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In this work we are consider a possibility to create schemes of open key distribution in the groups meeting conditions C(3)-T(6). Our constructions use the following algorithms.1. The algorithm that solves the membership problem for cyclic subgroups, also known as the discrete logarithm problem.2. The algorithm that solves the word problem in this class of groups.Our approach is based on the geometric methods of combinatorial group theory (the method of diagrams in groups).In a cryptographic scheme based on the open key distribution one-way functions are used, i.e. functions direct calculation of which must be much easier than that of the inverse one. Our task was to construct a one-way function using groups with small cancelation conditions C(3)-T(6) and to compare the calculation complexity of this function with the calculation complexity of its inverse.P.W. Shor has shown in the paper that there exists a polynomial algorithm that can be implemented in a quantum computer to solve the discrete logarithm problem in the groups of units of finite fields and the rings of congruences mod n. This stimulated a series of investigations trying to find alternative complicated mathematical problems that can be used for construction of new asymmetric cryptosystems. For example, open key distribution systems based on the conjugacy problem in matrix groups and the braid groups were proposed.In the other papers the constructions used the discrete logarithm problem in the groups of inner automorphisms of semi-direct products of SL(2,Z) and Zp and GL(2,Zp) and Zp. groups. The paper of E. Sakalauskas, P. Tvarijonas, A. Raulinaitis proposed a scheme that uses a composition of two problems of group theory, namely the conjugacy problem and the discrete logarithm problem.Our results show that the scheme that we propose is of polynomial complexity. Therefore its security is not sufficient for further applications in communications. However the security can be improved through combining the word problem with other algebraic problems such as the problem of the membership in the cyclic subgroups and the conjugacy problem.

The paper considers the issues of designing the two-zone digital microwave sensors for the car alarm systems with high stability characteristics and capable of adaptation to external noise.The existing analog circuit-based microwave sensors for car alarm systems have a number of essential drawbacks:-- high level of intrinsic noise to cause the "false" alarm of response sensors;-- non-stable characteristics caused by the application of analog components at the environmental temperatures from -30 tо +60 С. This requires sensor readjustment during the transition from the summer season to the winter one, that is, essentially, hard to implement;-- uneasy adjustment of a mounted sensor with variable resistors;-- adjustment characterstic nonlinearity and high power consumption;-- impossible to implement the auto-compensation and adjustment algorithms to the repetitive external actions.To overcome abovementioned drawbacks the paper offers a circuit of digital microprocessor-based (PIC12F683 processor) sensor with HF oscillator running in pulse operation mode (pulse ratio 20). It allows 6-8 times decrease of power consumption up to 2.1 mA and twice reduction of noise amplitude. Filters with useful output signal are of digital implementation. This enables us to reduce the number of electric components of sensor in half and to increase characteristics stability.For remote adjustment of sensor (with the key fob of car alarm or by GSM link) 16 gradations of sensitivity are entered for zones of warning and alarm. The reference levels of digital comparators at each gradation of sensitivity are so generated that the sensor has a linear adjustment characteristic (distance of movable object detection versus gradation number).An application of digital signal processing and sensor capability of data exchange with the main alarm module through the bus allows us to implement the original algorithm of automatic correction of sensitivity across the warning zone of sensor. It means that the sensitivity gradually decreases under repetitive external effects (downpour, passing cars in the streets with heavy traffic, etc.) and with returning to the level of preliminary adjustment as the intensity of external effects decreases. Circuit engineering solutions and algorithms of digital signal processing are implemented in line-produced sensors of car alarms with a trademark “Excellent” (Magic Ring Ltd).

In this paper we consider the arithmetic properties of values of generalized hypergeometric functions and their derivatives (including those with respect to parameter). Some parameters of these functions are irrational. The research aims at refining the lower bound estimates of the modules of heterogeneous linear forms with coefficients from some imaginary quadratic field of the abovementioned values (heterogeneity here is understood in the sense that the function values are considered together with the unit). To solve this problem we use the effective construction of simultaneous approximations. The degrees of polynomials to form such a construction we choose in a special way. The latter circumstance allows more accurate estimates of the modules of corresponding linear forms.To solve similar problems a Siegel's method is, usually, used. This is well known in the theory of transcendental numbers method in which functional approximations are constructed by Dirichlet principle. The advantage of this method is the generality of results. In case of irrational parameters such method cannot be applied directly because the minimal common denominator of the hypergeometric series coefficients with irrational parameters grows too fast. Therefore, the first estimates of linear form modules from the values of hypergeometric functions with irrational parameters have been obtained via effective construction of linear approximating forms. Subsequently, the method has been developed, comprising both the elements of Siegel's method and those of the method based on the effective construction of linear approximating forms. Using a combined method enables us to estimate the linear forms under consideration in the most general situation. This method, however, has not been used yet to study the arithmetic nature of hypergeometric function values differentiated with respect to parameter.Note that all known estimates of the type under consideration still fall far short of expectations. This remark refers just to the heterogeneous case; some of the known estimates of homogeneous linear forms in most cases cannot be further refined. Generalization of the results in this paper seems to be accomplished by abovementioned combined method, which includes both the generality of Siegel's method and the capabilities of effective constructions.

The paper considers topical issues of constructing relay systems to control spacecraft attitude and stabilization with no speed sensors (SS) owing to use of internal feedback (IF). To research this system by point methods, e.g. a point mapping method, is difficult because of the need to solve the transcendent equations containing parameters both of control object and of IF. We propose the “diagram of superimpositions" (DS) method based on topological transformations of the phase space and introduction of a relative time, which enables us to solve engineering problems in analysis and synthesis effectively.The concept of the method is based on the assertion that there is an unambiguous dependence between quality of dynamical regimes in the control system and characteristics of IF transition function. To justify the method a simplified mathematical model of spacecraft motion is applied. The following conditions are accepted: perturbations can be neglected; when the control function is activated, the signal of IF is equal to zero. To the phase surfaces are applied topological symmetry transformations, alignment and projection onto the plane with one of its coordinates being the relative time.The paper gives specific examples of systems with aperiodic feedback (AF) for two versions of parameters to satisfy the requirements: I – in quality of self-oscillation mode (by pulse width in the limit cycle); II – in quality of transition process (lack of sliding modes). It is shown that the requirements II and I are contradictory for the system with AF while the sliding modes are unacceptable.It is shown that DS can be used to synthesize the IF to meet requirements of both steady and transient processes consistently. Using the IF it is possible to implement the shutdown laws of the control action on the DS without SS, the same as in case of using the SS. It is shown that in sliding modes transient processes poor in quality can be completely eliminated by choosing the proper form and parameters of the transition function of IF.The DS topological structure features representing object and IF parameters separately are advantages of the method. A character of the transient process and its quality characteristics are defined by the views and parameters of the curvilinear stairs to DS, squeezing into the limiting cycle. An available binary field of curvilinear coordinates makes it easy to do geometric constructions. DS is of great value for analytical solution of problems concerning IF analysis and synthesis.

Mechanoluminescent sensing elements convert mechanical stress into optical radiation. Advantages of such sensors are the ability to generate an optical signal, solid-state, simple structure, and resistance to electromagnetic interference. Mechanoluminescent sensor implementations can possess the concentrated and distributed sensitivity, thereby allowing us to detect the field of mechanical stresses distributed across the area and in volume. Most modern semiconductor photo-detectors can detect mechanoluminescent radiation, so there are no difficulties to provide its detection when designing the mechanoluminescent sensing devices. Mechanoluminescent substances have especial sensitivity to shock loads, and this effect can be used to create a fuse the structure of which includes a target contact type sensor with a photosensitive actuator. The paper briefly describes the theoretical basics of mechanoluminiscence: a light signal emerges from the interaction of crystalline phosphor luminescence centers with electrically charged dislocations, moving due to the deformation of the crystal. A mathematical model of the mechanoluminescent conversion is represented as a functional interaction between parameters of the mechanical shock excitation and the sensor light emission. Examples of computing the optical mechanoluminescent output signal depending on the duration and peak level of impulse load are given. It is shown that the luminous flux, generated by mechanoluminescent sensing element when there is an ammunition-target collision causes the current emerging in photo-detector (photodiode) that is sufficient for a typical actuator of the fuse train to operate. The potential possibility to create a contact target type sensor based on the light-sensitive mechanoluminescent sensor was proved by the calculation and simulation results.

Compressibility of air used as a working medium in pneumatic control systems raise certain difficulties in calculating dynamic characteristics of the pneumatic drive and solving problems of its regulation. These difficulties are due to a number of factors: - flow of compressed air through the narrow working splits of distributive and throttling devices of pneumatic control; - filling in and discharging the pneumatic actuator cavities of variable volume (piston and rod cavities of the air-cylinder) under conditions of heat and mass transfer; - simultaneous filling in and discharging a pneumatic cavity of permanent volume (receiver); - pneumatic cylinder piston end positioning alteration under variable loading and at the moment of shutdown;A number of factors have a significant impact on the piston end positioning alteration value, namely an initial positioning of the piston at the moment of its shutdown, which determines the volume of the pneumatic cylinder cavity; a value of the permanent component of the load at the moment the piston shuts down and its change during keeping time period; transmission coefficient of the positioning component of the load; a working area of the air-cylinder piston and also an atmospheric pressure reduction, which can significantly affect the operation of control systems of a small aircraft at high altitudes.With a view to deepening the problem of calculation and design of pneumatic actuators, it is shown that the relationship between the parameters of compressed air and their changes is determined by the properties of thermodynamic processes under conditions of heat and mass transfer. In pneumatic actuators for general industrial use, the pressure of compressed air does not exceed a value equal to 1 MPa. In this case, the working medium can be regarded as an ideal gas in simplified calculations.Based on the general equation of thermodynamics, the paper considers the particular cases of a changing gas state process under its constant temperature, pressure, and volume and also in the absolute or partial absence of heat exchange with the surrounding medium. The inconstancy of the compressed air mass during filling in and discharging of pneumatic cavities of variable volume causes non-stationary thermodynamic processes in the pneumatic actuators and requires their specifying in conditions of heat and mass exchange.The pneumatic actuator piston speed is related to the peculiarities of the working medium movement through the narrow slits of distribution and control devices of pneumatic automation due to dependency of the flow on the outflow parameter, which in turn is related to the criticality of the outflow process (the ratio of the pressure at the outlet of the throttling device and at its inlet).It is shown that when calculating and designing the pneumatic drives, including closed-loop ones, as well as for evaluating their dynamic characteristics, a system solution of the equations determining the processes of filling and discharging the cavities of the pneumatic cylinder is required, taking into account the peculiarities of compressed air movement through the narrow slits of pneumatic automation devices.The outflow parameter available in the equations of the pneumatic drive dynamics and determined by the outflow process criticality and by the heat exchange conditions (a poly-tropic index) requires their numerical solution.

In this paper, we simulated and studied the penetration process of 7,62 x 63 mm bullets "NATO Ball" (with a soft lead core) and 7.62 x 63 mm ones «APM2» (with hard steel core) in three kinds of aluminum plates, namely AA5083- H116, AA6082-T4, and AA7075-T6 with three different thicknesses of 10 mm, 20 mm, and 30 mm. The impact velocity was 830 m / s in all tests. Based on the test results and numerical calculations, all plates and a bullet were modeled as the deformable ones with modified constitutive Johnson-Cook relationship and Cockcroft-Latham fracture criterion. Then they were used in modeling by three-dimensional nonlinear finite element in Ansys Ls-Dyna package. The influence of the finite element size in the finite element model on the length and results of calculations has been investigated as well.The main calculation results, we have received, include the residual bullet velocity and the residual kinetic energy of the bullet after drilling a hole in the plate and plate failure mechanism for each type and thickness of the plate with two types of bullets. We have noticed that the residual velocities of the bullets for small thicknesses of aluminum alloys (up to 10 mm) have relatively equal values upon penetration of the bullets "NATO Ball" and «APM2» (a bit more), as well as the calculation-obtained failure mechanisms are adequate to experimental. In addition, resistance of AA7075-T651 aluminum alloy to penetration is higher than that of AA5083-H116 and AA6082-T4 ones.It should also be noted that the accuracy of the results depends mainly on the size of the grid elements. The more is the number of elements, the higher is the accuracy of the results, but the longer is the solution time. Therefore, we advice to use the finite element size of 0.2 mm, at most, to obtain the highly accurate results that are adequate to the experimental results.

The paper studies the convective heat exchange intensification due to two-dimensional depressions formed on the initially flat surface. This problem is of interest for engineering applications because many different convective surfaces have cavities and depressions of constructive or random occurrence. During flow around a depression the boundary layer separation and its reattachment result in occurring specific phenomena, which have a significant impact on drag and heat exchange.The work involved an experimental study of hydrodynamic and heat characteristics of the turbulent boundary layer formed when there was an external airflow of the flat surface with a single transversal separation trench.The experimental part used an open subsonic low-turbulence wind tunnel operating in suction mode. A numerical simulation involves hydrodynamics and heat exchange parameters analysis via solution of the system of differential equations, which describe momentum and heat transport processes using ANSYS Fluent solver.The experimental data of this study are compared with numerical simulation results obtained by solving the steady Reynolds-averaged Navier-Stokes equations (RANS) with a two-parametrical Menter k-ω (MSST) turbulence model.The comparison shows that simulation results are in good agreement with experimental data, heat exchange surface profiling by a transversal trench system with or without flow separation does not lead to increasing surface drag and, moreover, at the certain ratios of geometrical parameters (cylindrical trenches with h/S£ 0.5) it can decrease the surface drag. Surface conjugations in these depressions should be smooth without any sharp curves and transitions, which can lead to forming stagnation regions.The reason for raising heat exchange is a spatial non-uniformity of the generated turbulence field. During flow analysis there were two sources of turbulence generation found out, namely a wall (heat exchange surface) and a mixing zone of main and trench flows.

Recent development of the parallel mechanisms theory has resulted in an increase of the actual machines, which are built using the conceptual schemes of such mechanisms. The advantages of parallel kinematics over conventional open-chain design, such as increased stiffness or lower inertia of moving parts, allow, in theory, higher performance rates in pick-and-place or machining applications. However, the practical usage of parallel mechanisms may be problematic due to their drawbacks, such as restricted workspace area and presence of singularities.The paper discusses a modification of the milling machine “Tetra” developed in “Modular Mechanics”, ltd. (BMSTU), which consists of two identical modules based on planar parallel kinematics mechanism. The loss of module stiffness in certain positions of the end-effector was noticed after experiments on the prototype, thus indicating the presence of singularities. Since this problem is a manifestation of fundamental properties of the chosen kinematic scheme, it was decided to change it.A scheme with three linear rails and three drives, as well as a scheme with a single rail and with four drives were considered as alternative options. The first option was discarded because it requires manufacturing a massive base plate. The second option was selected for future development. In this case, as compared to the previously known design, a configuration of the intermediate links was changed. The use of “lambda”-shaped elements makes it possible to distance the drive supports from the end-effector.For a chosen scheme an inverse kinematics problem was solved. Using constraints associated with the placement of all four drive supports on a single rail and stiffness requirements as well, a one single solution was selected among sixteen possible solutions.The further investigation will include a workspace and singularity analysis and an optimization of geometric parameters of the mechanism.

Deformable alloys of the Al-Mg-Si system are widely used in aviation industry, rocket engineering, shipbuilding, as well as on railway and highway transport. These alloys are characterized by high stamping ability, weld-ability, and machinability with a comparatively high strength and corrosion resistance in a heat-strengthened state. A promising alloy of the Al-Mg-Si system with increased structural strength and manufacturability is on par with foreign analogues in properties is the V-1341 alloy [1, 2].The properties of heat-treatable aluminum alloys strongly depend on the cooling rate of the product during quenching [3-12], which determines the structure and level of residual stresses. Decrease in structural strength, tendency to pitting and inter-crystalline corrosion with slow cooling from the quenching temperature is caused by formation of coarse unequiaxed precipitate, precipitates-free zones, and also by decreasing proportion of inclusions of the strengthening phase [3-12].Thus, the relevant task is to study the effect of isothermal quenching modes on the structure of deformable V-1341 aluminum alloy thermally hardened.The paper studies the impact of isothermal time in quenching on the composition and morphology of breakdown products of the V-1341 alloy solid solution. It is shown that at isothermal time under the solid solution breakdown, at first on the dispersoid surface and then in the solid solution are formed and grow large needle-like crystals of the β'-phase which are structural concentrators of stresses. An increasing isothermal time leads to decreasing solid solution super-saturation by doping elements and vacancies. This leads to a decrease in the fraction of the coherent finely dispersed hardening β '' phase, and also to an increase in the width of the precipitates-free zone.

The analytical review gives the basic concepts of the aero-optics problem arising from the radiation propagation in the region of the boundary layers of a laser installation carrier aircraft. Estimates the radiation wave front distortions at its propagation in the near and far field. Presents main calculation approaches and methods to solve the gas-dynamic and optical problems in propagating laser radiation. Conducts a detailed analysis of the flows and their generating optical aberrations introduced by the aircraft turret (a projection platform of the on-board laser). Considers the effect of various factors (shock wave, difference in wall and flow temperatures) on the flow pattern and the optical aberrations. Provides research data on the aero-optics obtained in the flying laboratory directly while in flight. Briefly considers the experimental research methods, diagnostic equipment, and synthesis of results while studying the aero-optics problem. Discusses some methods for mitigating the aerodynamic effects on the light propagation under flight conditions. Presents data about the passive, active, and hybrid effects on the flow in the boundary layers in order to reduce aberrations through improving the flow aerodynamics.The paper considers operation of adaptive optical systems under conditions of aero-optical distortions. Presents the study results concerning the reduction of the aero-optics effect on the characteristics of radiation in far field. Gives some research results regarding the effect on the efficiency of the adaptive system of a laser beam jitter and a time delay in the feedback signal transmission, which occur under application conditions. Provides data on adaptive correction of aero-optical wave fronts of radiation. Considers some application aspects in control systems of the on-board adaptive optics of adaptive filtration as a way to improve the efficiency of adaptive optical systems. The project in mind is to use obtained results, conclusions, and recommendations in development of technical specification for such systems of adaptive optics.

Currently, a promising trend in remote sensing of environment is to monitor the vegetative cover: evaluate the productivity of agricultural crops; evaluate the moisture content of soils and the state of ecosystems; provide mapping the sites of bogging, desertification, drought, etc.; control the phases of vegetation of crops, etc.Development of monitoring systems for remote detection of vegetation sites being under unfavorable conditions (low or high temperature, excess or lack of water, soil salinity, disease, etc.) is of relevance. Optical methods are the most effective for this task. These methods are based on the physical features of reflection spectra in the visible and near infrared spectral range for vegetation under unfavorable conditions and vegetation under normal conditions.One of the options of optoelectronic equipment for monitoring vegetation condition is laser equipment that allows remote sensing of vegetation from the aircraft and mapping of vegetation sites with abnormal (inactive periods of vegetation) reflection spectra with a high degree of spatial resolution.The paper deals with development of a promising dual-spectrum method for laser remote sensing of vegetation. Using the experimentally measured reflection spectra of different vegetation types, mathematical modeling of probability for appropriate detection and false alarms to solve a problem of detecting the vegetation under unfavorable conditions (with abnormal reflection spectra) is performed based on the results of dual-spectrum measurements of the reflection coefficient.In mathematical modeling, the lidar system was supposed to provide sensing at wavelengths of 0.532 μm and 0.85 μm. The noise of the measurement was supposed to be normal with zero mean value and mean-square value of 1% -10%.It is shown that the method of laser sensing of vegetation condition based on the results of dual-spectrum measurement of the reflection coefficient at wavelengths of 0.532 μm and 0.85 μm makes it possible, even with a measurement error of 10%, to detect vegetation sites that are under unfavorable conditions, with the probability of appropriate detection close to 1 and the probability of false alarms close to 0.

To date the developed and newly created laser systems (radar, range finding, altimetry, etc.) use (to ensure eye safety) the infrared (> 1.4 μm) range. At the same time, an ultraviolet range is of interest too. The most promising here is a wavelength of 0.355 μm (third harmonic of a YAG laser: Nd), since the atmospheric ozone absorption is still low (in the spectral range of 0.25 - 0.38 μm ozone absorption is increased with decreasing wavelength).The paper presents an experimental study of the statistical characteristics of lidar signals at the eye-safe wavelength of 0.355μm. As the statistical characteristics, were used a mean value and a standard deviation of lidar signal.Aerosol inhomogeneity available in the atmosphere has impact on the statistical characteristics of the received signal. Thus, the analysis of these characteristics allows us to view that in the atmosphere there is aerosol inhomogeneity. The article shows that the standard deviation of the signal caused by inhomogeneity is much higher than the standard deviation caused by the shot noise of signal and background as well as by the noise of electronic circuit.The article gives examples of the field of a coefficient of variations. After filtration the field also permits viewing the available atmospheric inhomogeneity of the backscattered signal.

In calculating gas-dynamic characteristics by the universal modeling method it is necessary to determine a non-incidence flow rate through the blades of an impeller because of its relationship with the magnitude of incidence losses. The flow area decreased by the blades of finite thickness and the blades load have impact on the critical streamline direction. The universal modeling method in primary designing uses for this a scheme of replacing the influence of the blade load by the vortex effect with identical circulation. Finally, calculating the inviscid flow around the blades allows selecting a value of the inlet blade angle. For impellers with small design flow coefficients, the condition of the non-incidence inlet for the primary design and for the calculation of the inviscid flow is significantly different. The calculating correctness of the non-incidence regime for the non-viscous flow was checked earlier by measurements of the flow in the impellers. The paper presents CFD calculations of twenty impellers in a tenfold range of design flow coefficients. To provide correct comparison, it takes into account the differences in the value of the loading factor calculated by the programs of inviscid quasi-three-dimensional calculation and CFD programs. Shows the identity of inlet conditions for both methods. To increase primary design accuracy, the calculation model was refined. The formula for calculating vortex-induced velocity involves an empirical coefficient. The analysis of data for 32 impellers with different blade profiling allowed working out formulas for calculating empirical coefficient, depending on the type of an impeller, the blade load and the width of the throat at an impeller inlet. The new scheme-based calculation with the empirical coefficient is accurate enough for the primary design.

The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

The aim is to analyze the possibility for using the 08YUT steel separator tape to manufacture separators, which are to be further applied to the bearing assembly via projection welding.Reliability of rolling bearings is determined by many factors such as surface quality of balls and rings and assembly precision, including the seal strength of hemiseparators.The technology based on the double-pulsed condenser projection welding belongs to one of the most efficient technologies to provide the assembly of bearing, for it allows welding of separator simultaneously in all currents. The paper shows that the required condition to assure high reliability of the bearing is induastial development and implementation of an effective and positive quality control system, which will reduce the probability of damages occurring both when welding and in the course of operation.The work used the static tensile test methods, as well as metallographic analysis.The experimental study used the 08YUT steel hemiseparators. A tape thickness of the hemiseparators was of 1.5mm. The number of simultaneously welded points were 8. The experimental studies of the metal damage of welding joints of the the 08YUT steel separator have shown that with a wide range of the changing welding current and compressed electrode force the quality assurance of welding points at the parent metal level could not be retrieved.The metallographic analysis of the metal damage nature of a welded joint revealed that between the atoms on the surfaces of hemiseparators there are no strong bonds – a bond was formed in the contact zone. This phenomenon leads to reduced tensile seal strength.The study has shown that aluminum and titanium added to the low-carbon steel in order to have a more fine-grained metal structure has a negative effect on the quality of welded joint via projection welding.

This paper presents a review of the references on solar sails, which implies that this subject is relevant and actively developed by various researchers from around the globe. It points out that an important role is played by various imperfections, which would affect the parameters of real solar sails compared to the ideal model.The differential equilibrium equations of the blades of a heliogyro solar sail considering small deformations are written at the beginning of the article. The blade is loaded by light pressure and centrifugal forces, and is fixed at one end in the rotation axis while the other end is free. The differential equation for the blade deflection is obtained. This equation is solved in a statement that the reflection coefficient is independent on the mechanical stress. The deflection function has a simple analytical formulation. The differential equation for the transverse deflection of the solar sail blade is also solved analytically in the formulation of the linear dependence of the reflection coefficient on the tensile stress. The results obtained in both derivations are compared at the maximum amount of deflection of the blade of heliogyro solar sail. It is proved that the maximum difference in the magnitude of the deflection is achieved at tip section. An analytical expression for the relative change in the maximum deflection of the sail blades is given. The chart of this dependency is given for the blade of perspective solar sail with a length of 1000m and made from PET material, which is considered in the linear-elastic formulation.To calculate the projection of the resultant vector of light pressure on the axis of rotation the hypothesis is introduced that the decrease of the reflection coefficient of the material exactly equals to the increase in the transmittance, and vice versa. Considering this hypothesis for PET material the proportionality factor is found, showing a decrease of the reflection coefficient with increasing tensile stress.The expression for the infinitesimal light pressure force on the blades of the element of blade of a solar sail in the projection on the axis of rotation is given. This expression is numerically integrated by two formulations for the ideal and non-ideal solar sail. The numerical value characterizing the reduction of the projection of the main vector of the light pressure force for the non-ideal solar sail is obtained. By analyzing the references it is shown that the obtained difference in the light pressure is substantial and can lead to a change in ballistic performance of solar sails.

When operating the anvil hammers there occur impacts of die tooling and as a consequence, virtually instantaneous impact stops of motion of drop hammer parts. Such operating conditions come with accelerated failures of the anvil hammer rods because of emerging significant wave stresses. Engineering practice widely uses variation, difference, and integral methods to calculate wave stresses. However, to use them a researcher has to acquire certain skills, and the special programs should be available. The paper considers a method for estimating the wave stress changes in the anvil hammer rods, which is based on the wave equation of the Laplace transform. It presents a procedure for generating differential equations and their solution using the operator method. These equations describe the wave processes of strain and stress propagation in the anvil hammer rod under non-rigid impact with the compliance obstacle of the drop hammer parts. The work defines how the piston and rod mass and also the mechanical and geometric parameters of the rod influence on the stress level in the rod sealing of the hammer ram. Analysis of the results shows that the stresses in the rod sealing are proportional to the total amount of wave stresses caused by the rod and piston impact included in the total weight of the system. The piston influence on the stresses in the rod under impact is in direct proportion to the ratio of its mass to the mass of the rod. Geometric parameters of the rod and speed of drop parts before the impact influence on the stress value as well. It was found that if the time of impact is less than the time of the shock wave running in forward and backward direction, the impact with a compliance obstacle is equivalent to that of with a rigid obstacle, and the dependence of the wave stresses follows the Zhukovsky formula of direct pressure shock. The presented method of stress calculation can be successfully used to select the optimal mass and the rod and piston geometric parameters under non-rigid impact without damping and taking into account the energy dissipation until stiff stop of drop hammer parts.

The paper deals with the problem of small oscillations of bilayer liquid separated by a membrane in a closed vessel. This problem arises when studying the behavior of the liquid component of the fuel in the spacecraft tanks in their interaction with the elements of systems providing the start-up of the propulsion system. The problem of small oscillations is considered in the linear formulation. We consider symmet- rical motion of liquid. The membrane is assumed to be thin, elastic, and non-inertial. The liquid completely fills the cylindrical vessel. We consider motion of an ideal and viscous incompressible liquid. On the vessel walls the flow tangency condition is fulfilled. The liquid container volume satisfies the condition of continuity, which in the area under consideration takes a form of the Laplace equation. The differential equation of membrane motion is written with the right-hand side, which includes the hydrodynamic liquid-induced pressure. Restricted deflection of the mem- brane center and zero movements of the membrane contour stipulate boundary conditions for the equation of membrane motion. Integrating the Laplace equation we obtain the expression for the liquid velocity potential in the areas above and below membrane. Writing the equation of the membrane motion for deflection rate, representing the function of membrane deflection rate in accordance with the Fourier method as a product of functions of coordinates and time, we can integrate the expressions for the function of membrane deflection. Fulfilling the boundary conditions for the function of membrane deflection together with the boundary conditions for the Laplace equation, we can obtain an analytical expression for the function of membrane deflection and a frequency equation for the given boundary value problem. It can be seen that for a range of tensions typical for used materials, which are considered, for example, in V.M. Polyaev's monograph, the frequency values of natural oscillations of the membrane will be much higher than the frequency of natural oscillations of the liquid that fills the cylinder of a given radius and height determined from the known relationship.

Assembly process engineering is one of the biggest challenges in modern preproduction engineering. The quality of the process largely depends on the sequence of machine or device assembly. With increasing number of parts in the engineering system the number of allowable assembly sequences is rapidly increasing. It is impossible to analyse this copious combinatorial space without using the cutting-edge methods of mathematical modelling. The paper offers the algebraic models that can be used to select the rational design solutions at the preproduction engineering stage of the assembly operation. When assembling any engineering system the coherence and sequence conditions should be met. It is shown that an adequate mathematical description of sequential and coherent assembly operation is shrinkage of edges of the hyper-graph, which describes a mechanical structure of the product. For the product and its parts must be provided a property of the independent assembly. It is shown that this property can be represented as an action of the closure operator on a set of the product parts. The representations of this operator are parts to be assembled independently (the s-sets). Arranged by inclusion, an aggregate of all the sets is a lattice. The lattice is an algebraic structure where are specified two stable operations, namely: lattice intersection and lattice jog. It turned out that it is possible to use this structure, as a universal generating medium to a diversity of design options for the assembly conversion. The lattice terms are used to describe the sequences of product assembly and disassembly, the sequences of assembly and disassembly of the assembly units, the multi-level diagrams of the assembly decomposition, etc. The properties of the independent assembly are required not only to provide the assembly. A lot of design and technology operations can be performed, provided that a set of the parts has a stable and coordinated configuration within the product, i.e. an s-set of the lattice. For example, those are adjustment operation, various types of tests, fitting and trial assembly, etc. One of the most important operations when designing the engineering system is the synthesis of a rational system of design dimension chains. It is shown that the lattice operations can be used to find the minimum length design chains. The lattice structure allows us to state and solve a problem of minimizing the number of tests for geometric solvability (geometric access) while assembling the products of complicated Science & Education of the Bauman MSTU 231 configuration. It is shown that the set of all solvable configurations is the sub-lattice within the lattice of all the assembled configurations. This allows us to solve the problem of minimizing the number of geometrical tests through the algebraic lattice restoration methods.

The article describes the satellite's trajectory calculation algorithm for near-circular orbits using TLE (two-line element) files in the simplified SGP model. The aim of the algorithm is to obtain the array of satellite's azimuth and elevation required to control the antennas of ground station. The initial conditions of motion in TLE format are very widespread nowadays, they are being used by many calculation software, nevertheless there is a deficit of information concerned with this format in Russian literature. The report presented at NASA web-sites by Dr. T.S. Kelso contains the descriptions of satellite's trajectory calculation algorithms in case of various models (SGP, SGP4, SDP4 etc). The realization of these algorithms demands for the executer's experience because speaking about Russian and the American scientific schools there are differences both in measure units and in approaches to satellite's trajectory calculation.Moreover, in opposite to series of related publications all the calculation sequence to obtain the values of antenna pointing is given in this article, the described algorithm is pretty simple and clear. It is not enough to have the satellite's coordinates and velocity in Earth inertial equatorial system to calculate azimuth and elevation. One has to bind the ground station situated at the surface of the Earth, which is involved in complicated motion, to a point in inertial space using Local Sidereal Time. Several issues propose the utilization of Astronomical Almanac. But the exploitation of the Almanac is not convenient when it is required to get the arrays of values of antenna control angles as functions of time. The article contains the methodology given in foreign issues which allow the calculation of Local Sidereal Time. This methodology is an adjacent part of the trajectory calculation problem with respect to ground station.The calculation results obtained using the described algorithm were compared with the data from well-known Orbitron software where more precise model SGP4 is implemented. The comparison was executed in case of several types of near-circular orbits. Speaking about antennas with wide radiation patterns (up to 30°) the obtained inaccuracies are not very critical especially if the antenna is equipped with system of correction and auto-tracking. Nevertheless, if the calculation accuracy presented in the paper is not enough for the concrete task, the described algorithm can be transformed to the full versions of SGP or SG4 models; the only part is to be changed is the unit responsible for precise calculation of perturbations which influence on the satellite's motion.

The article describes the models of metallic materials used in the calculation of deformation and destruction of engineering structures. The reliability of material models can adequately assess the strength characteristics of the designs of new technology in its designing and certification.The article deals with contingencies and true mechanical properties of materials and presents equations of their relationship. It notes that in the software systems mechanical characteristics of materials are given in the true sense.The paper considers the linear and exponential models of materials, their characteristics, and methods to implement them. It considers the models of Johnson-Cook Steinberg-Guinan, Zerilli-Armstrong, Cowper-Symonds, Gurson-Tvergaard that take into account the strain rate and temperature of the material. Describes their applications, advantages and disadvantages. Considers single- and multi-parameter criteria of materials fracture, the prospects for their use. Gives a rational justification for using a piecewise linear plasticity material model *MAT_PIECEWISE_LINEAR_PLASTICITY (024), LS-DYNA software package for the engineering industry, and presents its main parameters.A technique to identify parameters of piecewise linear plasticity metal material models has been developed. The technique consists of the stages, based on the equations of transition from the conventional stress and strain values to the true ones. Taking into consideration the stressstrain state in the neck of the sample is a distinctive feature of the technique.Tensile tests of the round material samples have been conducted. To test the developed technique in the software package ANSYS LS-DYNA PC have been made tensile sample modeling and results comparison to show high convergence.Further improvement of the technique can be achieved through the development of a statistical approach to the analysis of the results of a series of tests. This will allow a kind of conditional diagram of material tension that provides a safety margin or ensures the required strength properties of products and designs. There are also plans for further work to develop techniques in terms of using the more complex models that could take into account the temperature, strain rate and other factors.

The cutting-edge engineering maintenance software systems of various objects are aimed at processing of geo-location data coming from the employees’ mobile devices in real time. To reduce the amount of transmitted data such systems, usually, use various filtration methods of geo-coordinates recorded directly on mobile devices.The paper identifies the reasons for errors of geo-data coming from different sources, and proposes an adaptive dynamic method to filter geo-location data. Compared with the static method previously described in the literature [1] the approach offers to align adaptively the filtering threshold with changing characteristics of coordinates from many sources of geo-location data.To evaluate the efficiency of the developed filter method have been involved about 400 thousand points, representing motion paths of different type (on foot, by car and high-speed train) and parking (indoors, outdoors, near high-rise buildings) to take data from different mobile devices. Analysis of results has shown that the benefits of the proposed method are the more precise location of long parking (up to 6 hours) and coordinates when user is in motion, the capability to provide steam-oriented filtering of data from different sources that allows to use the approach in geo-information systems, providing continuous monitoring of the location in streamoriented data processing in real time. The disadvantage is a little bit more computational complexity and increasing amount of points of the final track as compared to other filtration techniques.In general, the developed approach enables a significant quality improvement of displayed paths of moving mobile objects.

To obtain the qualitative experimental data about acoustical characteristics of light propeller aircrafts is a relevant problem when conducting the full-scale tests at the local aerodrome. For such tests [1 - 3], it was very important that a desired signal level was significantly higher than the ambient background noise.In this regard, it is relevant to form a databank both of the spectral structure of aerosphere acoustical radiation, corresponding to the ambient background noise for various climatic zones and natural landscapes, and of the basic regularities to form an ambient background noise in a bottom layer of aerosphere.The article describes the authors’ developed procedure of data acquisition about a spectral structure and the procedure to form a bank of statistical data about spectral and integrated characteristics of an ambient background noise.The article provides measurements of spectral characteristics of an ambient background noise taken in conditions of local aerodrome. It shows the normalized graphical matrixes of 1/3- oktave spectra of the sound pressure levels (SPL) of an ambient background noise. The paper also estimates confidence intervals to assess mathematical expectation of the spectral sound pressure levels of a background to have a reliability level of 90 % for various values of the meteorological parameters characterizing aerosphere condition. In the course of tests, the aerosphere parameters were changing within the following ranges: wind speed - 0-6 m/s; temperature - 8- 30оС; relative humidity - 30-59%; air cover condition - from «clear sky» to « cumulus clouds».The obtained data allowed us to find that the acoustical radiation corresponding to the ambient background noise is broadband, within the range of frequencies of 16-10000Hz. In the background noise spectra, it is possible to distinguish, at least, four frequency ranges, which have the notable characteristic frequency-changing levels of spectral components. It may be possible that these frequency ranges match to various sources (or mechanism of sound generation) of a natural origin.It is shown that even in conditions of flat ground, spectral levels of the background ambient noise can be rather unstable even in a time interval, equal to one minute, with no or low (up to 2 m/s) wind speed. And, on the contrary, a change of the spectral levels of sound pressure can be poor in a time even with increasing (up to 6 m/s) wind speed.

Roller screws (RS) featuring very high operational parameters are the most promising transformers of rotational motion into translational motion. The original gear design with a number of peculiarities and precision accuracy in manufacturing its essential details, first of all, thread ones allow us to have high operating parameters of RS. Errors of manufacturing special thread of such details greatly affect the load carrying capacity, precision, reliability, and endurance of RS. That is why the challenge is highly accurate metrological control of errors, which have the greatest influence on specified parameters, and processing of measurement results. Major errors include deviations of real pitch of thread from nominal ones and deviations of real thread profiles from nominal ones. The aim of this paper is to determine abovementioned errors, which were measured by high-precision computerized devices, namely: MITUTOYO CV-2000 contour measurement instrument; Form Talysurf PGI 420 contour measurement instrument. Both have a measurement range of 100 mm and resolution of 0.2 μm. As far as a rental cost of the contour measurement instrument was rather high and a software of this device did not allow us to obtain all required information on the thread profile errors of interest, a thread profile was measured using a contour measuring device on the sampling length. Measurement results were copied to the USB flash drive, and then conversion of obtained results and calculation of all errors of interest were carried out on ECM by means of specially designed software. For example, when using a contour measurement instrument MITUTOYO CV-2000, to make measurement of RS screw on the sampling length of 100 mm along one path, the longitudinal and transverse coordinates of 57411 points of thread profile were obtained. Specially developed mathematical support was used as the basis for software. Programs written in Delphi language have been sent to the Federal Institute for Industrial Property of the RF for registration. Calculation results represent information on the left and right side of each turn of measured detail and final parameters for all measured turns. Developed software may be applied to process results of control of RS thread details as well as high-precision screws and nuts with metrical, inch and trapezium thread.

The most important quality indicators of machining tool are accuracy and productivity. The most important factor affecting these two indicators is the stiffness of the supporting structure of machine. The processing in machining tools is based on the relative movement between the working billet and the cutting tool. The aim of the research is to improve the processing accuracy through equalizing the pressure in guides.The paper describes an optimizing method of the cutting area in machining tools, solving the tasks of the active working zone, and processing accuracy. The plot of pressure in guides is limited to straight or plane. There are three options: 1) diagram of uneven pressure distribution along the non-full length of guides; 2) diagram of uneven pressure distribution along the full length of guides; 3) diagram of even pressure distribution along the full length of guides. For optimizing the processing accuracy of a positioning system should be determined coordinates of the cutting zone, at which the pressure in guides must be as even as possible.The study was based on mathematical modeling and optimization of the cutting zone coordinates. We found the formula to determine the pressure in guides surface. Parameters to be optimized were selected force vectors and magnitudes of saddle in guides. The calculation technique was implemented in matlab 12b. The analysis of calculating results shows that the function η of active working zone and the difference ∆р of maximum and minimum pressures are approximately linearly changed. The graphs show an impact of the different factors on the function η and the difference ∆р of pressure, and alleviate finding the most optimal solution.As a result of the study it has been found that: 1) the developed technique enables us to determine the active working zone, in which the pressure is distributed along the full length of guides; 2) the dependence of the processing accuracy on the parameters of the active working zone is defined; 3) there is the possibility to improve the processing accuracy through appropriately varying parameters of the positioning system.

The article describes a new approach to solving the problem of parrying the negative impact of the random wind loads at the initial stage of aircraft flight. Based on applied research and many years of practice is proved the usefulness of measures to eliminate the deviations caused by the wind at initial flight path.The paper provides a theoretical justification and formulates the basic law of control to parry the product reversal under the action of random wind. Via example of a modified ballistic target the logic of the functioning of a promising technique for correcting orbital speed is clearly illustrated. This study analyses the influence of the wind load on the dispersion characteristics of the product impact points. To identify the qualitative picture of the process under study was examined flight of the aircraft in the vertical plane. In comparison with uncorrectable case, a trivial example of a mathematical model is used to have an initial assessment of the proposed technique effectiveness. As a determining parameter, was considered a changing angle of the aircraft attack during flight. Using authors-developed algorithms, significant reduction in the dispersion of the product impact points was revealed upon performed calculations, thus bearing evidence of using this method in promising aircrafts of the class under consideration.

Currently, there is a tendency to increase the proportion of thread milling operations, among other ways of tapping, which is associated with increasing number of CNC machines, flexibility and versatility of the process.Developments presently existing in the RF and used in the thread mills deal, mainly, with the thread milling cutter designs, to process internal and external thread with straight flutes made from high-speed steel.The paper presents a technique to calculate and select the initial design parameters, i.e. the external diameter of the tapping part of thread milling cutter, which is chosen as a basic computational design. The analysis of directories of tool companies containing foreign de-signs of solid thread end-milling cutters has shown that most of them rep-resent the thread cutter designs made of solid carbide. There are solid and interlocking side milling cutters, which use a tapping part both as a single-disk and as a multi-disk one; chip flutes are made to be both as direct and as screw; solid designs of cutters are made from carbide with a diameter of up to 20 ... 25 mm; thread cutters can be left- and right-hand cutting; Designs of the combined thread mills are proposed; internal channels are used for coolant supply.It is shown that the purpose of the external diameter of the tapping part of the thread mill should take into account the effect of the thread mill diameter on the milling process performance, precision of thread profile received, taper thread, tool strength, and the volume of flutes.The analysis has shown that when choosing the external diameter of the thread mill it worth taking its maximum diameter to improve the char-acteristics of the process under the restrictions imposed on the accuracy of the formed thread.

A problem to measure the teeth wear of rotating gear wheels and a possibility to create simple, reliable and inexpensive mobile systems of diagnostics allowing to record the wear in the course of use are presently relevant. The paper presents implemented technical solutions as a result of work. The aim of the work was to prove experimentally that it is possible to measure the teeth wear of a gear wheel using a passive inductive sensor and a positioning disk. The technique to determine the wear uses a phase-chronometric method developed at BMSTU.To reach the objective, an experimental installation was designed and made. Works are performed, and experimental results of used stationary inductive sensors of passive type to measure the ferromagnetic gear wheels wear of reducers in use are received. The technique for defining the points at the output signal of the inductive sensor, which correspond to the specified points of the tooth profile and, in particular, to the profile points on a pitch circle of the tooth of gear wheel has been developed. Experiments allowed us to define the main dependences of signal parameters on the sizes and arrangement of the sensor magnet with respect to the passing tooth in the course of rotation, as well as on the number of the sensor coil turns, speed of gear wheel rotation, and on the gap size between the end face of the sensor and the top of a tooth.The technique for positioning the sensor with respect to tooth has been deve loped. In particular, it allows us to position a sensor at any point of the involute, including also a point of the profile on a pitch circle. This is necessary to adjust the sensor. The conducted researches allowed us to develop a technique for exact measuring system adjustment to a hitch circle of the gear wheel and to develop for this purpose a system of diagnostics and measurement of teeth wear with the wheel being rotated. The results of work performed at the JSC ELARA in Cheboksary city allowed us to develop a design and make a pilot batch of standard ind uctive sensors, which can be used in mechanical engineering in systems of diagnostics of reducers in a diversity of machines and mechanisms.

The aim of the study was a quantitative analysis of the level of interference with radar monitoring characteristics of surface targets, caused by the scattered electromagnetic field, arising due to the interaction between radio waves and sea surface, which is a study aspect a radiooceanography encompasses. Backscatter signal, arising from the interaction of radio waves and sea surface, extends in a direction opposite the probing radar signal of spread marine and coastal radar stations.With radar sounding of sea surface at high incidence angles of radio waves, a basic physical mechanism to form the received signal is resonant (Bragg) scattering, and at small incidence angles of radio waves it is quasi-specular reflection. Consequently, the energy of electromagnetic radiation, backscattered by the sea surface, depends on the type of wave polarization: for horizontal polarization it is less than for vertical one.The paper presents a mathematical model, which describes dependence of interference level caused by interaction between radio waves and sea surface, on the radio wave polarization for the case when the same polarization is used to sent-out and receive a radio wave.To determine the noise reduction to be achievable with radar monitoring the surface targets by selecting the polarization of the probing radar signal, a signal/noise ratio is analyzed for its different polarizations.It is shown that in order to reduce the noise level caused by the interaction between radio waves and sea surface, it is possible to use the differences in the level of scattered radio signals of different polarization: with horizontally-polarized radar operation at incidence angles of 75°- 85° a signal/noise ratio is by 20-35 dB higher than that of vertically- polarized one.

The article proposes population system models for an isolated population system consisting of the human stem cells of four types: normal cells, abnormal cells of two types (for example, aneuploidic and polyuploidic) and practically \immortal" (cancer) cells. The population system develops in vitro. When dividing, the normal cells, as a result of mutations, may become abnormal cells of one of the two types; subsequently, as a result of further mutations, abnormal cells of either type may become practically \immortal". Transformation of abnormal cells of one type into abnormal cell of the other type is assumed to be impossible. Two models of cell population dynamics have been developed: with no resource limits and in a competitive resource environment. By specifying the dependences of the cell division rates on the number of cells in the population the mathematical model takes into consideration a competition in limited resources. The article discusses piece-wise linear and exponential dependencies. The models allow us to study the processes of forming abnormal and \immortal" cell populations, as well as the processes of their parallel development. Analysis of model trajectories shows that the trajectories starting in the first octant stay within it. This is in compliance with biological interpretation of the models. The paper presents results of numerical modeling.

The aim of the work is the choice of turbulence model for the closure of the Reynoldsaveraged Navier-Stokes equations for calculation of the characteristics of small-size centrifugal compressor. To this were built three-dimensional sectors (as the compressor axisymmetric) blade impeller and the diffuser of the centrifugal compressor on the basis of which they were created two grid models. The dimension of the grid model for the calculation models of turbulence komega and SST was 1.4 million. Elements and the dimensionless parameter y + does not exceed 2. turbulence model family k-epsilon model grid was also 1.4 million. Elements, and the dimensionless parameter y + was greater than 20, which corresponds to recommended values. The next part of the work was the task of boundary conditions required for the correct ca lculation. When the impeller inlet pawned pressure working fluid and the total temperature at the outlet and the gas flow rate through the stage. On the side faces sectors pawned boundary cond ition «Periodic», allowing everything except the wheel, but only axisymmetric part, which significantly reduces the required computational time and resources. Accounting clearance in addition to the meridional geometry construction additionally taken into account boundary condition «Counter Rotating Wall», which allows you to leave the domain in the rotating disc fixed coa ting.The next step was to analyze the results of these calculations, which showed that the turbulence model k-epsilon and RNG does not show the velocity vectors in the boundary layer, and "pushes" the flow from the blade using wall functions. At the core of the flow turbulence model k-omega shown for the undisturbed flow, which is not typical for the compressor working on predpompazhnom mode. For viscous gas diffuser vane for turbulence models SST, k-omega, RNG k-epsilon and has a similar character.The paper compares the characteristics of pressure centrifugal compressor stages, where for large values of the cost of the working fluid turbulence model SST has minimal pressure characteristics.Consequently, for further calculations can be recommended turbulence model SST, which qualitatively describes the separation zone on the surfaces of the blades and the core flow. But, despite this, these calculations need to be validated with the experimental integral values.

The low-carbon steels have good corrosion and technological properties. Hot deformation is the main operation in manufacturing the parts from these steels. So one of the important properties of the material is a property of plasticity. The grain size significantly influences on the ductility properties of steel. The grain size of steel depends on the chemical composition of the crystallization process, heat treatment, and steel machining. There are plenty methods to have grain refinement. However, taking into account the large size of the blanks for the hydro turbine parts, the thermal cycling is an advanced method of the grain refinement adaptable to streamlined production. This work experimentally studies the heat treatment influence on the microstructure of the low-carbon 01X13N04 alloy steel and proposes the optimal regime of the heat treatment to provide a significantly reduced grain size. L.M. Kleiner, N.P. Melnikov and I.N. Bogachyova’s works focused both on the microstructure of these steels and on the influence of its parameters on the mechanical properties. The paper focuses mainly on defining an optimal regime of the heat treatment for grain refinement. The phase composition of steel and temperature of phase transformation were defined by the theoretical analysis. The dilatometric experiment was done to determine the precise temperature of the phase transformations. The analysis and comparison of the experimental data with theoretical data and earlier studies have shown that the initial sample has residual stress and chemical heterogeneity. The influence of the heat treatment on the grain size was studied in detail. It is found that at temperatures above 950 ° C there is a high grain growth. It is determined that the optimal number of cycles is two. The postincreasing number of cycles does not cause further reducing grain size because of the accumulative recrystallization process. Based on the results obtained, the thermal cycling was chosen to obtain a homogeneous fine-grained structure. This heat treatment allows a grain size reduction from 35±11µm to 6±2 µm.

The automated testing tools becoming a frequent practice require thorough computer-aided testing of large software systems, including system inter-component interfaces. To achieve a good coverage, one should overcome scalability problems of different methods of analysis. These problems arise from impossibility to analyze all the execution paths. The objective of this research is to build a method for inter-procedural analysis, which efficiency enables us to analyse large software systems (such as Android OS codebase as a whole) for a reasonable time (no more than 4 hours). This article reviews existing methods of software analysis to detect their potential defects. It focuses on the symbolic execution method since it is widely used both in static analysis of source code and in hybrid analysis of object files and intermediate representation (concolic testing). The method of symbolic execution involves separation of a set of input data values into equivalence classes while choosing an execution path. The paper also considers advantages of this method and its shortcomings. One of the main scalability problems is related to inter-procedural analysis. Analysis time grows rapidly if an inlining method is used for inter-procedural analysis. So this work proposes a summary-based analysis method to solve scalability problems. Clang Static Analyzer, an open source static analyzer (a part of the LLVM project), has been chosen as a target system. It allows us to compare performance of inlining and summary-based inter-procedural analysis. A mathematical model for preliminary estimations is described in order to identify possible factors of performance improvement.

The modern methods to solve the practical tasks related to designing the information security systems in automated systems of different purpose rather often use models of the theory of games. The work, for resource distribution between securable objects, formulates a task of the two players’ game (a defender and a forward) with the zero-sum. The possible loss of a defender is used as a score. The statement of problem for each player, when holding the other player’s solution, is the task of linear programming with one restriction. For the solution of similar tasks the paper offers a linear programming method.For a defender to search a solution, it is offered to use a saddle-point criterion. If the saddle point is not found, a criterion of the guaranteed result is used. For search of the saddle point, two algorithms are offered. Originally, an optimization algorithm, based on the sequential solution of the optimization tasks by each player, seeks the saddle point. If the first algorithm does not find the saddle point, there is a developed search algorithm of the saddle point based on the support of equal security of some objects of a securable system. For the support of equal security of some objects an offer is to solve a system of linear equations. For algorithm are formulated and proved sufficient conditions that the received solution is the saddle point.If both algorithms did not find the saddle point, for a defender to obtain the solution, using a principle of guaranteed result is offered. The search algorithm of solution has been developed to provide the guaranteed result based on the algorithm of support of equal security in which it is possible to use the initial quality score or, in case there is no information about forward ‘s resources, the heuristic scores.Results of the task solution of resource distribution with the given basic data, as well as test results of the developed algorithms are provided.

The paper suggests an algorithm for solving the problems of optimal design of multicomponent disperse-reinforced composite materials, which properties are defined by filler concentrations and are independent of their shape. It formulates the problem of conditional optimization of a composite with restrictions on its effective parameters - the elasticity modulus, tension and compression strengths, and heat-conductivity coefficient with minimized composite density. The effective characteristics of a composite were computed by finite-element solving the auxiliary local problems of elasticity and heat-conductivity theories appearing when the asymptotic averaging method is applied.The algorithm suggested to solve the optimization problem includes the following main stages:1) finding a set of solutions for direct problem to calculate the effective characteristics;2) constructing the curves of effective characteristics versus filler concentrations by means of approximating functions, which are offered for use as a thin plate spline with smoothing;3) constructing a set of points to satisfy restrictions and a boundary of the point set to satisfy restrictions obtaining, as a result, a contour which can be parameterized;4) defining a global density minimum over the contour through psi-transformation.A numerical example of solving the optimization problem was given for a dispersereinforced composite with two types of fillers being hollow microspheres: glass and phenolic. It was shown that the suggested algorithm allows us to find optimal filler concentrations efficiently enough.

One of the approaches to solving terminal control problems for affine dynamical systems is based on the use of polynomials of degree 2n − 1, where n is the order of the system in question. In this paper, we investigate the terminal control problem for which the final state of the system coincides with the origin in the phase space. We seek a set of initial states such that the solution of the terminal control problem can be constructed by using a polynomial of degree 2n − 2.Note that solution of the terminal control problem in question can be used to solve the problem of stabilizing the zero equilibrium in a finite time.For the second-order systems we prove the necessary and sufficient conditions for existence of the polynomial of the second degree which determines the solution of the terminal problem. The solutions of the terminal control problem based on the polynomials of second and third degree are given. As an example, the terminal control problem is considered for the simple pendulum.We also discuss solution of the terminal problem for affine systems of the third order, based on the use of the fourth and fifth degree polynomials. The necessary and sufficient conditions for existence of the fourth-degree polynomial such that its phase graph connects an arbitrary initial state of the system and the origin are obtained.For systems of arbitrary order n we obtain the necessary and sufficient conditions for existence of a solution of the terminal problem using the polynomial of degree 2n − 2. We also give the solution of the problem by means of the polynomial of degree 2n − 1.Further research can be focused on extending the results obtained in this note to terminal control problems where the desired final state of the system is not necessarily the origin.One of the potential application areas for the obtained theoretical results is automatic control of technical plants like unmanned aerial vehicles and mobile robots.

The aerosol lidars intended for expeditious monitoring of the atmosphere allow us to define remotely characteristics of atmospheric aerosol and cloudy formations in the atmosphere. When designing the laser systems, one of the first tasks to be solved is to determine a potential range of laser system operation. The laser system operation range depends on the algorithm for processing laser signals used in laser system. It can be estimated from an equality condition (for the limit range) between the power characteristics of the useful laser signal (coming to the receiver) and the threshold power characteristics of the laser system receiver. Today, practically, all the existing aerosol lidars operate with rather low repetition rate and with rather powerful single pulses. An alternative to it is operation with high repetition rate and with a low power of single pulses. The paper presents comparative analysis of a sounding range for the Aerosol Lidar in UF (0.355 microns), visible (0.532 microns) and near infrared (1.064 microns) spectral ranges for various lidar options (with different repetition rates of laser pulses and different algorithms to process laser locational signals). To estimate the limit sounding ranges L three different algorithms were used: - equality of useful signal power and threshold power of the receiver; equality of useful signal power in the no-accumulation mode and minimum detected (threshold) power in the no-accumulation mode; equality of useful signal power in the accumulation mode and minimum detected (threshold) power in the accumulation mode. Results of mathematical modelling show that the signals accumulation mode provides significantly longer sounding range, than the signals no-accumulation mode. The limit sounding range in the mode of signals accumulation is defined by dependence of the laser pulse power on the repetition rate.

The paper discusses prospects of using blisks with shrouded blades. Increasing an engine life and efficiency as well as mass reduction can also be achieved by increasing blade numbers and decreasing disk diameter. But design engineers are faced with the problem of blade placement because of the disk size and root dimensions.The problem of increasing life and cyclic durability, vibration strength, and lightweight design of the turbine gas turbine wheels, can be solved by an elimination of blade - disk locks.The technology of manufacturing one-piece blisks by connecting the blades with the disc part using hot isostatic pressing was developed. This technology allows us to use blades with shrouds. It is necessary to increase efficiency and to improve high cycle fatigue performance of rotor blades.One of the pressing problems is to ensure the necessary position of shrouds in relation to each other in the manufacturing process as well as in the service. Numerical studies of the influence of the shroud mounting position on blade strength during operation allowed us to develop a methodology of choosing a shroud mounting position.Based on the two turbine wheels (LPT and HPT) calculations advantages of blisk design with respect to the lock-based design were shown. Application of bimetallic blisks with shrouded blades resulted in a lifespan increase and weight reduction.In addition, other advantages of blisk design are as follows: possible reduction in the number of parts, elimination of leaks and fretting that take place in the blade - disk locks, exception of expensive broaching operations and disk alloy saving. The shortcoming is elimination of damping in root connection. In addition, there are no widely used repair methods.Despite these disadvantages the usage of bimetallic turbine blisks with shrouded blades is very promising.

Student’s meta-subject (cross-curriculum) competences are a part of his/her metacompetences that include also metacognitive and meta-creative competences. By the metasubject competences the Federal State Educational Standard means student’s learning outcomes as a result of the universal learning activities to ensure gained knowledge of key competences being a basis of ability to study, as well as learning outcomes of cross-curriculum concepts (meta-concepts). The aim of the paper is to assess student’s learning outcomes when having a meta-concept based curriculum.The offered approach uses a cognitive student’s card (CSC), which formalizes his/her understanding of some fragment of the subject semantic net (SSN) and, theoretically, coincides with this fragment. The assessment for the student’s knowledge of the conceptual constituents of this fragment of SSN is controlled by comparison of the SSN sub-graph corresponding to this fragment with the graph which is defined by the corresponding CSC.Since both so-called meta-subjects and traditional subjects can provide a meta-subject learning proficiency we consider two approaches to test student’s knowledge of meta-concepts. The first one is based on the meta-subject ontology while the other one uses the ontologies of traditional subjects.The Ministry of Education and Science of the Russian Federation supported (project 2014- 14-579-0144) this work.

When protecting (isolating) the facilities of engineering objects from intensive mechanical excitations the factors of vibration (impact) of strength and stability are distinguished, with deviation of operational parameters not exceeding the allowable levels (safety factor). Isolation systems (IS) protecting from single shocks absorb the kinetic energy of the impact due to residual deformation of a sensitive element. There are isolation systems of external, internal and combined type. It is shown that a IS uniform force characteristic is optimal. Its level is determined by the desired degree of object overload reduction. The “real" model takes into account the initial, increasing portion of the force curve.The proposed criterion of the protection effectiveness is a ratio of theoretical minimum and actual values of the stroke of object. The system of differential equations to describe the functioning insulation system is reduced to a dimensionless form. The results of numerical solution of the system have a generalized nature and can be used to choose the IS design parameters. The structural IS classification is based on the character of the sensitive element deformation which directly perceives the external dynamic load. The IS implementing the principles of plastic (or elastoplastic) deformations, cutting, and brittle crushing, permitting dynamic as well as kinematic loading schemes can be distinguished. The paper gives experimentally obtained force characteristics of the sensitive elements of various IS types. Experiments, conducted in the laboratory, confirm that the proposed mathematical model is adequate. The carrier enclosure and the object of protection are treated as rigid bodies. A more rigorous solution of the problem has to take into account the properties of the real engineering object as an elastic vibrating system, characterized by the natural frequencies spectrum and selectively responsive to external excitations. Development of the method of designing an effective IS requires a thorough study of dynamic forces in the operation environment of the engineering objects.

Processing the test results of the composite, which is a mechanical mixture of metal particles with a plastic polymer binder, has shown that its deformation and strength properties are substantially different from those of stable plastic material. The specimen tests for tensile and compression with measuring transverse deformations, as well as torsion tests of tubular samples have revealed that the process of its deformation is accompanied by a change in the original structure.The composite instability is caused by the fact that during this process, it acquires considerable loosening that depends on the type of the stress-state. Hard metal particles are hardly deformed at any stress-state, but they form a layer of bonds that affect the mixture behavior under force action. The total deformation is the plastic flow of the binder on which deformation, caused both by sliding and by loss of the surface layer bonds, is superimposed.The analysis shows that with destruction at tensile test the non-linear part of the bulk deformation (dilatancy) is 6 times more than "conditionally" elastic (3.5 times compressed). The objective of this work is to develop a technique for determining a dilatancy, define its influence on deformation and strength properties of the composite, and improve the mathematical model of the material. The proposed model based on the tensor-nonlinear equations describes loosening, as an additional component of the mean deformation and as a mean stress component, hereinafter referred to as: the first - by the deformation, the second – by the stress. A ratio value of the nonlinear part of deformation with the quadratic tensor argument to the linear part, which reaches 0.3, shows the need for such equations. It also shows the influence of deformation on the relationship between the deviators.To enhance capabilities of mathematical model is possible after including therein the equations for the spherical part of the tensor of deformation and stress, derived from the initial M. Rayner equations (M. Rheology. - M.: Nauka (Science), 1965. 223 pp.). To bring together the non-linearity of the relationship between deviators with nonlinearity between the spherical tensor of stresses and deformations, parameters are introduced. To define them is developed a technique. The parameters as the functions of a stress-state angle are defined by the selection of their values when the theoretical curves in the best way overlay the experimental curves for secant moduli and coefficients of transverse deformationsThis experimental data processing procedure allows us to find both the parameters and the bulk compression modulus. Parameters allow us to more accurately reflect the changing bulk deformation and mean (hydrostatic) stress.Graphs present all the features and parameters found. Using them, we have obtained dependences for ratios of dilatancies to the value of maximum dilatancy in tension. As a result, dependence of ratios on deformations can be graphically shown for different types of stress-state. To check calculations are presented three theoretical curves for the mean stress - maximum stress ratio (mean stress module in compression) to compare them with the corresponding theoretical curves, which define the mean stress as the third part of the stress along the axis of the specimen in tension or compression. Their overlapping each other proves the non-contradiction of a relation equation of the spherical tensors and the accuracy of determining parameters, which define dilatancy, according to stress. The paper shows how the ratio of these dilatancies to the value of maximum dilatancy in tension depends on the deformation for different angles of the stress-state.Using a mathematical model that takes into consideration the features of unstable media, the accounting for non-linearity with defining tensor dilatancy allows us to find a logical approach to defining the relationships between dilatancies and deformation and strength properties. This is achieved by using tensor - nonlinear equations which include the non-linear characteristics and parameters. The latter refine the calculation of the strength characteristics through the use of information about the additional bulk deformation and additional mean stress.The main results of the work are as follows:a) characteristics of deformation and characteristics in the main directions, taking into account the dependence of the composite properties on the level and type of stress-state, are defined;b) is shown that to the tensor ratios of deviators relation are needed equations for bulk deformation and mean stress, with parameters depending on the type of stress-state, which allow to assess the effects of dilatancy caused by the loss of bonds at the surface of the metal filler;c) a technique is developed to determine parameters intended to bring the theoretical curves into line with the experimental ones for the bulk deformation and the mean stress, taking into consideration the detected change of the composite structure;d) limits of deformation and stress dilatancy as a function of the angle of the stress-state are investigated, and the possibility to use information about them ,as the convenient indicators to assess the applicability of the classical strength hypotheses, is shown.

The work objective is to offer a methodological approach to the development of multiagent systems (MAS) in the energy sector. The agent approach is declared as an integral part of the Smart Grid concept (intelligent energy systems), but so far there is really neither methodological development and nor implementation in this area. The problem to estimate the states of electric power systems (EPS) is one of the most important in the energy sector. Decentralization of calculations, when estimating the EPS states, allows reducing the host control center load and the amount of data transferred through the network.To achieve this aim were used the theory and methods for estimating the EPS state, artificial intelligence techniques, methods of object design and programming, multi-agent technologies, and algebraic Joiner-net network.The work analyses existing agent-based solutions, reveals their weaknesses, and proposes author's approach to MAS development in the energy sector, which includes 5 steps: 1) description of the future system, 2) construction and description of the agent-based scenarios, 3) MAS architecture development 4) MAS engineering design 5 ) MAS implementation.A novelty of the proposed approach lies in introduction of the agent interaction scenarios and application of Joiner-networks for scripting of scenarios. Agent-based scenarios allow nonprogrammers-experts to change the programme algorithm. A Joiner-network of the scenario consists of the functioning processes of agents (nodes), and the events that trigger or end the process. Output event of one process can be the input event for another.The operation algorithm of the EPS estimation system is developed. The first step is to provide decomposition of a nodalization diagram into the areas corresponding to the levels of node voltages. Then diagrams resulting from decomposition are distributed between the agents of EPS estimation and calculated in parallel. At the next stage, all diagrams are connected again to become a single one. The paper presents future system architecture, shows the Joiner- network of the agent-based scenarios describing operation algorithm of the system, and describes starting and flag functions. A breakdown agent is designed to be responsible for diagram decomposition into separate subsystems. Computational experiment based on the illustrative model was conducted.The described approach is used to develop the specific MAS for estimating EPS states, but it cannot be replicated to solve other typical problems. Its using enables making changes in existing system, scaling and adding functionality without any need to edit the source code of already existing modules.

The paper considers an experimental study of special aspects of disturbed flow region dynamics that is formed when an injected high-pressure gas jet interacts with a supersonic crossflow of gas nearby a surface of a nozzle or a plate. The study objective was to determine a difference of the pressure distribution in the region and its sizes under dynamic action from stationary flow characteristics.The experiment involved measuring pressure distribution on the surface of a nozzle or a plate along with high-speed filming of the flow.The study has revealed that the difference in size of the disturbed flow region and the flow distribution is observed only in transition segments: under injected jet stagnation pressure increase or decrease. The region is formed with a time lag close to zero under pulsation frequencies used. The disturbed flow region size and boundary shape and pressure distribution in constant pressure segment are independent of jet pulsation.It was determined that the dynamic properties (i.e. time of formation) of disturbed flow region depend of induced force and crossflow properties.Disturbed flow region size behavior in time domain can be represented by an aperiodic element with a time constant significantly smaller than that of the gas-feed circuit.The results gained make it possible to state that in assessing dynamic properties of combination jet effectors it is sufficient to take into account gas generator and gas-feed circuit which response is significantly slower than that of the disturbed flow region.The recommendations based on the study results can be used for supersonic and hypersonic flying vehicle design.

Решение современных задач оптимизации проектных решений, зачастую, сопряжено с большими затратами вычислительных ресурсов. В настоящее время одним из наиболее перспективных методов повышения эффективности работы алгоритмов для решения подобных задач являются распределенные параллельные вычисления. В тоже время, простого увеличения вычислительных мощностей недостаточно для решения практически значимых задач. Необходима разработка специализированных алгоритмов, ориентированных на конкретную параллельную систему, что позволило бы повысить эффективность метода, благодаря использованию особенностей архитектуры вычислительной системы. В данной работе предложен параллельный гибридный алгоритм эволюции разума HMEC, который относится к классу меметических алгоритмов глобальной оптимизации. Отличительной особенностью алгоритма является использование ряда различных мемов, позволяющих алгоритму адаптироваться к разного рода целевым функциям. Под мемом понимают какой-либо алгоритм локальной оптимизации, уточняющий текущее решение исходной задачи оптимизации на определенных шагах выполнения основного алгоритма. В широком смысле, меметические алгоритмы представляют собой гибридизацию одного из популяционных алгоритмов глобального поиска и одного или нескольких алгоритмов локальной оптимизации. Алгоритм ориентирован на использование в слабосвязанных вычислительных системах, состоящих из персональных компьютеров. В рамках работы выполнена программная реализация данного алгоритма с использованием декомпозиции области поиска на стадии первичной инициализации Наука и образование. МГТУ им. Н.Э. Баумана 451 популяции. В качестве инструментов реализации использовались язык программирования Python и интерфейс обмена сообщениями MPI, как один из наиболее распространенных и ориентированных на слабосвязанные системы интерфейсов. Широкое исследование эффективности алгоритма проведено на наборе тестовых модифицированных функций Розенброка, Вейерштрасса, Гриванка и Швефеля. Эффективность алгоритма оценена с помощью таких показателей, как оценка вероятности локализации глобального экстремума, среднее число итераций и среднее число испытаний. Также определено и проанализировано число побед мемов в ходе локальных состязаний в процессе мультистарта для каждой тестовой функции. Результаты исследований показывают, что параллельный меметический алгоритм HMEC позволяет во многих случаях с высокой вероятностью и точностью локализовать глобальный экстремум для заданной целевой функции чем последовательная версия алгоритма. Результаты исследования показывают перспективность дальнейших модификаций и развития параллельных мультимемеевых алгоритмов глобальной оптимизации., This paper deals with the development and software implementation of the hybrid multi-memetic algorithm for distributed computing systems. The main algorithm is based on the modification of MEC algorithm proposed by the authors. The multi-memetic algorithm utilizes three various local optimization methods. Software implementation was developed using MPI for Python and tested on a grid network made of twenty desktop computers. Performance of the proposed algorithm and its software implementation was investigated using multi-dimensional multi-modal benchmark functions from CEC’14.

The state-of-art technical devices - from the aircraft and missile equipment to mobile machines in sphere of construction and agriculture -widely use hydraulic drives based on adjustable axial-piston hydraulic machines. During operation of such hydraulic drives, pressure fluctuations and power fluid flow rate occur, and it results in vibrations of hydraulic machine housing and its components and acoustic radiation of units. Such processes arise from the wave transients that may appear when a mode of operation is changed, or are available when the hydraulic machine separate units are in operation. Origination specificities of these processes and their development are not well studied. So implementation of such hydraulic machines in hydraulic drives of equipment with a wide variety of dynamic loads requires additional experimental and theoretical investigations.The objectives of this paper is to develop a hydraulic drive model based on adjustable axial-piston hydraulic machines and to investigate transients that are available in the operational cycle of a hydraulic drive.To study transients a method of mathematical modeling was used. For hydraulic drive mechanism with rotational displacement, a model with lumped parameters was developed. The model takes into consideration the kinematic and physical features of hydraulic drive components structure, peripheral devices and physical and mechanical properties of power fluid, thereby partially solving the task of investigating transients.There is no possibility to describe all aspects of transients within the framework of a mathematical model with lumped parameters. Difficulties spring up when modeling the wave processes that occur at transient of pumping unit hydraulic cylinders between the suction and discharge zones.For modeling the power fluid transient from pumping unit into discharge line, was developed a two-dimensional turbulent model with distributed parameters. An equation of state for two-phase power fluid in baratropic approximation was obtained.Based on the computational experiment results, it is found that unloading pressure fluctuations, which occur at transients in a pumping unit, considerably change the power fluid pressure distribution along a discharge line, and must be taken into consideration when modeling the dynamic processes in hydraulic drives based on adjustable axial-piston hydraulic machines.

Currently, the problem of growing air pollution of the Earth is of relevance. Many countries have taken measures to protect the environment in order to limit the negative anthropogenic impacts.In such a situation an objective information on the actual content of pollutants in the atmosphere is of importance. For operational inspection of the pollutant concentrations and for monitoring pollution sources, it is necessary to create high-speed high-sensitivity gas analysers.Laser meters are the most effective to provide operational remote and local inspection of gas pollution of the Earth atmosphere.Laser meter for routine gas analysis should conduct operational analysis of the gas mixture (air). For this a development of appropriate information support is required.Such information support should include a database with absorption coefficients of pollutants (specific to potential sources of pollution) at possible measuring wavelengths (holding data for a particular emitter of the laser meter) and an efficient algorithms to search the measuring wavelengths and conduct a quantitative analysis of gas mixtures.Currently, the issues, important for practice and related to the development of information support for the laser gas analyzer to conduct important for practice routine measurements remain unclear.In this paper we develop an algorithm to provide an operational search of the measuring wavelengths of laser gas analyser and an algorithm to recover quantitively the gaseous component concentrations of controlled gas mixture from the laser multi-spectral measurements that take into account a priori information about the source-controlled gas pollution and do not require a large amount of computation. The method of mathematical simulation shows the effectiveness of the algorithms described both for seach of measuring wavelengths and for quantitative analysis of gas releases.

The article deals with the important problem of the development of mathematical methods of processing expert judgments and transferring them into a quantitative form.In contrast to the traditional methods of paired comparisons this paper suggested the use of the method of ternary comparisons. This method assumes that the analyzed objects are already ranked and numbered in order of preference. For every three standing nearby objects the quantitative measure of local ("ternary") degree of preference of the object occupying the second place is introduced. The unit of measurement is the degree of preference of the first object over the last. Simple qualitative and quantitative scales were developed, which are suggested to be used by the experts to describe their opinions about the desirability of objects in each triplet. The formula for finding the final quantitative assessment of the preference of these objects based on their local estimates, the unit of measurement being the degree of preference of the best object in comparison with the worst in the initial ranking.The situation was also analyzed, when an assessment is conducted by the team of experts. In this case, it is proposed to calculate for each object the weighted average assessment of the local preferences on the basis of estimates given by each expert. The weight is the "degree of confidence" team leader has to the opinion of each expert. Total quantitative assessment is calculated using the same formula as in the case of an individual expert.A distinctive feature of the proposed model of experts’ assessment is the use of local ternary qualitative and quantitative scales. This approach can significantly simplify the formalization of expert opinions and their subsequent aggregation. The proposed model can be used in various fields of human activity, that use expert judgment: from the evaluation of the flavor of food and drinks to assessing the acceptability of possible policy options or economic decisions.

The offered work presents analysis of extinction mechanisms and justification of light scattering model in ultrasonic cavitation area to justify a control method of ultrasonic cavitation through its optical sounding by low-intensity laser radiation and through photo-detector record of last radiation.The analysis of the extinction mechanisms has shown that the most essential mechanism causing a change of the transmission coefficient with time is dispersion on pulsating cavitation bubbles. Other extinction mechanisms lead to the time-constant reduction of last radiation intensity and can be taken into consideration by normalizing a recorded transmission coefficient for a previously measured liquid transmission coefficient when there is no cavitation.The feature of light scattering on the cavitation bubbles is primary dispersion in a forward direction that is connected with great values of bubbles radius from units to hundreds of micrometers. In case of single bubbles, dispersion can be described by Mi's theory, and, as to the cavitation area, it is reasonable to use the theory of V. Tversky for multiple light scattering. Thus, dispersion section, according to the paradox of extinction, can be considered to be equal to doubled geometrical section of a bubble. With increasing bubble radius the transmission coefficient monotonically decreases. So, the law of bubble pulsations and the model of light scattering define the law of changing transmission coefficient.Therefore, the cavitation area with its optical sounding acts as a peculiar opto-acoustic modulator. Thus, the demodulated signal of a photo-detector comprises information on pulsations of bubbles.The paper examines the influence of cavitation area thickness and bubbles concentration on the transmission coefficient. It shows a type of transmission coefficient dependence on the radius of cavitation bubbles.The optical sounding method is attractive because it allows us to obtain data on the radius of pulsating bubbles in real time, without dithering in the acoustic field. Thus, data acquisition for the separate cavitation area parts determined by the probing beam diameter is possible.The offered model of light scattering is used as a basis to formulate requirements for a source of the probing radiation and a photo-detector.

Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.