. Namely: the presence of analytical expression for the structural factor; application to describe the electronic and atomic properties of melts. The optimal methods for obtaining optimal values for the theoretical calculation of the structural factor of the proposed model were determined. As a result of the analysis of existence of correspondence between the calculated and experimental structural factors it is established. This led to the conclusion that the possibility of applying the model of rigid to calculate the equilibrium and kinetic properties of melts exists. It is determined that the model of rigid spheres could be used as an approximation to describe the structure of both one-component and multicomponential melts (liquids).

DEGENERATE BOUNDARY-VALUE PROBLEMS WITH A PERTURBING MATRIX FOR A DERIVATIVE

In the paper, there is considered degenerated Noether boundary value problem with a perturbing matrix for a derivative, in which the boundary condition is given by a linear vector functional. We have proposed an algorithm to consrtuct a set of linearly independent solutions of boundary value problems with a small parameter in the general case, when the number of boundary conditions given by a linear vector functional does not match with the number of unknowns in a degenerate differential system. There is used the technique of pseudoinverse Moore-Penrose matrices. Applying the Vishik-Lyusternik method, the solution of the boundary value problem is obtained as part of the Laurent series in powers of small parameter. We obtain conditions for the bifurcation of solutions of linear degenerated Noether boundary-value problems with a small parameter under the assumption that the unperturbed degenerated differential system can be reduced to central canonical form.

LINEAR CONJUGATION PROBLEM WITH MULTIPOINT NONLOCAL CONDITION FOR A PARABOLIC-HYPERBOLIC EQUATION IN CYLINDRICAL DOMAIN

The linear conjugation problem with multipoint nonlocal condition in the time variable for a mixed parabolic-hyperbolic equation of the second order in a cylindrical domain, which is Cartesian product of the time segment and the spatial multidimensional torus, is investigated. The conditions of the existence and uniqueness of а solution to the problem in the scale of Sobolev spaces are obtained. It has been proved that these conditions fulfill for almost all (with respect to the Lebesgue measure) values of the left node of the multipoint condition.

INVESTIGATION OF PARAMETERS OF HYDROMONITOR JET OF A BIT

The movement of drilling mud through hydromonitor nozzles is investigated in the work. On the basis of the theory of destruction of rocks by a liquid stream the necessary values of pressure on hydromonitor nozzles of a drilling head for concrete values of mechanical properties of the drilled breed are found. The results of the performed analytical researches were used for modeling of processes of movement of a stream of washing liquid through hydromonitor nozzles of a bit with use of the Flow Simulation CAD / CAM package of the Solid Works system. During the simulation following parameters were investigated: the location of the nozzles at different distances from the axis of the bit and from the bottom of the well, pressure distribution at the bottom of the well at the exit of the flushing fluid from each nozzle and the velocity of the jet and the wall of the well, the vorticity of the jets on the bottom and the walls of the well. According to the results of research design of the hydromonitor unit of the drilling head was improved and new tests were carried out in industrial conditions.

ESTIMATION OF THE VALUE OF OIL LOSS DURING THE SEALING OF THE LINEAR PART OF THE PIPELINE

The characteristics of the oil transportation system of Ukraine are presented, the emergency risks of domestic oil transportation pipeline sys­tems are established. The analysis of the accident rate of oil pipeline trans­port in Ukraine was carried out. The technique for estimating emergency oil leakages in the main pipeline depending on the energy characteristics of the fluid flow and changes in its level in the cross section is developed allowing to determine the volume of oil leakages into the environment from the de­tection of pressure drop to the establishment of stationary conditions of the pipeline operation and its final stop for the purpose of carrying out repairs. Based on the results of the calculations, the graphs which demonstrate the nature of the formation of soil pollution area by leakage from the pipeline are constructed. The linear part of the main oil pipelines is the most dangerous object, as all emergency situations are associated with emergency processes of dif­ferent intensity in the form of oil leakage into the environment and in fact are dangerous when system failures appear. The process and the time period for the formation of the ecological danger zone depend on the amount of oil leakage, its intensity. Emergency leakages of oil and petroleum products from pipelines enter the environment, which is often the soil, forming an area of gassiness, and then reach the surface, polluting the atmosphere.

METHOD OF PROCESSING RESULTS OF FACTORY EXPERIMENT

Two plans were used: classical and factorial (rational) during experimental research. Classical plan is used when the number of external independent factors is not more than two. Increasing number of external factors leads to using of rational experiment planning which allows to significantly reduce the number of combinations of these factors. For example, with four external factors that change at four levels according to the classical plan number of combinations 44=256. Rational planning of the experiment reduces number of these combinations to 16. To process results of the factorial experiment using two methods proposed by M. M. Protodiakonov and R. S. Yaremiychuk. The article presents a step-by-step method of processing the results of a factorial experiment with an example of simultaneous use of these methods. Comparing the results of processing, the authors believe that the best results are obtained using the Protodiakonov’s method. The authors tested two types of multifactorial empirical model of multiple correlation, one of which is given by the product of partial empirical dependences, the second – by the sum. Using these models there were found that the results of factor experiment processing should be represented by a multifactor empirical model, which is presented by the product of partial empirical dependences.