#### A balance of the homogeneous rod in an arc ellipse shape in the water stream

Abstract
Calculation method to determine the equilibrium conditions of the arc in the form of the ellipse, then streamlined homogeneous liquid.

The outer shell is an important constructive element of roller one-way clutches. Currently, for the calculation of the stress state of the outer shell using the mathematical models obtained based on the essential assumptions. In the article the analysis is carried out and recommendations about use of design mathematical models are made. It is established that at change of number of wedging rollers in a range from 3 to 10 there is a reduction of value of the maximum stress, and in a range from 10 to 20 – increase of stress.

The results of the solution of the integral equations of motion numerical method presented in dimensionless form related to the relative inertia of the particles and the relaxation time of the particle. It is found that when the increase in the relative inertia of the particles, decreases the coefficient of turbulent diffusion of the dispersed phase compared to the ratio of the carrier medium. Increase from-wearing leads to an increase of the coefficient of turbulent diffusion of particles. It is shown that the calculation of the coefficient of vertical diffusion of dispersed impurities in watercourses must take into account not only the turbulence characteristics of the carrier medium, but also the relative inertia of the particles.

The outer shell is an important component influencing on the working capacity of roller one-way clutches. The analysis is carried out and recommendations about use of mathematical models for calculation of deformation of outer shell are made. It is established that at change of number of wedged rollers in a range from 3 to 7 there is a nonlinear decrease of value of a radial deformation, and in a range from 7 to 30 its increase.

In this article, I determine the grouped hyperplane distribution of the affine space An (SH-distribution) and prove the relevant existence theorem. I perform internal normalizations of the main structural subbundles of the SH-distribution in first and second-order differential neighbourhoods. Normal and tangent affine connections of the main structural subbundles of the SH-distribution are introduced.

This article formulates the problem of simulating extreme processes in the Earth's low-latitude ionosphere and describes the model equation imple-mentation methods based on an electrodynamically coherent mathematical mo-del of the equatorial F-layer of the ionosphere.

This article considers the problems of information support and automa-tion of loading and unloading processes in the sea zone of multimodal con-tainer terminals (berthage). The authors present the organization and algo-rithms of automated loading planning and complete and partial container loading and unloading at the transit terminal are presented.

There is a quantum statistical model of prototropic tautomeic transformation caused by vertical transition between different adiabatic potentials with two minima divided by potential barrier offered. Formula for the probability function defining time of tautomer transformation without regard to vibronic relaxation is received.

Group of scientists of the Immanuil Kant Baltic Federal University (I. Kant BFU) in 1989 developed a three-dimensional code to study equatorial F-spread (EFS) studying. The Naval Research Laboratory (NRL, Washington, DC, USA) in 2008 developed a three-dimensional code to study equatorial spread F (ESF) also. Comparison of these models is made. Differences in number of ions and the accounting of electrons speeds and inertial terms are found.

An approach to the method of cyclic reduction for the system of equations with block-tridiagonal matrix of arbitrary dimension is presented. Formulas for elimination of unknowns in arbitrary order are obtained. Algorithms for the first and second boundary problems are described.

For solving systems of linear equations with block tridiagonal matrices there is considered an efficiency of multi-grid method with semi-coarse as smoothing iteration. Numerical results are presented.

The second-order curvature object contains the curvature object of the fundamental-group connection defined in the principal bundle; the curvature object of an affine connection over a manifold; second-order components. Differential comparisons for the components of the object of curvature of the second- order fundamental-group connection are made. These comparisons show that the curvature object forms a geometric object only in combination with components of the second-order connectivity object. In the general case, the object of curvature of the fundamental group connection of the second order does not form a tensor.

The Cauchy-type integral with a fixed point in the kernel is in the as-sumption that fixed point is on the exterior of a circle of RADIUS one. Set fields non-analyticity and the analyticity of the integral. Area non-analyticity naturally splits into two subareas , each of which the integral is calculated ac-cording to a specific formula. Non-analytical functions, which have integral Cauchy type with a fixed point in the kernel satisfies a certain differential equations. Using the method of linear differential operators is link integrals with a fixed point in the kernel with integral Cauchy type.

The problems connected to a technique of mathematical processing of measurements results in a laboratory practical work are considered. The purpose of measurements results processing is optimization of procedure of random error calculation.

The construction of an AG-code and the process of decoding are described by the Rimann-Roch spaces.

Various algorithms for finding of the order of Jacobian, their range of use and efficiency are considered.

Algorithms for constructing three-dimensional models of microseismic activity fields are described. The first approach is based on voxel models and involves the construction of polygonal surfaces of interpolated parameters of microseismic events. The second approach uses a triangulation algorithm based on the Delaunay criterion and α-shapes method. Software developed on the basis of the proposed algorithms, offers advanced graphical tools for the analysis and interpretation of microseismic multiparameter data

Results of passive microseismic monitoring of water injection into one of the wells of the carbonate deposits are presented. The maps of the spatial distribution of sources have prepared and the analysis of the dynamic parameters of microseismic events together with graphs of pressure and injection volumes has done. The possibility of operational control of the process of flooding is shown on the example of Northern Truva.

A system predator-prey is explored and the parameters, by which its operating is stable. Biological balance of the system species is defined by mathematic methods.

A quantum statistical model of intramolecular tautomeric transformation is offered, accounts for the vibration of a proton as a result of its interaction with the surrounding medium simulated by the quantized field of radiation. Effective adiabatic potentials of the proton are approximated by the parabolas of various curvatures. The estimation for the vibrational relaxation time and the formula for the constant of tautomeric equilibrium.

The mathematical model for research of the non-stationary processes proceeding in ionosphere and plasmasphere of Earth is presented. This model allows to investigate dynamics of interaction charged and neutral components of ionospheric plasma, and also to reveal a contribution of various processes to formation of ionosphere. Results of computing experiment indicate strong dependence of electronic concentration on high-rise distribution of nitrogen. The accounting of oscillatory excitement of molecular nitrogen leads to noticeable variations of electronic concentration and temperature at ionosphere F2 layer heights and improves a consent of results of model calculations of variations of electronic concentration with experimental data. It is shown that the contribution of small component in aeronomiche processes is essential.

Wave propagation through coupled elastic-acoustic media for marine seismology, comparison of reflected waves in fluid-filled and infinite thin crack model and underwater objects detection are simulated using discontinuous Galerkin method on triangle unstructured meshes.

In this article a representation of the elements of the Jacobian of a Picard curve is considered, which allows us to construct an algorithm for the reduction of divisors with complexity O(deg(D)). Addition of divisors can be performed using the reduction algorithm.

In article is stated the method of acceleration of procedures of addition and doubling points Jacobian of a hyperelliptic curve in affine and projective coordinates. Corresponding modified Miller algorithms are developed. In affine coordinates an expense for group operation of doubling there are more than expenses for group operation of addition, therefore it is more favorable to realize consistently two additions, than doubling and addition. Estimations of efficiency of the modified algorithms are received.

The results numeral analysis structure of flat vertical lager that is formed triangle prism are presented. Complex analyses had unequivocally revealed presence of quasiperiodic structure in distribution particle. Is being offered a hypothesis about the nature of this reveal.

A multiple RuO2-chip thermometer based on commercial Vishay RCW575 chips for applications in 0,02—30 K range is proposed. Possible design and packaging of the sensor are suggested. Thermometer saturation and thermal resistance of our sensor are measured and compared with a single-chip configuration and commercial Lakeshore ROX-102A thermometer.

The network structure of formalization of the technological scheme of mining operations by dragline was offered. The adaptive algorithms based on CASE-statements and run-time libraries are applied to carrying out mathematical calculations under control of similar structure. Division of calculate modules into a number of stages—formation of tables of basic data, a formation of tables of operating variables, calculation and record of resultant parameters and geometry in tables was proved.

The modernization of the metal tile production line is described. It was required to transfer the line to domestic components and introduce devices for fine lubrication of metal tiles to improve the quality of products and reduce the number of rejects. A parametric model of the hydroelectric station was built, a mathematical model of the temperature change inside the hydroelectric station was developed, the type of transfer function was determined, a block diagram of the control algorithm for a metal tile production line was developed, software was developed for the equipment of the "Овен" brand of an automated line: a logical controller PLC160 and an operator panel SP310-R.

The paper considers various aspects of attracting customers to use SaaS solutions from company X. As a test solution, an advertising company aimed at the Latin American region was considered. Based on the obtained data, a mathematical model was built that showed the most "weak" points in the advertising company and allowed us to evaluate its effectiveness. As a result, the process of attracting customers was adjusted, and its effectiveness was increased.

The algorithm of the solution of the task of permission of signals in communication systems with not orthogonal carrier frequencies is provided. A basis are provisions of the theory of optimum reception in the annex to communication systems. It is shown that the system of equations of credibility allows to solve for communication systems the problem of permission of signals in the field of their nonorthogonality. It is shown that the solution of the task of permission of signals in communication systems can be consolidated to the task of filtering with original pulse and frequency responses.

The paper is devoted to issues of semiotic approach for the design of information security systems, based on knowledge extraction from semistructured sources. The problems of developing of optimal variants for the prevention of threats to decision support systems. The technique continuous monitoring of text messages, identify the events and situations and develop scenarios possible development of crisis situations is proposed.

The classification of machine learning methods is given depending on the technique of learning, the main algorithms of machine learning and the scope of application are considered. Particular attention is paid to reinforcement learning based on Markov decision processes.

The paper considers the main mechanisms of non-financial attraction and customer retention in the banking sector. The following factors are analyzed: convenience of the bank application; speed and quality of solving customer problems; technological aspects of the bank; special client programs and privileges; the availability of banking tools. Formulated actions to increase customer loyalty of banks.

A mixed derivatives influence in during three-dimensional simulation of ionosphere by difference methods is considered.

Moisture transport in soils under conditions of drainage on the basis of an agreed account of the capillary and the description of moisture transfer on porous surfaces is simulated.

Norden 1st and 2nd kind inner normals of the L-, E-subbundle of a special class (SH -distribution) of the regular threefold distributions (H -distributions) of the projective space are constructed.

A nonlinear correction of the finite-differential scheme for solution of the cross convection-diffusion equations within models of the Rayleigh — Taylor instability in the equatorial region of the Earth ionosphere is considered. For test problems the experimental value of the approximation order of the offered method of non-linear correction of the finite-differential scheme for different types of limiters is received numerically.

Differences methods of the approximate solution of the two-dimensional equation of ions diffusion with the mixed derivatives and the first derivatives of a divergent look are considered. Test calculations on a modeling task with the known analytical decision are carried out. Operability of algorithm is shown and the estimation of speed of its convergence is given.

Compact presentations for solution of the generalized Padè problem are presented, that have been known only for the Padè problem (so called compact Nutall presentation). Using them determinant presentations for the approximants [M – 1 / M], [M / M] и [M / M – 1] were obtained.

The paper studies design and development of expenditure accounting system of an online shop using the fuzzy sets theory and fuzzy logic. It has also considered the construction principles of complex information systems and formulated the requirements for the system under design. Apart from that the authors dwell upon the fuzzy problem of multi-criteria optimization on basis of interval estimation. The program interface has been designed and main principles of work created by informational system have been described.

The paper introduces internal affine (tangent) and normal (centroprojective) connections on normalized (Norden’s framed) hypersurface n-1() Pn in its various subbundles. Coverages of the corresponding curvature 2 forms and curvature tensors of its connections are given.

For solving systems of linear equations with dense system matrix there is presenting a parallel algorithm of SOR-method. There is showing OpenMP-programm for the parallel algorithm. There are giving the results of numerical experiments.

This paper presents an implementation of 1-Wire communication interface based on STM32 microcontroller with the usage of hardware timer. Implemented low-level library uses minimum of MCU resources, has address search functionality and can be applied for polling sensors in wired networks based on this interface.

This paper is devoted to contemporary the concept of developing a software module that calculates the radio wave propagation zone for the Global Maritime Distress and Safety simulator complex. Adjustments were made to the calculations that optimize the operation of the module. The algorithm is implemented on modern cross-platform approach. The main result of the developed module is demonstrated.

The problem of transformation of some elementary closed and non-closed curves by means of successive iterations of conformal mapping is considered. Since the analytical description of the equations of images for some conformal mappings is quite complicated, it is convenient to use the Maple computer algebra system to implement the iterative process.

The article presents the architecture, basic elements and implementation of the prototype of the tool for the development of functional hybrid intelligent systems with a heterogeneous visual field. Such systems are capable of simultaneously simulating collective verbal-symbolic reasoning and activating the visual-figurative reasoning of users. The use of such systems in the practice of solving problems, in particular when managing regional electric networks, will allow users to «see» the problem situation and its possible approximate solutions, which can subsequently be justified and refined by the methods of logical-mathematical reasoning.

Complicating diagnostic tasks inevitably lead to the mistakes during decision-making and to the increasing complexity and workload of the features for automated decision in heterogeneous problem environment. Researches in this field are focused on formalization and exploration of the processes of finding, identifying of the heterogeneous diagnostic task and the synthesis of the method for its solving. This paper presents the results of the development of the algorithm for the synthesis of the method for solving of the heterogeneous diagnostic task, which establishes the integrated model under the approach of hybrid intelligent systems. Such model is relevant to diagnostic situation and combines the set of heterogeneous models of the theoretical, professional knowledge and the experience.

The methodology of integration of computing and natural experiments on lecture and laboratory researches is offered at studying physic-technical disciplines.

The article is devoted to the development of a small-sized antenna system characterized by uniform input impedance over the entire operating frequency range, and structurally implemented on the basis of the fractal structure, as well as the optimization of its parameters in order to improve the basic operational characteristics of the system.

The diffuse pollution is considered taking into account the lateral inflow. In the calculation scheme, the impurity has a small inertia, the deposition of particles is steady. Background values are set as initial conditions for the concentration and in the initial section of the watercourse, and the intensity of the diffuse discharge along the shoreline is set. The results of solving the boundary value problem by numerical method in Mathcad are presented. The results of the study of the profiles of dimensionless concentration of the precipitating admixture are shown. Graphs are presented in dimensionless variables.

The article analyses the peculiarities of indirect observation of NQR nitrogen signals and determines the conditions for the enhancement of

spin systems efficiency in static magnetic fields. It allows keeping records of the 14N spectra in the range below 1 MHz at room temperature.

This method may be used for researches on low isotope matters.

A simulation of dynamical anthropogenic perturbations of ionosphere-magnetospheric plasma, in particular a moving of ions O+ and H+ is considered.

Some results of numerical modelling of mechanical factors of cranial-cerebral injury caused be percussive stress are described. The usage of grid-characteristic method on unstructured grid is discussed. The authors intro-duce some mechanical-mathematical models of brain teguments and provide results obtained using different models.

In this paper we discuss electrical manipulation of a spin an electron in quantum dot within a weak magnetic field. Approach to describing this process is based on Lewis — Riesenfeld dynamical invariants. Necessary conditions of a spin-flip process are derived.

We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluids.The problem reduces to consecutively solution three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations and one first-order ordinary differential equation for a viscous fluid.

Check of working capacity of multidimensional non-stationary model of F-region of ionosphere on the basis of comparison of the given modeling calculations and the data received from empirical model IRI is spent.

Features of physical and chemical conversions in the reacting powder system NiO-Al were investigated by computer simulation methods.. Multivariability of the synthesis of nickel aluminides in powder systems with varying degrees of concentration inhomogeneity is taken into account. The estimates of the state parameters of reacting system at all stages of physical and chemical transformations was obtained.

The authors construct Foss and Green's normalizations in Norden's sense internally invariantly. The research sets tangent affine connections and tangent central affine connections of the main structural subbundles of H(L, L)-distribution of affine space.

The authors study the application of calculation method of radio signal attenuation in atmospheric gases, proposed by International Telecommunication Union [1]. The paper describes the algorithm of attenuation calculation, created in MATLAB program and calculated resulting attenuation for latitudes are greater than 45°.

The problems that arise when setting the tasks of active audit of information security of automated control systems for technological processes when using data transmission in real time at the enterprise are considered. The features of the methodology for determining the safe active audit of automated process control systems when they work together with other systems are indicated. The features of determining the parameters of a secure audit of multi-level APCS are considered.

The article proposes ways and principles of creating automated training systems using the example of a training program for studying a radio monitoring and signal analysis complex (Kassandra class) for training information security specialists, which can be used by educational organizations and training centers conducting training in this area.

The problems arising during the audit of automated control systems for technological processes and the corporate network of an enterprise are considered. The features of the formation of the audit model of automated control systems in the presence of built-in SCADA-systems are considered. The possibilities of using the audit model in the operation of control systems in real and protected time modes are considered.

This is the sixth paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices andxed point theory. The sixth paper of this series deals with the basic results in the theory of !-algebraic systems over quemirings generalizing the classical context-free grammars generating languages overnite and innite words. The presentation of these results is based on continuous starsemiring-omegasemimodule pairs. We dene !-algebraic systems and characterize their solutions

of order k by behaviors of algebraic nite automata. These solutions are then set in correspondence to !-context-free languages. Then we introduce rational and algebraic transducers, and abstract !-families of power series over quemirings and prove that rational and algebraic power series of nite and innite words constitute such abstract !-families of power series.

This is the fth paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices and xed point theory. The fth paper of this series deals with the basic results in the theory of nite automata over quemirings generalizing the classical nite automata accepting nite and innite words. The presentation of these results is based on semiring-semimodule pairs, especially on Conway semiring-semimodule pairs. A Conway semiring-semimodule pair is a pair consisting of a

Conway semiring and a semimodule that satises the sum-omega equation and the product-omega equation. We dene these Conway

semiring-semimodule pairs and state some of their important properties. Then we introduce nite automata over quemirings and prove a Kleene Theorem. Furthermore, we introduce linear systems over quemirings as a generalization of regular grammars with nite and innite derivations, and connect certain solutions of these linear systems with the behavior of nite automata over quemirings.

This is the seventh paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices and xed point theory. The seventh paper of this series deals with tree (series) automata and systems of equations over tree. The main topics of the paper are the following. 1. Tree automata (resp. nite, polynomial tree automata), whose behaviors are tree series over a semiring, and systems of equations (resp. nite, polynomial systems of equations), whose least solutions are tuples of tree series over a semiring, are equivalent. 2. A Kleene result: the class of recognizable tree series is characterized by rational tree series expressions.

This is the eighth paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices and xed point theory. The seventh paper of this series deals with tree (series) automata and systems of equations over tree . The main topics of the paper are the following. 1. Pushdown tree automata, whose behaviors are tree series over a semiring, and algebraic tree systems are equivalent; moreover, the class of algebraic tree series is characterized by algebraic tree series expressions (a Kleene result). 2. The class of recognizable tree series is closed under nondeterðministic simple recognizable tree series transductions.3. The families of recognizable tree series and of algebraic tree series are full abstract families of tree series (full AFTs). 4. The macro power series, a generalization of the indexed languages, and the algebraic power series are exactly the yields of algebraic tree series and of recognizable tree series, respectively; there is a Kleene result for macro power series; the yield of a full AFT is a full abstract family of power series.

The task is to define a function EH(λ), such that if { n } are the points of the continuous spectrum of operator H and n λ λ , then EH(λ) is defined and is non-zero.

In the present paper the generalization of Legendre polynomials with the help of generating function is studied. The explicit form of considered functions is found. Some special cases are considered. Particular attention is paid to the case when the parameters defining the studied functions are different, symmetric about zero real numbers. Some properties of constructed functions are obtained. Based on the results of numerical experiment a hypothesis about zeroes of these functions is stated.

Described and analyzed in terms of computational efficiency different types of pairings on hyperelliptic curves, especially on curves of genus 2 and p-rank one for the cryptographic applications.

It is considered a possibility of generation of exact solutions for Friedman equations by Darboux transformation, for which Cardy — Verlinde formula is valid. Two modifications of Darboux transformation are offered, which let generate such solutions. Exact solutions are obtained, for which Cardy — Verlinde formula is valid at least near some singularities.

The main problems the process control system design control of complex objects in CAD. The main structural solutions and implementation features of subsystems and modules developed by managing complex УК-01. The problems of the universality of the Criminal Code with respect to data sources, build and implementation of the original information and special software УК-01.

The non-cyclic geometric phase of nuclear quadrupole resonance (NQR) signals, which is induced by the trajectory of nuclear magnetization motion upon the external pulse r. f. excitation, was studied. Analytical expressions for the geometric phases of NQR signals were obtained for the case of nuclei with spin I = 3/2. The powder sample of KClO3 was served as a material for experimental part of studies reported. It was proposed an alternative variant of the nutation experiment, which allows one to obtain the asymmetry parameter η on the base of locations of frequency singularities in the nutation phase spectrum.

On the basis of the analysis of principles of antennas’ system work on radiation the way of their operative emergency definition taken as a principle the developed device is developed. Introduction of a quantitative estimation of transmit system efficacy, will allow to solve a problem of automatic radio stations᾿ control under influence of negative factors.

The article tackles the problem of the reconstruction of ionospheric electron density height structure by means of GPS/GLONASS systems.

Hierarchies of smooth manifolds in the form of sequences are given. The sequence of zero order consists of the parallelized manifold, Lie group and Abelian group of Lie. Each of three sequences of the 1st order for the ho-lonomic, semi-holonomic and the non- holonomic smooth manifolds includes base of the parallelized bundle of linear coframes, in other words, base of space of expanded affine connection, base of space of affine connection torsion-free and affine space.

For describe the hydrodynamic and thermal processes in the ladle in the time of blowing argon Steel developed a mathematical model of convective heat transfer in the Boussinesq approximation. We give a statement of the problem of this description, the translation model in dimensionless criterial form diver-gent representation in the form (Θ, ω, Ψ)-system.

A method of filtering radar pulse on the background of the focus obtained by frequency interference. The basis of the method are the principles of the theory of optimal reception and position of the linear space of signals. Derived the basic expressions when filtering of the signal strength in the area of orthogonality of signal and noise, and their non-orthogonality. Equations for impulse and hour-tonyh characteristics of filters.

Presents the results of model studies of the possibilities of a filtration of pulse centered on the background frequency interference maximum likelihood method. Basis are the principles of the theory of optimal reception and submission of the linear space of signals. Shows odnosno-ness of the solution of the filtering problem in the field of orthogonality of signal and noise, and their reorthogonalize . Submitted to evaluation of the dynamic range of the filter.

A mathematical model of the mechanism of anti-symmetric vortex at the confluence of fresh water to sea water, observed, in particular, the output of the Baltic Canal connecting Visla Lagoon to the Baltic Sea is constructed. It is shown in particular that the main reason the vortex formation in this case is the Coriolis force. Also analytically calculate the exact dependence of circula-tion rates from time to time for the three simplest forms of "language" of the intrusion of fresh water.

The article examines the influence of potassium impurity on the critical behavior of Na1-xKxNO2.

The influence of the Coriolis force on the peculiarities of the formation and propagation of forced sea waves is studied. The generation of long waves by a focused monochromatic source is observed. Two cases — the low frequency and high frequency waves are investigated.

An integrated approach to solving problems of the transport type associated with the construction of transport routes is presented. We offer to determine the optimal path, based on a new technology - evolutionary modeling by the using of methods inspired by natural systems. The critical issue is a reconciliation of the concepts of biology, information technology and artificial intelligence

Results of the early establishment of a system fault diagnosis equipment and principle of operation of the hardware simulation tools such faults.

Results of the development control unit individual heater and individual room climate are presented.

The article discusses Two mathematical models of housing and utilities services organization as an example of a managing company are considered. The first model is based on balance equations of the organization. It takes into account and systematizes income and expenses of a managing company. The second model is presented in the form of the optimal control problem. Wherein, the discounted profit of the company was selected as an optimization element, whereas the costs of housing modernization were chosen as a control element.

In this paper were investigated the change of parameters of structures of thin film during ion implantation. Thickness of thin films before and after ion implantation were investigated by X-ray reflectivity. Also, crystal structure, average crystallite size and lattice constant were investigated by X-ray diffraction. The possibility of using ion implantation technique as method of changing grains size in structures was demonstrated.

This paper presents the results of studies of the parameters of optical components of a glassceramic material CO-115 by X-ray diffractometry. The possibility of technological precision quality control glassceramic parts using X-ray diffraction methods. The direct dependence of the temperature coefficient of linear expansion of the integrated intensity of the X-ray diffraction peak at the glassceramic.

Numerical experiments are performed to investigate the dispersion distortions of chirp pulses propagating in the ionosphere with taking the three-dimensional non-uniformity, anisotropy, and dispersion of ionosphere in dependence on geophysical conditions into account. Propagation, absorption,and the time delay of ordinary and nonordinary waves are analased.

The object of the research is a power supply system based on a solar power plant with a non-stationary load on the example of an automatic trading unit (vending machine Coffemar G-546). The aim of the work is an experimental study of the influence of solar radiation power dynamics on the volume of electricity generated, the study of the energy balance of the test facility, the study of the possibilities and development of recommendations for optimizing energy losses in the low-voltage mode of the equipment.

The availability of a suitable web-application (a full-fledged program that interacts with users (stakeholders), meets their requirements and returns the expected results) greatly simplifies the process of monitoring the construction of residential building. The main stakeholders involved in the life cycle of the residential building are considered, the interface of the web-application and the functionality for linking the database with the modules of this application are developed.

The equivalent circuit is developed to describe the electrical processes in the receiver path of the leaky wave antenna. The line has the slot-type radiator which is considered as a resistive-capacitive non-uniformity. The slot in the waveguide wall is considered as non-uniformity of resistivecapacitive type. The system of equations is composed and solved to investigate the balance of power in the receiver path and found the electrical parameters of the scheme.

Analytical comparison of hyperbolic system consists of four equations for moments of the distribution function of relativistic electron beam (REB), the modeling transportation processes in the gas environment and the equations of gas dynamics of ideal polytropic gas was carried out. The found analogy between these models allowed to specify mathematical statement of a problem for REB and to facilitate a choice of edge conditions of the task.

Mathematical models for an estimation of quality of road-building materials are considered. The mathematical model of the modern asphalt-concrete factory with several asphalt-mixing installations is constructed. The technique of definition of reliability of work of a factory on release asphalt-concrete mixes is given.

A mathematical model of filtration of moisture in heavy soils. The transfer of a film of moisture on the surface took into account.

The paper presents a description of three levels of visual meta-language developed for hybrid intelligent systems of electrical networks management: 1) tasks and problems; 2) patterns for expert reasoning; 3) integrated models of collective intelligence. Visual metalanguage qualitatively changes the work mode of a managed subject, allowing them immediately to recognize the problematic situation and «see» its solution without logical inferences.

The article offers a new, non-contact method of measuring the specific electrical resistance of liquid metals in the high-temperature range, which is exceptionally simple. The essence of the method is the measurement of the electromotive force induced by a high-frequency electromagnetic field in two circuits of different diameters placed coaxially in the middle of a cylindrical sample, which is a thin-walled ampoule filled with some low-melting metal. The authors substantiate the feasibility of a contactless method for measuring the specific electric conductivity of both solid and liquid metals in the hightemperature range. Result-processing methodology is given as well as the recommendations on the optimal geometry of the contours and the sample for increasing the measurement accuracy.

The article is dedicated to the methodological bases of the application of digital electronic technologies in engineering pedagogic on the

example of complex approach to teaching in the framework of electrodynamics processes in real and virtual digital spaces.

The article considers the peculiarities of research and education activity in professional digital environments.

An optimization procedure for constructive parameters of the log-periodic C-band antenna developed in the patent No. 2571607 “Microstrip logoperiodic antenna” is investigated. The electrodynamic model of the log-periodic microstrip- type antenna for the C-band has been developed.

Problems of erosion of elements of stationary plasma electric rocket engines are considered. Modern tasks require the engine significant resource characteristics, confirmed by long-term ground tests. In the paper, the possibility of applying accelerated tests for solving the problem of confirming the correspondence of the engine to the required resource characteristics is justified.

This article provides results of the cathode of stationary plasma engine thermal vacuum test with various operating modes simulated, a thermal calculation and the cathode thermal mathematical model verification. Based on the calculations, the cathode thermal model and operating performances were assessed, the most efficient required cathode life time characteristics were selected, which are related to the cathode heater power and operating time with provision of emitter optimal temperature in the automatic mode and welded joints leak-tightness. It was determined that the minimum heater power for cathode start-up is 60 W, the time to prepare for a start-up is 140 sec. To improve the cathode stable operation it is recommended to replace the tail piece and getter cover material for Molybdenum М99.95-МП.

Proposed project content of the laboratory practical work on atomic and quantum physics as a subsystem of professional education for future engineering physics.

There is described multifunctional surface small aperture aerial technology of microseismic monitoring. This technology is used for monitoring of hydraulic fractioning, fluid injection and for other well interventions. In addition it allows to describe crosshole block discontinues structures of collector in the mode of long passive microseismic monitoring. First in the world, there is presented crosshole block discontinues model of hydrocarbon field obtained based on microseismic monitoring.

The special class of the threefold distributions of the projective space Pn — VH -distribution — is considered. In each center X of VH -distribution the incidence relation of the elements of the -, M-, H-subbundle has an appearance X r Mm Hn1, where r m n 1. This class is characterized by the fact that the pairs (, ), (L, ), (M, E) of the main structural subbundles of this threefold distribution are mutual. Invariant dual normal connections induced in bundles of the 1st and 2nd kind normals of the L-subbundle of this VH -distribution are examined.

In projective space a Grassman-like manifold of centred planes is considered. The normal affine connection, associated with the manifold, is set in generalized fibering. Field of the affine connection object defines torsion and curvature tensors contained one elementary and one simple subtensor every. A canonical case of normal generalized affine connection is considered.

Necessary and the sufficient condition almost periodicity of conversion of the Bochner in Banach space is found.

Norden inner normalization fields of basic structural subbundle of hyperband distribution are constructed in second order differential neighborhood of affine space. It is showed that first order normal (L-virual affine normal, Blashke normal, Trenson normal) corresponding to each of subbundle belongs to the same sheaf in any center A. Sheafs of second order normal of Λ-, L-, H-subbundle correspond to them in the Bompiani–Pantazi bijection. Analytical coincidence features of H -distribution and its Λ-, L-, H-subbundle was clarified.

The Laptev projective structure of the 1st order presented a fibering of special linear coframes with multidimensional gluing is considered. The Laptev linear connection by means of the object containing a tensor is set in this fibering. If the tensor vanishes we have preprojective connection from which canonical connection is marked out. The Cartan projective connection and its canonical version are obtained from a projectivity condition. On the other hand, the projective structure is presented in the form of the principal fiber bundle of the special center-linear coframes. The giving fundamental- group connection in this fibering is made by means of the center-linear connection object, not coinciding with the previous objects of connections.

The author pioneers to study a special class of the grouped hyperplane distributions — the H(, L)-distribution of affine space. He introduces Bompiani — Pantazi correspondences associated with the main structural subbundles of the H(, L)-distribution of affine space. Norden’s normalizations of the main structural subbundles in the differential 1st and 2nd order neighbourhoods of H(, L)-distribution are constructed.

Modern education requires different approaches to improving the efficiency of services for citizens in the public information centers. The article focuses on the methodology for a queue processing and, in particular, on automatic query distribution. The authors developed a system of management quality assurance.

Mission and proof of existence theorem for hyperband m n SH A which carrier conjugated system (; * ) of planar elements are examined: the tangent subbundle of (; * ) -planes (-subbundle) and the tangent subbundle of lines (* -subbundle). Internal beams of normalizations of hyperband m SH and its tangent subbundles in the second-order differential neighborhood are constructed.

It is proved that mean value of almost periodic function with values in Banach space is an internal point of a solid cone.

The article describes numerical modelling of fluctuations of an aerosol column in pipes at resonant frequencies. The author suggests a mathematical model of dynamics of the heterogeneous medium-mix with approximately equal component mass fractions. The mathematical model suggests the solution of a dynamics equation system for each of the mix component. The carrier medium is a viscous, compressible, heat-conducting gas. The dispersed component of the aerosol is described by the equation of conservation of average density, the equations of the pulse components conservation, the equation of energy conservation. The mathematical model considers interaction forces of gas and particles of aerosol, as such forces is considered, Stokes's force, Archimedes force and force of the attached masses, as well as heat exchange intercomponent. Within the system of the equations of mathematical model, eight equations were solved by means of the final and differential algorithm implemented as a program code. The equations of mathematical model were complemented with the corresponding entry and boundary conditions. Having obtained the numerical model, the author studies the regularities of the redistribution of the aerosol dispersed component density of in wave fields. The research reveals the influence of droplet size on the distribution of the dispersed component of a multiphase medium in the process of resonant oscillations in pipes.

The article is devoted to the definition of methodological approaches to the development of multi-channel duplex radio communication systems that ensure reliable operation on a surface vessel. The research provides analytical expressions for the calculation of the possible number of transmit-receive channels in the model, depending on the signal spectrum width in the channel. The proposed software allows you to quickly calculate the parameters of the communication system.

Seismic response from the cluster of vertical oriented cracks is simulated using grid-characteristic method on parallelepiped structured meshes. Synthetic seismograms and wave fields are calculated. The structure of the response including dependency on type of saturator (gas, fluid) is analyzed. Numerical experiments showed the effect of high-frequency daisy-chain wave’s generation from 3D periodic structures.

It is shown that the first four primes 2, 3, 5, 7 generate finite subsets of primes, assuming the principle of interchangeability. In is established that any prime p(11 p 41, p 19), added together with two preceding primes generates a prime and that any prime p (5 p 31, p 13), added together with two consequent primes generates also a prime.

For the first time we used a global three-dimensional theoretical model of the thermosphere-ionosphere system for the description of inhomogeneous anisotropic medium in the simulation of radio wave propagation. It is shown that the results obtained with joint using GSM TIP model and radio wave propagation model adequately describe HF radio paths in the Earth's ionosphere in quiet conditions and at the recovery phase of geomagnetic storm.

The collision of polymer composite parts with a steel hammer is simulated using grid-characteristic method. To verify the method a comparison with analytics for distribution of spherical explosion in a homogeneous medium is given. The potential fracture zones in composite parts are analyzed.

Wave processes in elastic-acoustic problems are simulated with the help of grid-characteristic method, in particular, for the offshore seismic prospecting. We consider systems of water-soil-hydrocarbon-bearing layer and ice-water-soil-hydrocarbon-bearing layer

Processes of development of instability of Rayleigh-Taylor in the equatorial region of the ionosphere from accidentally given small perturbations of lower part of F-layer of the ionosphere

The algorithm of the numerical realization of a fundamental solution of a Cauchy problem for the one-dimensional Schrodinger equation with polynomial potentials is described. The stationary Schrodinger equation for a proton in the double potential well is solved by using Ritz variation method. The Green’s function is formed on a discrete spectrum of these solutions and after that the fundamental solution of the non-stationary Schrodinger equation is numerically calculated and applied to compounds with intramolecular hydrogen bonds.

Some results of numerical simulating of the problem of detecting of ultraweak diffractors in a complex acoustical medium are represented. The term “ultraweak” here means that the diffractors are not determined by standard depth migration. To solve the problem of detecting we use two procedures: Reverse Time Datuming (RTD) and Common Scattering Point (CSP). The first procedure (RTD) extends (synthetic) wave field from the day surface down to some level that is sufficiently close to diffractors. Then the diffractors are determined by CSP-method. The numerical model of an acoustical medium and synthetic data were obtained in Shell company. Further processing has been performed in RIAIMG of Immanuel Kant Baltic Federal University.

The work is devoted to the problem of determining small sound speed fluctuations in glandular tissue for specific breast model (2D). Our approach is based on visualization of acoustical medium (inclusions and unknown inner boundary between fat and glandular tissues) and determination of sound speeds in inclusions using kinematic argument. The results of numerical simulation (2D) of the problem are presented in the paper.

The problem of 1D acoustic wave initiation by a rise of water masses is formulated as a boundary problem at half space . The atmosphere is modeled as a multi-layer gas with an exponential structure of density in each layer. The boundary conditions at determine the direction of propagation, by link between dynamic variables (pressure, density, and velocity) of the wave. It defines the dynamic projection operators on the subspaces of z-evolution for each layer. The universal formulas for the perturbation of atmospheric variables in an arbitrary layer are derived in frequency and time domains. The explicit expressions for vertical velocity are built by the stationary phase method considering z as large parameter. The resulting formulas can be used to calculate the ionospheric effect by the explicit formula for electron density evolution. This set of explicit relations form a base for a quick algorithm for early diagnostics of tsunami waves.

Environmental protection is a global problem many research works have been devoted to finding ways of reducing the anthropogenic load on the environment. This article describes an algorithm of an analytical system for the

It is shown that the equations of Gurvitz and Mozyrsky for a system consisting of a qubit interacting with a fluctuating environment in certain conditions are reduced to evolution equations of the qubit. Such evolution equations for the qubit can be generalized to the form, which implies the existence of entangled states of the combined system. Among these entangled states two are symmetric, and two — antisymmetric. One symmetric state is stationary.

We study the Darboux and Laplace transformations for the Boiti — Leon — Pempinelli equations (BLP). These equations are the (1+2) generalization of the sinh-Gordon equation. In addition, the BLP equations reduced to the Burgers equation in a one-dimensional limit. Localized nonsingular solutions in both spatial dimensions and anti ”blow-up” solutions are constructed.

This paper presents a new method for analysing complex NMR spectra. This method is based on creating entangled spin states of a selected group of nuclei. The approach is tested through analysing the NMR spectrum of ethyl alcohol.

Integral systems with four independent variables have special signifi-cance in mathematics and physics. The discovery of inverse scattering method played an important role in reconsidering the place of integrable systems of nonlinear partial differential equations in mathematical sciences. The search for a systematic approach to developing exact solutions of such systems has become one of the main problems in the theory of integrable systems.

The paper analyzes the advantages of the CRM system when it is used in the activities of retail stores. Seven main advantages were identified through a systematic analysis. The analysis of the requirements for the CRM system implemented in the retail enterprise is performed. According to these requirements, it is possible to select the system that is most suitable for a particular store.

The article deals with the problems that arise when detecting network attacks using intrusion detection systems in the corporate network of an enterprise. The features of the formation of signatures of network attacks are considered. The problem of coincidence of parameters of network intrusions and parameters of damaged packets is investigated. To assess the suitability of the rules for detecting network attacks and their subsequent control, a method for upgrading the component composition of intrusion detection systems has been redesigned. A method of mathematical evaluation of the suitability of the rules for detecting network attacks is considered.

We demonstrate that such distinct equations as the KdV, mKdV, NLS as well as the Calogero–Degasperis, Toda and Volterra equations can generated from each other via the discrete symmetries chains. Interestingly, the key ingredient in this process is none other but the famous KP equations.

A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: the impacton. The explicit form of the curvature and torsion of corresponding vortex filament are calculated.

Some multiprocessors realizations of the α–β-iteration algorithm for solution of five-dots difference equations systems are considered.

A variant of multigrid method for solving large systems of linear equations with block tridiagonal matrices that have higher robustness properties is presented.In this method the construction of coarse grid correction operators is based on approximation of the Schur complement. Numerical experiments show high efficiency of presented methods.

A preconditioner for large systems of linear equations based on an incomplete block-decomposition for a block-tridiagonal matrices is considered. This method generalizes methods are developed by Buzdin and Wittum [1; 2]. A method of choosing quasioptimal parameters for consequences of tangential and two-frequencies decompositions based on analysis of model problems is developed. It’s convergence rate is better than ADI’s convergence rate in commutational case..

Difference methods an approximate solution of a three-dimensional equation of ions diffusion with mixed derivatives and divergence first derivatives are considered. The task is reduced to a chain of three two-dimensional parabolic equations on base of the summary approximation method. Difference operators are constructed, and an analysis of its properties, test calculations and an estimate of a mixed derivatives role are carried out.

For backbone complex of the human’s spine with alternative of a cuneiform strain mean backbone the stabilizing rigid lamina (for front and

back abutment complexes) holds optimization of stiffness of stabilizing of a lamina Ссt1 on an objective function of offset 2 backbone, at its sufficient mobility.

Concerned issues are related to the modeling of high speed impact with different variants of the smoothed particle hydrodynamics method and applying this method to the solution of problems of mechanics of the deformed solid body.Results of solution of the problem of disintegration of discontinuity were obtained and comparative analysis was performed.

New exact solutions are obtained for a spatially non-local wave equation with sources. The results are set out in the terms of the heat transfer theory. The non-locality of the problem is determined by the value of the fourth spatial derivative. We considered two types of volume energy sources which are alternating with respect to the temperature. For a technical source the derivative is positive, since «higher» temperatures arise from the energy release. For a biological source the source function is negative inclined, because a biological tissue gives off heat in the region of «lower» temperatures. The external influence on a non-local medium is simulated by spatially nonuniform energy source, and we have considered five types of such sources. The analytical solutions are presented in the finite form. The effects of monotonous and nonmonotonous (impulsive) reonomic sources are compared. The conditions for a transonic transition are indicated for the wave of perturbation in the temperature set. Resonance occurrences in the system «medium — energy source» are studied. The limits of oscillation stability/instability are determined. We found a dimensionless criterion including the inclination of the source function and the parameter of the medium non-locality. The criterion affects the correlation «oscillation frequency — fading parameter».

A method for construction of exact cosmological solutions of Einstein equations is developed. The method is based on representation of these equations as a second-order linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants, using any known solution. Also it is shown, that in a specific case new classes of exact solutions have singularities with the following property: a geodesic, which begins or ends in the singularity, has an infinite length. Such a singularity leads to an absence of event horizons (if this is a future singularity). In this case it might prove possible to construct cosmological model, satisfying every consistency requirement during a universe lifetime.

A promising concept for managing the work of heat-paragraph shall ated microdistrict from several houses is described. The possibility of an adaptive optimal control of several parameters — temperature, ambient air, the dynamics of change, direction and speed of wind, sun exposure facade.

Construction of virtual model of AR-600 robot by using robot operation system environment is described.

The basic principles of geological interpretation of the scattered waves field are represented. One the basis of scattered waves sections and map analysis had made the forecast of fracture cavernous reservoirs. These reservoirs are very perspective object for oil deposits exploration. The researchers are based on original prestack migration method — Common Scattering Point, which makes it possible to get two independent time cubes: reflected waves cube and scattered waves cube. The last are generated in fractured zones.

The model of microseismic noise in block structuring rocks is offered. Results of numerical researches of the signal form and spectral structure of microseismic noise in productive block structuring layers, dependence of the correlation radius of mid-frequency noise on the receivers position in relation to a layer generating noise are resulted. Recommendations about algorithms of the useful signal allocation and a location of internal seismic events on the basis of the inverse kinematic problems decision are made.

Covariant derivatives of tangent tensor and pseudotensor are considered. Parallel displacements of tangent tensor and pseudotensor are described.

The article is focused on various generalizations of the Deuring Reduction Theorem. Our research proves that the most appropriate theorem for further elaboration is the one that relates the decomposition of pK into prime ideals with the decomposition of A[p] into indecomposable BT1-group schemes up to isomorphism. The article investigates basic problems of the theorem's further generalization and some ways of solving them as well as formulates tasks for further work in this direction.

The article describes the development of the structure and functional nodes of the receiving antenna of the short-wave range for moving objects. The authors define the ways to solve the problem of improving the range properties, increasing the sensitivity of the radio reception and ensuring the electromagnetic compatibility of radio electronic means located within limited space of the mobile object and integrating the antenna into the object’s housing elements.

The article presents the analysis of activity regulation issues in the regional power supply complex and the main ways to improve the efficiency of its subjects. The authors also focus on the issues of automated tariffs setting for production, transportation and transfer heat and electric power. Main attention is paid to automated registration of losses during producing and transferring heat and electric energy.

Projective connections defined by projection and associated to subbundles , L, E of the strong dual threefold distribution (the SH -distribution) of the projective space are constructed. Coverages of torsion-curvature tensors components of the constructed projective connections , , of subbundles , L, E of the SH -distribution respectively are given. The way of creation of dual projective connections , , corresponding to connections , , is specified.

Results of numerical simulation of the Rayleigh — Taylor instability for different geometrical characteristics of the initial irregularities for evening equatorial conditions based on electrodynamically coherent mathematical model of the equatorial ionosphere F-layer are given. It is shown that increase only in the vertical extent of initial irregularity significantly accelerates development a rayleigh-Taylor bubble whereas increase only in lateral dimensions of initial irregularity insignificantly slows down this development.

A creation of decision support self-organising intellectual computer system based on the analysis of an interaction between participants on example of multi-agent system is considered. The universal structure of system implementing proposed method is presented. The results of testing different types of architectures for probability of arising of the synergetic effect and estimation of its impact on the quality of solutions to complex problems are given.

A model of a high-level control system of mobile robot is described. The structure of the system is a neuron growing net. Basic concepts of neuron growing nets theory are given. Main components of the system are de-scribed.

In n-dimensional space of affine connection An,n with Cartan’s structure equations Ricci’s and Bianchi’s identities were received. Their invariance has been shown. After prolongation of the structure equations using Laptev’s lemma semiholonomical, holonomical and trivial manifolds are defined. The Ricci’s identities allowed us to prove semiholonomicity of the space An,n. This semiholonomicity preserves in the space without torsion A’n,n and in the space without curvature ‘An,n , besides the locally affine space Ά’n,n is trivial. Tensor of non-holonomicity of the space An,n is introduced. Vanishing of this tensor makes the space holonomic, H n n A . Also curvature tensor of associated space of affine connection without torsion A’n,n was introduced. It’s vanishing characterizes trivial space of affine connection, Tn n A .

Regular hyperband distribution of an affine space (H-distribution) is given and its existence theorem is proved. Conditions of holonomic H-distribution is determined and Bompiani—Pantazi bijection between the first kind normal and the second one for associated with H-distribution H-, Λ- and L-subbundle is introduced.

The article is devoted to the development of a transmitting antenna system, characterized by an increased coefficient of the traveling current wave, realizing one of the ways to create phased antenna arrays of the short wave and ultrashort wave bands, in the conditions of the limited surface of their placement on ships, in order to improve the electromagnetic environment of radio electronic means.

The paper considers the topicality and challenges of the approach for improving the quality of diagnosis by modelling of the image of diagnostics medical problem as an imitation of integrated combined visual-figurative and verbal-sign representations of the diagnostic problem by experts, and also by modelling collective restructuring of the reduced representation of the problem according to the conception of the council using hybrid intelligent systems as diagnostic decision support systems with cognitive visualization of medical diagnostic problems.

We discuss the structure of optically detected magnetic resonance (ODMR) spectra of diamond crystal. We propose the new approach to the calculation of hyperfine interaction in composed system, consisted of negatively charged nitrogen-vacancy (NV) center and nearby C13 nuclear spin. Energy levels, rule selection and radiative transitions are obtained by new method. It is obtained the estimation of the carbon hyperfine splitting parameters in the diamond NV- center from side-resonance frequencies in the frame of this method. The base of this method is the using of entangled spin states.

The paper presents the results of the study according to day 27 at different longitudes by solar and geomagnetic activity in January 2012-2015. The dependence of the daily variations of NmF2 of the level of solar activity. It is shown that the dependence of NmF2 and solar activity is linear in nature, different at different stations.

The authors consider the methods and algorithms for calculating the characteristics of hydro-mechanical processes in the flow of viscous liquid (water) with dispersed inclusions of close density. In particular, the dependences of the dimensionless intensity of the pulsation energy dissipation on the inertness of inclusions at different loads are investigated. The paper presents the results of the solution by the boundary numerical method in Mathcad. It is found that the intensity of the pulsation energy dissipation of the carrier medium is directly proportional to the ratio of the distributed density of the dispersed phase and the carrier phase depends on the inertia of the inclusions, characterized by a dimensionless value.

The interaction of concrete aggregates and cement alkalis can lead to serious, even catastrophic, destruction of concrete structures. We offer the results of our chemical analysis using a color test, which uses sodium cobalt nitrite Na3[Co (NO2)6].

Construction of a general theory of a special class (SH -distribution) of the regular threefold distributions (H -distribution) of the projective space Pn consisting of a basic distribution of the 1st kind of r-dimensional planes r are equipped with the distribution of the 1st kind of m-dimensional planes Mm (m r) and equip distribution 1st the first kind of hyperplane elements (hyperplanes) Hn-1 with the ratio of the incidence of the corresponding elements in the common center X: X M H is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the SH -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements (n 1)-dimensional linear elements and hyperband distribution. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately. Research was carried out by G. F. Laptev method. Determinations of the H -distributionand existence theorems are given in the frame of zero order. Requiring that Λ-, L-, E-distribution were mutually associated we introduce a special class of threefold distributions, which we call strongly associated distributions or SH -distribution. Definition of SH -distribution is given in the frame of the 1st order and the existence theorem is proved.

Construction of a general theory of a special class ( -distribution) of the regular threefold distributions ( -distribution [1]) of the projective space consisting of a basic distribution of the 1st kind of r-dimensional planes are equipped with the distribution of the 1st kind of m-dimensional planes and equip distribution 1st the first kind of hyperplane elements (hyperplanes) with the ratio of the incidence of the corresponding elements in the common center is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements [2], (n-1)-dimensional linear elements [3] and hyperband distribution [4]. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately.

A field of some geometrical objects internally connected with a complex (n-parametrical family) of the central nondegenerate hyperquadrics in n-dimensional affine space are defined and their geometrical sense is found out.

The concept of the generalized arithmetical progression of the power k and difference d is given. For k 1,7 formulas of nth member of such progressions and for k 1, 2, 3 formulas for the sum of the first n its members are obtained. Progressions ( ) , k p d M with the first member prime number p and difference being a positive even number d 2m (m ) are considered. Such progressions define subsets ( )

, , k h p d M of h prime numbers (h ). For k 20, p 95467, d 108 all subsets (1) h,p,d M with h 15 prime numbers are obtained. Some properties that connect the power k of generalized arithmetical progression and its difference d for 2 k 60, p 1014, h 5 are established.

The short outline of the establishment and development of the graphs’ theory and the general theory of systems is stated. It was shown that graphs are the natural and structural models of systems.

The authors have developed a prototype of that information and analytical technology for modeling dragline waste rehandling in three-dimensional space through two-dimensional numerical algorithms. Using the methods of analytical geometry and mathematical statistics, a number of problems of transforming basic data to net models, creating average sections and local systems of coordinates, modeling routes of excavators in local systems of coor-dinates, and return transformation of modeling results to the initial system of coordinates have been solved.

Values for quadrupole energy levels of CD3 molecule are obtained. Besides the energy values stationary states of this system is marked by total spin projection on the molecular symmetry axis. Nuclear selection rule for radiative transitions is M 1. The radiative transition frequencies are calculated and it is obtained, that spectrum have a dublet and triplet structure.

The article establishes that Euler’s problem of two attractive centres contains another conservation law alongside with the energy conservation

one, which is also quadratic in velocities. These conservation laws and elliptic coordinates considerably simplify the procedure of trajectory equations generation.

The article uses the method of spatial point reflection for the definition of complex potentials of filtrational flows in an area limited by

rectangle. The article considers possible conditions and generates solutions in the form of infinite series. For point source the series are presented by means of the Jacobi theta-function or the Weierstrass sigmafunction.

A detection of spin polarized tunneling current through the quantum dot in a circularly polarized magnetic field is investigated. Current operators and proposed of successive iterative procedure for elaboration those operators are introduced.

An unfluence of duration and conditions of storage on quality of the initial components used by manufacture of metal-plastic profiles is investigated. It is shown, that the storage period and humidity of air render essential influences on physic-technical characteristics of initial materials and on quality of the products made of them.

The hybrid algorithm of the decision of problems of a design of elements of digital techniques is presented. Statement of a considered optimizing problem is formulated. The description developed heuristics, operators and search strategy is resulted. The generalized schemes of search of optimum decisions are given. The basic results of computing experiments are resulted

The new method of processing of the information in location systems is presented. It is based on positions of the theory of optimum reception. As the accepted message dependence of pressure on an exit radar-tracking the receiver from a corner of scanning is used by the diagramme of an orientation of antenna system. Theoretical positions and results of preliminary modeling calculations are resulted. Possibility of increase in the azimuthal permission of two purposes without change of spatial base of a signal is shown.

Obtained the characteristic system of equations of complex geometrical optics for the case of real ray trajectories.

Using the derivation formulas of Akivis and the Laptev structure equations for smooth manifolds, two methods yield corresponding formulas and equations for an affine space are received. The hierarchy of smooth manifolds and a principal bundle of linear coframes over a smooth manifold are used.

A creation of geometric objects of the hyperband distribution (H -distribution) of affine space An in the differential 1–3rd orders neighborhoods is continued. As a result a number of new normalization in Norden's sense of the main structural subbundles of this H -distribution are constructed (are found) internally invariantly.

In this article, we present a method and an algorithm for calculating the dynamic characteristics of gas flow in a cylindrical channel at a subsonic speed, in the presence of dispersed particles in the gas. The problem of identifying the dynamic characteristics of dispersed particle- containing inert gas feed into ladles and the converter is used to improve the accuracy of inert gas dosing. The relevant boundary value problem has no analytical solution. We consider the dynamics of a steady flow of a perfect gas containing dispersed particle in a vertical channel. Numerical methods are used to obtain a solution to the boundary value problem in the Mathcad environment. We present the results of a study of changes in gas parameters along the channel at different gas flow rates. The graphs show dimensional variables. We consider the distributed density of the dispersed phase, the temperatures of the carrier and dispersed phases, the Mach number M, the Reynolds number Re, the Nusselt number Nu, and the Stokes number Stk.

A multivalue method for decision of differential equations including fractional derivatives is offered. A research of approximation and stability of the method is carried out.

Problems of development and realization of an efficient parallelized algorithm to solve elliptic curve discrete logarithm problem (ECDLP) based on Pollard’s rho-method in the computational model SPMD using technology of message passing are considered. It is researched how many central processes are needed and what proportion of distinguished points is needed to be set to optimize an expected working time of this algorithm under the constraints of available memory; analyses the testing results of the developed program.

Attached results is analysis of plane vertical layer of triangle prisms structure. Analysis proved the existence of periodic structure concerning the width and height. While forming the layer.

Evolution operator of a combined system consisting of the measured qubit and the auxiliary system is derived. Conditions on the choice of parameters in the formula for the reconstruction of the measured qubit states are obtained. The evolution operator of the combined system leads to the probability operator (or effect) with a structure that corresponds to unsharp measurements.

Investigated by atomic force microscopy and Auger electron spectrometry the surface of films CdS, formed by hydrochemical deposition on textured silicon substrate. It is shown that the film CdS thus manufactured characterized inhomogeneous distribution of size structural elements and chemical composition over the surface. These films are appropriate for use in photovoltaic solar power converters on based heterostructures CdS/Si(p).

A problem of operational industrial planning at а machine-building enterprise with custom-made, small-scale character of manufacture is considered, and an approach to decision of similar problems on the basis of methodology of functional hybrid intellectual systems with coordination is described.

A model of a knowledge base based on Petri net is considered.

In this article, we examine barotropic geostrophic currents in a Cartesian and the polar coordinate system. The polar system is preferable for analysing geostrophic currents, since radial symmetry is intrinsic to these currents. We obtained ratios between the general hydrodynamic properties. The expressions of geostrophic current velocity components in terms of pressure were the most important among them. The procedure of deriving the expression of vorticity in terms of pressure was carried out. We determined that isobaths coincided with streamlines in stationary barotropic geostrophic currents. The radially symmetrical geostrophic current was studied in detail.

In this paper, we describe three levels of a visual meta-language for hybrid intelligent systems of electrical grid management: 1) hierarchies of resources, actions, and properties; 2) spatial and operational-technological structures; 3) situations and states. A visual metalanguage qualitatively changes the performance of the subject of management and allows them to recognize a problem at a glance and see a workable solution without drawing logical inferences.

The paper considers the possibility of using data collected by the CRM system for working with Bank clients to analyze the efficiency of Bank employees. An analysis of the CRM system functions was performed, from which about 20 attributes were obtained for forming the employee profile and by which it is possible to calculate its integral efficiency.

In 2007, Howgrave-Graham proposed attack against NTRU cryptosystem, which consists of two parts, combining lattice reduction technique and a combinatorial method called meet-in-the-middle (MiTM). In this article, we apply hybrid attack to the Learning with Errors Problem (LWE) with sparse secret. The LWE problem is considered to be one of the most important in lattice-based cryptography. Large number of cryprographic schemes ranging from basic signature and encryption schemes to advanced schemes like group signatures and fully homomorphic encryption, base their security on the hardness assumption of LWE. In this paper, we review the hybrid attack and the algorithms it is based on. It is required for further practical implementation of the attack, whose main objective is to verify correctness of MiTM to the hybrid attack against the LWE problem.

The didactic possibilities of virtual instruments in the engineering education are studied. Defined eight system characteristics of this technology: means of measurement, metrologichnost, real-time, communication, information content, poliontizm, the variation of the scale interval.

Problems of information security of the firm (manufacture) are considered. Their decision assumes studying of forms, ways and methods of revealing and the danger prevention in information sphere, and also the optimal control of system of maintenance of information security and a rational choice of protection tools of the confidential information.