IKBFU's Vestnik

# Physics, mathematics, and technology

### 2015 Issue №10

#### An analysis of mathematical models of the stress state of the outer shell of the roller one-way clutches

Abstract

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.

#### A calculation of the diffusion coefficient of solids in watercourses

Abstract

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.

#### An analysis of mathematical models of the deformation state of the outer shell of the roller one-way clutches

Abstract

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.

#### A Grouped Hyperplane Distribution of an Affine Space

Abstract

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.

Abstract

#### A mathematical simulation and a numerical investigation of dynamics of intramolecular tautomerny transformation without considering processes of a proton relaxation. Part I. A description of a mathematical model

Abstract

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.

#### 3D-simulation of equatorial F-spread: a comparing MI3 with SAMI3

Abstract

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.

#### About geometrical objects fields of the -framed hypersurface of the projective space

Abstract

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.

#### About properties of Cauchy-type integral with a fixed point in the kernel in С1 space

Abstract

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.

#### Algorithms and software for building three-dimensional models of microseismic monitoring data

Abstract

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

#### Experience of applying microseismic monitoring for control waterflood into Northern Truva deposits

Abstract

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.

#### Mathematical Model of Intramolecular Tautomeric Transformation and the Processes of a Relaxation of the Proton

Abstract

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.

#### An oscillatory excited molecular nitrogen in the ionospheric plasma

Abstract

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.

#### Acceleration of Computations in Jacobian Hyperelliptic Curve

Abstract

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.

#### Application of managing structures for the organization of adaptive computing process of modeling of dragline rehandling

Abstract

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.

#### Quantative characteristics of the CSP method

Abstract

The quantitative characteristics of the CSP method, which poses to estimate its effectiveness for fracture hydrocarbon reservoirs imaging using scattered seismic waves, are defined and investigated. The most important is the sensitivity coefficient, which shows how small diffractors, compared with the shadowed reflectors, may be to be detecting by the CSP method. These dependencies from acquisition geometry and other parameters are numerically studied.

#### Bases of the theory of digital communication systems with not orthogonal carrier frequencies

Abstract

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.

#### A semiotic approach to construction of information systems in the field of security

Abstract

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.

#### Non-financial mechanisms for attracting and retaining customers in the banking sector

Abstract

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 model of mid-scale irregularities of the low-latitude Earth ionosphere : evaluations of a non-linear correction method for the Z-scheme

Abstract

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.

#### Cyclic version of “ – ” iterative method. Estimations of speed of algorithm convergence

Abstract

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.

#### Designing and developing a complex social engineering system based on fuzzy interval estimates

Abstract

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.

#### Development of software module calculating area of the ground wave propagation for the Global Maritime Distress and Safety System

Abstract

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.

#### Development tools of functional hybrid intelligent systems with heterogeneous visual field

Abstract

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.

#### «Virtual council». Part 2: The synthesis of the method for solving of the heterogeneous diagnostic task

Abstract

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.

#### Dipole antenna with stabilized input impedance

Abstract

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.

#### Numerical study of distribution of an impurity on watercourse with diffuse pollution

Abstract

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.

#### One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid

Abstract

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.

#### Computer simulation of synthesis processes in NiO—Al system

Abstract

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.

#### Formal Languages and Automata VI:-algebraic systems and transducers

Abstract

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 andxed 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 overnite and innite words. The presentation of these results is based on continuous starsemiring-omegasemimodule pairs. We dene !-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 innite words constitute such abstract !-families of power series.

#### Formal Languages and Automata V: Conway Semiring-Semimodule Pairs and Finite Automata

Abstract

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 innite 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 satises the sum-omega equation and the product-omega equation. We dene 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 innite derivations, and connect certain solutions of these linear systems with the behavior of nite automata over quemirings.

#### Formal languages and automata VII: Formal tree series (Part I)

Abstract

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.

#### Formal languages and automata VII: Formal tree series (Part II)

Abstract

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.

#### Generating function and its application for generalization of Legendre polynomials

Abstract

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.

#### Generation of exact solutions of Fridman equations leading to Cardy–Verlinde formula by Darboux transformation

Abstract

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.

#### Features of practical implementation of the system of control over the design process within CAD CS complex technological objects

Abstract

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.

#### Geometrical phase of NQR signals

Abstract

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.

#### Hierarchies of smooth manifolds up to zeroth and first orders

Abstract

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.

#### iltering of signals from noise by maximum likelihood method

Abstract

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.

#### Modeling studies of filtering process of the radio pulse from noise

Abstract

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.

#### Inertial oscillations induced by the propagation of the Vis-tula Lagoon waters in the coastal zone of the Southeastern Baltic Sea

Abstract

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.

#### Integrated approach to solving routing problem

Abstract

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

#### Examples of the mathematical model of the management company

Abstract

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.

#### Investigation of changes in the paramets of thin films structures during ion implantation

Abstract

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.

#### Investigation of dependence of temperature coefficient of linear expansion on integrated intensity of the main peak of pyroceramics substrate

Abstract

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.

#### Investigation of distortions of the chirp signals in the neighborhood of critical frequencies of ionospheric plasma

Abstract

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.

#### Investigation of operating modes of a mobile solar power plant with non-stationary load

Abstract

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.

#### Development of a web-application for interaction of in-terested stakeholders in the life cycle of a residential house

Abstract

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.

#### Investigation of the receiver path of the leaky wave antenna by the method of equivalent circuits

Abstract

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.

#### Mathematical model of transportation of relativistic electronic beams. Analogy to the equations of gas dynamics

Abstract

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.

#### Metalanguage for hybrid intelligent systems of electrical networks visual control: problems and models

Abstract

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.

#### Non-contact method for measuring the specific electrical resistance of liquid metals in the high temperature range

Abstract

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.

#### Development of an erosion model of a discharge chamber of a stationary plasma engine

Abstract

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.

#### Modeling of the cathode thermal conditions

Abstract

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.

#### Role visual models of the functional hybrid intelligent system with the heterogeneous visual field

Abstract

The paper presents role visual models of a homogeneous and heterogeneous problem, an autonomous and integrated method, an element that is an expert of collective intelligence, a functional hybrid intelligent system that is artificial collective intelligence. The proposed models are the basis for visual modeling of hybrid intelligent systems that dynamically synthesize an integrated model and method over heterogeneous model and visual fields and simulate the cooperation, relativity and complementarity of collective intelligence for finding solutions on verbal-symbolic and visual-shaped languages.

#### New possibilities of passive microseismic monitoring applying for structural-tectonic features detection of oil and gas fields

Abstract

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.

#### Normal connections of the L-subbundle of a strongly mutual distribution of the projective space

Abstract

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  Hn1, 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.

#### Simulating of non-stationary processes in the ionospheric plasma

Abstract

A model of distribution of concentration, velocities and temperatures of ions along a geomagnetic flux tube is considered. The model also examines the main processes of chemical kinetics, ambipolar diffusion, influence of horizontal neutral wind and plasma heating by superthermal electrons. The article presents numerical calculation results of variations of charged particles concentration in the ionosphere and the plasmasphere. The comparative analysis of various hydrodynamic approximations for the description of the ionospheric and the magnetospheric plasma is carried out. It is made on the basis of the numerical solution of the system of equations of energy, continuity and motion for O+, H+ ions and electrons along a power tube of the geomagnetic field. Differences between the hydrodynamic description and diffusive approach are especially considerable in the plasmasphere. These differences manifest themselves both in concentration of ions and in their velocities and have little impact only in distributions of temperature.

#### Normal generalized affine connection associated with the Grassman-like manifold of centred planes

Abstract

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.

#### Normalization of basic structural subbundle of distribution in second order differential neighborhood

Abstract

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.

#### About generalizations of the Cartan projective connection on smooth manifold

Abstract

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.

#### Normalization of the basic structural subbundles of the H(, L)-distribution of affine space

Abstract

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.

#### Normalizations of hyperband

Abstract

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.

#### Numerical model operation of the mass transfer of the disperse phase of aerosol in nonlinear wave fields for axisymmetric quasithree-dimensional geometrical statement

Abstract

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.

#### Calculation method of the channel potential possibilities of surface vessel radiocommunication system in the mode of pseudo-random frequency tuning

Abstract

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.

#### Numerical modeling of wave processes in 3D fractured media

Abstract

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.

#### Numerical simulation of the ionospheric effects of geomagnetic storm on 2—3 may 2010 at the HF radio wave propagation in the low-latitude region

Abstract

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.

#### Numerical solution of the Schrödinger equations with polynomial potentials (Part II)

Abstract

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.

#### Numerical solving the problem of detecting of ultraweak diffractors in a complex acoustical medium

Abstract

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.

#### Seven stages of ADC connection for effective analog-to-digital conversion, minimizing noise elements

Abstract

High-frequency transformations require to correctly design the gain unit before the analog-to-digital converter. To achieve the optimum signal-to-noise ratio, you need to select the correct ADC, and also configure the circuit to receive the signal. The authors focus on several stages for successful conversion of an analog high-resolution signal.

#### On interaction of a qubit with a fluctuating environment

Abstract

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.

#### Nonlinear dissipative structures as model of two-dimensional optic solitons

Abstract

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.

#### A Lax pair for the (1+3) nonlinear equation

Abstract

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.

#### An impacton solution for the vortex filament

Abstract

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.

#### Optimal parameters for consequences of tangential and two-frequency decompositions

Abstract

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..

#### An mathematical simulation of ionosphere with due regard for its three-dimensional irregularity

Abstract

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.

#### Optimization of Repeatability Injured Backbone with the Help of Rigid Laminas on the Basis of a Mathematical Model of a Three-Vertebra System

Abstract

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.

#### Oscillations, resonances and waves in a non-local medium with sources

Abstract

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».

#### New classes of exact solutions and consistent models of cosmological evolution

Abstract

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.

#### Principles of geological interpretation of the scattered waves field

Abstract

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.

#### Modelling of microseismic noise of the block structuring rock massif

Abstract

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.

#### A review of the existing generalizations of the Deuring Reduction Theorem

Abstract

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 pK 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.

#### Receiving antenna system of a mobile object

Abstract

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.

#### Features of the account of thermal and electric energy network losses at the automated tariff setting in the system of regulating activity of the subjects of the energy supplying complex in the region

Abstract

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.

#### Representation of projective connections on the SH -distribution of the projective space

Abstract

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.

#### An influence of initial irregularities geometry on developments of the Rayleigh-Taylor instability in the equatorial F-layer of the ionosphere

Abstract

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.

#### Research of an self-organising effect in decision support computer systems on example of multi-agent systems

Abstract

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.

#### Semiholonomical, holonomical and trivial spaces of affine connection

Abstract

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 .

#### Ship transmitting antenna system

Abstract

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.

#### Modeling of the image of the problem situation of medical diagnostics: challenges and state of the question

Abstract

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.

#### Side resonances in diamond: influence of isotopic substitution of carbon

Abstract

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.

#### Simulation of turbulent flow of viscous liquids with dispersed inclusions of close density

Abstract

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.

#### Strongly associated threefold distributions of projective space

Abstract

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.

#### Strongly mutual threefold distributions of projective space

Abstract

Construction of a general theory of a special class ( -distribution) of the regular threefold distributions ( -distribution ) 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 , (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.

#### Subsets of prime numbers in the generalized arithmetical progressions

Abstract

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 application of the method of average sections with coordinate transformation in three-dimensional modeling of dragline waste rehandling

Abstract

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.

#### The calculation of the spectrum of nuclear quadrupole resonance deuterium replaced methyl group

Abstract

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 decision of problems of designing on the basis of hybrid genetic algorithms

Abstract

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 decision of the problem of definition of angular coordinates of object by the method of the maximum credibility

Abstract

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.

#### The Flow of Gas with Dispersed Particles in a Cylindrical Channel at a Subsonic Speed

Abstract

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.

#### Risk Analysis at Industrial Enterprises Exposed to Post-Earthquake Fires

Abstract

In this article, I analyse risks borne by businesses that have experienced seismic impacts aggravated by secondary fires. I suggest taking into account this circumstance as part of a mechanism to ensure the post-earthquake fire safety of industrial facilities. It is also important to consider aspiration flows as an influencing factor. The risk analysis employs an algorithm for ensuring complex system safety, which proves to be universal. The mechanism in question should be employed in both preparing architectural plans of buildings and structures and conducting rescue operations in emergencies. Based on this analysis, I draw a sample of categorized industrial facilities located in smaller cities and rural areas.

#### On the optimal passing of distinguished points for parallelized Pollard’s rho-method

Abstract

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.

#### The reconstruction of the measured qubit under the unsharp measure-ments

Abstract

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.

#### The research of surface features of the film CdS, fabricated by hydrochemical deposition on textured silicon substate

Abstract

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).

#### Towards a Theory of Barotropic Geostrophic Currents

Abstract

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.

#### A metalanguage for hybrid intelligent systems of electrical grid visual control: hierarchy, structure, situations, and states

Abstract

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.