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We consider research results on the effect of the active medium temperature, which varies with the operation of semiconductor and solid-state (DPSS) lasers of the visible range, on the output spectral characteristics. The paper presents the study results of the spectral-optical radiation parameters of semiconductor lasers, their coherence lengths, and the dependence of the spectral maximum position on temperature. This study is necessary for selection of the most optimal laser, which in the future is planned to be used in medical ophthalmologic diagnostics. The experiment was carried out by solid-state (DPSS) and semiconductor laser modules based on a laser diode. Spectral dependences on the active medium temperature of lasers were obtained, ranging from 300 to 370 K. The spectra were recorded with the use of an automated spectral complex based on the MDR-23 monochromator. We show determination possibility of the internal stabilization damage of laser modules  without mechanical intervention but only by applying their spectral characteristics. The obtained data give the possibility to take into account the temperature characteristics and perform further optimization for parameters of such lasers

 The necessity for stability assessment of consumer-grade digital color cameras as imaging devices is brought about by determination of the application possibility of color aerial images in correlation-extreme aircraft navigation systems. The paper presents the results of hypothesis experimental approval about small variability of obtained photos, depending on various camera models and the change in background conditions of the survey object. During the experiments, the photographing of the object is carried out under unchanged conditions by various cameras, and then by one camera, but with the use of various colored backgrounds. Analysis of the results showed that the differences in the color coordinates of compressed images produced by cameras of different models reach 70% that is unacceptable for application in algorithms of interest. The use of color correction in the graphic editor gives the possibility to reduce the spread to about 25% that is somewhat higher than the accepted maximum permissible level of image errors (<15-20%). In the case of "raw" data processing, the swing range is reduced to 15% that meets the criterion being advanced. The change in background conditions causes a small (8% in the worst case) additive error in determination of the color coordinates. According to experiment results, the transfer characteristics of the camera can be considered stable in time and from switching on to switching on. The results obtained make it possible to assert that the use of images in compressed formats may cause errors in the operation of the correlation-extreme aircraft navigation systems algorithms. The hypothesis that the distinction in the photographic images is small relative to the camera applied is recognized to be correct in case of the reception and subsequent processing of "raw" data, as well as the presence of at least one reference object with the color coordinates known in advance in the device field of view.

 Subject of Research.The paper considers the methods of optical coherence tomography (OCT) based on illuminating a sample by optical radiation with subsequent determination of light reflection degree through a sample depth. Illumination method defines basic characteristics of OCT system such as sensitivity and speed in studies of biological samples. In mechanical scanning-free OCT systems, line- and full-field illumination methods are applied utilizing object illumination by laser source with tunable wavelength. The study is aimed at energetic efficiency quantitative assessment of line-field OCT system with tunable radiation source and in comparison of line-field illumination method with full-field one. Method. Based on the model of OCT optical system, ray tracing has been carried out, and spatial distribution of energy reflected from a sample and registered by photo detector has been determined. Photoelectrical signal and signal-to-noise ratio have been evaluated.Main Results. It has been shown that line-field OCT system providessignificantly higher sensitivity (97 dB) compared to full-field system (78 dB). In addition, line-field system allows obtaining B-scan without moving of mechanical parts. Original scheme of lighting channel has been proposed providing uniform illumination spatial distribution along lighting line without sensitivity decay near edges of image field. Practical Relevance.The obtained results can be applied for creation of compact real-time spectral OCT system.

 Subject of Research. The paper presents the study of metafilm application possibility as a biosensor for blood glucose concentration estimation purposes. Method. The metafilm used in this research is a bandpass filter based on cross-shaped resonators for terahertz frequency range. Transmission spectrum of this filter is being affected by the changing optical properties of surrounding media (refractive index, permittivity and others). A change in glucose concentration leads to a change in blood optical properties, therefore, if a filter has a contact with blood, there is a shift of blood transmission spectrum observed. The shift is going to lower frequencies direction, and the shift value depends on glucose concentration. Three frequencies for more detailed study are chosen based on our previous research of blood permittivity dependence on glucose level correlation. All transmission spectra are obtained as the results of numerical experiments in COMSOL Multiphysics software. Main Results. The general algorithm is developed for selection of filter metafilm geometrical parameters based on cross-shaped resonators for given resonance frequency and Q-factor. This algorithm is used for calculation of three biosensor parameters with different spectral characteristics aimed at determination of the best properties of metafilm filter for biosensor purposes. The possibility of metafilm-based biosensor application was proved for determination of blood glucose concentration. Modelling showed that a filter with higher resonance frequency (0.5 THz) has a higher sensitivity (from 2.0 mmol/l to 0.5 mmol/l in the range of 3.0-9.0 mmol/l). Practical Relevance. This method will give the possibility to avoid puncturing during glucose concentration test, because the change in blood chemical composition may demonstrate the influence on skin refractive index. Moreover, biosensors of this type are highly sensitive to the changes in the material optical properties

 Subject of Research. The paper considers the problem of disturbance compensation for the class of linear time-invariant plants with known parameters and delay.Method. The disturbance is presented as a sum of irregular and regular components. An irregular component is treated as an unknown bounded time function. A regular component is described as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally allows applying certainty equivalence principle. In order to remove undesirable influence of delay, a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. Robust modification of adaptive algorithm is used for keeping stability of closed-loop system in the presence of irregular disturbance. As distinct from widespread approaches the proposed algorithm does not require identification of disturbance parameters and gives the possibility to discard from the control system such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of the proposed approach. The results illustrate the boundedness of all signals in the closed-loop system in the presence of external disturbance. It is shown that the proposed idea enables keeping system stability for different values of input delay. Practical Relevance. Thealgorithm of adaptive compensation is recommended for application in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal, control problems of robotic systems with periodical behavior, the problems of ship roll compensation, control problems of space plants in the presence of uncontrollable rotation.

 The problem of MIMO system robust stabilization is considered for the twin rotor MIMO system mechanical plant, where nonlinear dynamics and parametric uncertainties were considered as disturbances. The proposed control law consists of two components: the linear component homogenizes a closed-loop system with a chosen degree of homogeneity; the homogeneous component stabilizes the system asymptotically or in finite time depending on the degree of homogeneity. Due to homogeneity properties of the closed-loop system in the absence of disturbances, the synthesized control law ensures input-to-state stability of the closed-loop system. In comparison with other works, presented approach of control synthesis for twin rotor plant does not require the decomposition of the system and/or consideration of the cross-link effects as disturbances. To confirm the effectiveness of the presented results, an experimental approbation was carried out on the mechatronic plant.

 The porous polypropylene films, containing through channels and permeable for liquids, have been prepared by the method based on extrusion of polymer melt with subsequent annealing, uniaxial extension and thermofixation. We studied the effect of film preparation conditions on the characteristics of porous structure and functional properties of the films (porosity and permeability) at the stages of extension at room temperature ("cold" drawing) and the additional stage ("hot" drawing). Permeability, size and the number of through pores were measured by filtration porosimetry. Overall porosity is determined as a portion of the sample volume occupied by pores by measuring the density ratio of porous and nonporous films. The film surface images, which demonstrate the characteristic features of the porous structure, have been obtained by scanning electron microscopy. The effect of melt orientation degree during extrusion (spin draw ratio) on the films porous structure is determined. It was found that the increasing of spin draw ratio leads to the growth in through permeability, overall porosity and pore sizes of the films. It was shown that the growth of orientation degree at the additional "hot" drawing stage gives the possibility to increase the functional characteristics of porous samples. In the films preparation process, which includes two stages of extension ("cold" and "hot" drawing), the values of overall porosity and permeability of 60 % and 400 l/(m2×h×atm), respectively, were reached. They are ones of the highest values as compared with values of these characteristics presented in the scientific and patent literature for polymer porous films and they determine the efficiency of their practical application as filtration materials

 Subject of Research.We developed additives to shampoos based on different nature nanoparticles with micro- and nanoscale spatial resolution. The effect of the obtained nano-additives on the surface structure of hair fibers were studied. The aim of this work was to fabricate additive complexes of nanoparticles with various nature for shampoos and study of their effect on the hair cuticle structure by optical and atomic-force microscopy. Methods. The methods of chemical separation of elements, centrifugation, laser ablation, optical and atomic-force microscopy were used in the work. Main Results. The various types of hair structures were studied, such as normal, greasy, dry and animal hair, using optical and atomic-force microscopes. Сolloidal solutions of metals and their compounds were prepared (Ag, Au, Cu, Fe, Zn, Si, S, MoO3). Two types of additives for shampoos were fabricated: for greasy/normal and dry hair. The effectiveness of fabricated shampoo additives with complexes of different nature nanoparticles was shown. Practical Relevance. The development of new shampoos with the complexes of nanoparticles will increase the effectiveness of traditional types of shampoos, in particular, the recovery and maintenance of normal hair structure

 The paper presents the results of selenium nanoparticles synthesis in various liquid monomers by laser ablation.  The following substances were selected as the condensation liquids for laser ablation: isodecyl acrylate (IDA, Isodecylacrylate, Aldrich), carboxyethyl acrylate (2Car, 2-carboxyethyl acrylate, Aldrich), ethylene glycol phenyl acrylate (Aldrich), ethylene glycol phenyl acrylate, an available blend of Ebecryl monomers (Cytec Industries Inc.), currently one of the possible components of modern lacquer coatings for nail plates. Thus, a method is proposed for simultaneous synthesis and incorporation of selenium nanoparticles into a polymer matrix. It is established by scanning microscopy method that the sizes of the obtained nanoparticles are from 50 to 200 nm. Infrared spectroscopy results of obtained colloidal solutions showed zero interactions of selenium nanoparticles with monomers. Stable colloidal solutions of selenium nanoparticles were obtained, and solid polymer films promising for biomedical applications were synthesized. The polymerization of colloidal solutions with added monomers and/or mixtures of oligomers was carried out using photo initiator of polymerization 2.2-dimethoxy-2-fenilatsetofenol, sensitive in the UV region (365 nm). The results of IR spectroscopy of the obtained colloidal solutions and polymer nanocomposites showed the absence of interactions of selenium nanoparticles with monomers and polymer matrices. Such nanocomposites could be perspective for biomedical applications, for example, as fungicidal coatings of different surfaces.

Subject of Research. The paper proposes work organization schemes for the project and production companies of the Industry4.0 standard in the mould of «digital factory» and «smart factory». The companies of the «digital factory» and «smart factory» types are the basis for the high-tech production in the future, which are being developed in the Russian Federation as a part of the National technological initiative in the «Tekhnet» direction.Method.We applied organization methods for project and production works in the development and manufacturing of item designing components in the conditions of the future factories on the basis of the automated design general theory in the item designing field.Main Results.It is shown that implementation effect of the proposed organization principles for project and production companies in the factories of the future format can contribute to the transfer of the Russian Federation industrial economy sector to work with the digital technologies. The main research results are the project and production work schemes in the Industry 4.0 companies of «digital factory» and «smart factory» types. Practical Relevance. The results of this research can be applied in the development of automation design algorithms for instrument making (machine manufacturing) digital production operating in the conditions of the Russian Federation digital economy.

Subject of Research. The present work considers the problem of detecting replay attacks on voice biometric systems. Due to their simplicity, these attacks are more likely to be used by the imposters, and that is why they are of special risk. This work describes the system for detecting replay attacks that was presented on the Automatic Speaker Verification Spoofing and Countermeasures (ASVspoof) Challenge 2017 focused on this problem.Method.  We study the efficiency of deep learning approach in the described task, in particular, convolutional neural networks with Max-Feature-Map activation function. Main Results. Experimental results obtained on the Challenge corpora have demonstrated high performance of such approach in contrast to current state-of-the-art baseline systems. Our primary system achieved 6.73% EER on the evaluation part of the corpora which is 72% relative improvement over the ASVspoof 2017 baseline system. Practical Relevance. The results of the work can be applied in the field of voice biometrics. The presented methods can be used in systems of automatic speaker verification and identification for detecting spoofing attacks on them.

 A new solution method for a system of linear algebraic equations (SLAE), called matrix-iterative, is proposed. The method was obtained while analyzing the problem of space tomography scanning – one of the methods of multichannel tomography, which is being developed by the author. Practically all the methods of multichannel tomography are reduced to the restoration of the searched distribution of certain physical quantity by solving a SLAE, which is often underdetermined. The searched distribution is represented by vector-original. In tomography scanning  the point sources power distribution over the area review sector is restored. The task determines certain a priori data, which made it possible to develop a new method of solving a SLAE: the most components of a searched vector are equal to the background value, for example, zero, and exceeding values represent the d-shaped rare values. The resulting vector-matrix equation in the considered problem, identical to SLAE, is underdetermined and often includes a matrix of incomplete rank or badly conditioned matrix. In contrast to the known methods of solving SLAE with partial a priori information about the restored vector, the matrix-iterative method implies no transformation of the original equation preceding the solution. The method is simple in implementation and  contains no such ambiguous quantities as, for example, the regularization parameter. In essence, this is a software method quite easy to be realized. The alternative possibility to solve the SLAE without its preliminary transformations is the pseudo-inverse method, which needs no a priori information and gives either the solution with minimum norm (if it is the joint system), or the solution providing a minimum quadratic deviation. This method has served as a basis for matrix-iterative method, being, in particular, its first iteration. On the following iterations the columns are excluded from the system matrix, the ones corresponding to those values of the solution on the previous iteration, that had been identified as the background. The process of pseudo-inverse solutions with changing matrix is being repeated until all the results are more than the background value. The matrix-iterative method makes it possible to receive practically exact solution if vector-original comes in countless solutions of SLAE. If the vector-original is not included in the number of solutions of SLAE, because of the deviations of the task parameters, then, in this case, the method gives a fairly good result, confirming its stability.

 The paper is devoted to the cross-domain web author attribution (identification), where user's messages are obtained from several sources (web-sites). We focused on the problem of one web-site user identification by his messages from another web-site. We found that there is a stylistic difference between the texts of messages created by one user on different web-sites. The possibility of a single feature space forming for texts received from various sources was determined providing sufficient accuracy of linguistic identification. Two subtasks were studied: 1) mixed sources – training and test datasets include messages from mixed sources (web-sites); 2) separated sources –  the text messages sources of the training and test datasets do not intersect; training dataset includes texts from one source, test dataset includes texts from another.The experiment results showed that identification accuracy in mixed sources task is 0.82. The accuracy in separated sources task is 0.74. It is concluded that there is a stylistic difference between texts created by one user, but on the various web-sites. But at the same time, it is possible to form a single feature space for text messages received from various web-sites, ensuring sufficient identification accuracy.

 The paper deals with the problem of users' identity authentication during payment transactions with the use of mobile devices and web applications. Standard methods of users' identification are considered at performing a payment transaction. The subjects of discussion are the main criteria for the effectiveness of user identification systems in mobile devices and web applications, such as the identification accuracy of the modern systems, time and computational costs, the ability to distribute computations and user convenience. Particular attention is paid to computational and time costs, as they are the most significant for users who make use of practically applicable client-server mobile and web applications. The advantages and disadvantages of face recognition systems application for users' identification and verification are pointed out. Each system element participating in secure banking transaction is described in the course of the payment transaction. A new client-server model is presented for interaction of the face recognition system for security assurance while shopping with the use of mobile devices or web applications. Experimental estimates of the face recognition systems effectiveness are also given. The developed architecture gave the possibility to reduce the time spent by the client for the transaction by an average of 47%, compared with application of standard user authentication tools.

 Subject of Research. The paper considers one of the possible approaches to the study of Ethernet networks by simulating them in the OMNeT ++ environment with the use of the INET framework. The possibility of studying network models is shown in both the step-by-step execution mode and the mode of obtaining generalized statistical characteristics of their operation. Method. When presenting the proposed approach, the method of sequential complication of network models was used, taking into account the features of existing standard protocols and network implementations. The simplicity of the proposed approach is shown, which is based on a wide range of ready-made components for the description of various network elements within the INET framework. This fact gives the possibility to form quite complex network models by means of only the graphic editor and the built-in NED network description language. A brief description of INET framework main components is given that makes it possible to form the structure of the network under research in the graphical editing mode. Main Result. The paper presents technique for creation of network simulation models with a sufficiently detailed description of the main modeling stages. The simplest methods for launching the network model into work and analyzing the results are considered. The work shows the possibility of creating custom component modules in the INET framework projects, which, being ready-made components, can be used in models of more complex network structures. Based on the generated approach, models were built of both basic and mixed Ethernet topologies that gave the possibility to carry out a sufficiently detailed analysis for each of these topologies. Practical Relevance. The described toolkit makes it possible to carry out research on the justification of design solutions for design of distributed computer networks, as well as for creation of tools supporting the automated design of infocommunication systems and networks.

 In queuing systems modeling it is traditionally assumed that the distribution of the inter-arrival time between requests entering the system is unimodal. At the same time, in practice, systems with a multimodal inter-arrival time distribution having two or more modes are encountered. The multimodal distribution is usually replaced by a unimodal one with appropriate numerical moments, which simplifies the modeling process, but introduces a methodical error in the obtained results. The subject of the study is the analysis of properties of multimodal flows and the estimation of such an error. Simulation modeling in the AnyLogic environment is used as a re-search method provided to discover the error dependence on the system load. It was revealed that in the high-load systems the error introduced by the replacement is not higher than 15%, but with a decrease in the system load, the error increases and can reach hundreds of percent. In the course of extensive experiments, it was found out that with an increase in the inter-arrival time the value of the variation coefficient between incoming queries in a polymodal flow tends to a constant value not greater than unity. The practical importance of the work lies in simplification of design process for high-load computing systems with the use of simulation and analytical models by replacing the polymodal flows with unimodal providing required accuracy of calculations.

 Subject of Research. The paper considers the research of verification methods for behavioral models by the field-programmed gate array (FPGA). Applying verification with FPGA gives the possibility to identify functional errors, which are not determined at the verification phase of the traditional integrated circuits (IC) design. Method. The approach is recommendedto two-stage IC interface blocks prototyping with FPGA by means of standard IP-blocks and external devices. The addition of an extra verification phase was proposed carried out after the verification phase according to the traditional IC design path in the Cadence automated design system. Main Results. The approach was used to verify the block of the serial peripheral interface (SPI), which was included in the IC of the micromechanical accelerometer. The result of the interface block model verification showed that the first stage of prototyping with the use of standard interface IP blocks gives the possibility to reveal the existing functional errors in the device with minimal time. Without standard IP-blocks, the model of the verification device ought to be developed separately that can lead to malfunction risks of the final device. The second prototyping stage applying an external plug-in verification device makes it possible to get out of errors connected with signal propagation delays outside the IC and to avoid limitations connected with lack of necessary IP-blocks. Practical Relevance. Two-stage prototyping can be used in the design of IC interface blocks with a view to minimize the probability of errors in data transmission. Functional errors not detected during the verification phase of the traditional IC design were identified and corrected based on the results of two-stage prototyping of the SPI block model. The model designed by this approach was used to develop an IC for a micromechanical accelerometer.

 The paper proposes an algorithm for an object capturing and tracking in a frame for automatic phase focusing of a single-objective camera with a mirror obturator. The capture is performed by the object identification through the filtering of boundaries and edges by the Canny operator; then the Hough transformation is used to detect the characteristic lines of the object. Reliable support of the object is provided by a predictor/equalizer based on the Kalman filter. The proposed calculation algorithm makes it possible to achieve optimal performance, sufficient for the object capturing and tracking in the frame and its timely exposure. This algorithm was implemented to track an object within the scene, the trajectory and speed of which are unknown in advance that excludes the possibility of creation a self-learning algorithm. The Canny operator provides the most accurate detection of object boundaries from existing filtering methods that simplifies the subsequent image processing. The application of an additional Hough transformation makes it possible to speed up the calculations by reducing the amount of data processed, confirming the overall speed of the algorithm as compared to the classical filtering method. The usage of the Kalman filter as a predictor/equalizer  gives the possibility to pre-determine the point for focusing at the next time. The proposed calculation algorithm makes it possible to achieve optimal performance, sufficient for the object capturing and tracking on the stage, and also sufficient for timely exposure of the frame.

 We propose and study the algorithm of digital controllers implementation in fixed-point arithmetic based on the adaptive selection of a discrete transform and a discrete operator (z- or δ-operator). An experimental verification of the proposed criteria for the transform and operator selection is performed, also results of the proposed algorithm testing are given. Suggested approach made it possible to reduce the number of utilized logic elements in the FPGA or ASIC implementation of controllers up to 2-3 times and more in comparison with the traditional technique based on the application of the Tustin transform and z-operator, and also reduce the development complexity. The obtained results are of practical importance in the electronic units design for autonomous embedded systems, space vehicles and other objects with restricted mass, dimensions and power consumption, giving the possibility to overcome these restrictions.

Subject of Research. Thepaper presents analysis of the priority exchange effectiveness, taking into account the unreliability of transmissions in data transmission systems represented by multichannel queuing systems with a common queue. The aim of the work is the study ofefficiency upgrading possibility for priority data exchange in conditions of unreliable transmissions while communication channels are reserved. Method.The efficiency analysis of the redundant packet transmissions is carried out on the basis of simulation modeling. The complex efficiency of the redundant packet transmission is determined on the basis of the multiplicative index, which takes into account the error-free transmission and the average time margin relative to the maximum permissible transmission delay. Main Results.The simulation model of data transmission system with the introduction of priorities and transmission redundancy of time-critical queries is proposed. Simulation experiments were carried out on efficiency evaluation at the increase of priority and the redundancy multiplicity of time-critical queries.  The existence of effectiveness field for the application of priority redundant transmissions of critical-to-latency queries is shown.Practical Relevance.  The presented results can be used in the design of high-reliable computer systems including computer systems providing information services

 Subject of Research. The paper presents the review of existing platforms for development of mobile applications with outdoor-quests.  A method for automation design and planning of outdoor-quests is proposed.  The principles for development automation of mobile applications containing such quests are described. Method. The novelty of the proposed approach lies in procedural quest generation based on a set of limitations.  The architecture combines the usage of open technologies with quests generation and includes special tools for automated creation of outdoor quest templates on various subjectsas well as customizable application templates.  Main Results. Experimental research was carried out for evaluation of the proposed architecture features. By implementing quest generator and application templates a demo Android application was created. The application consisted of two quests: manually created and generated one. The generated quest was made by quest generator and extended by human. The application was published at Play Market Store. The experiment goal   was to measure how long will it take for application users to find different quest object and how long will it take to pass the quest all over in order to determine the differences in generated and manually created quests. As a result of comparative measurements a conclusion was made about allowable difference between quests because it was less than attention cycle duration for humans. This fact demonstrates that generated quests can be used in the same manner as manually created ones. Practical Relevance. The proposed quest generator can be used for wide range of topics because quest object selection is based on keyword search and quest route geometry criterion application. The solution also has practical significance because mobile applications developed with the use of the proposed architecture can be adapted to different domain areas. Wherein mobile application development time is reduced owing to automation and customizable templates usage.

 Subject of Research. The paper proposes a combined application of analytical-statistical modeling methods that makes it possible to accelerate the numerical calculation and analysis of the complex technical system characteristics by the method of machine simulation. The efficiency of joint application of analytical-statistical modeling methods was compared with direct modeling according to the number of tests. Methods. The layered modeling method gives the possibility to reduce the variance of the average characteristic estimation in comparison with the direct modeling method. The balanced modeling method enables a substantial reduction in the tests number without calculation accuracy loss. The joint application of analytical and statistical methods provides characteristics analysis acceleration for the systems  with a distributed structure by simulation method. Main Results. Interpretation and development of the stratification methods and balanced modeling are proposed with reference to system design problems. A test example is given demonstrating a possible gain in the application of analytical-statistical methods for simulation of unlikely events on the example of system reliability calculation. Practical Relevance.Joint application of the stratification methods and balanced modeling makes it possible to accelerate the algorithmic analysis of stochastic system models by the imitation method.

 Subject of Research.The paper deals with the problem of viscous film evolution on a surface of rotating cylinder. The objective of the work is stability analysis of such system in the cases when the cylinder axis is nearly vertical.Stability of uniform film on a strictly vertical cylinder is analyzed, and the system dynamics  under small time-periodic deviations of cylinder axis is studied.Methods. Initial Navier-Stokes equations, which describe dynamics of viscous fluids, are considered with introduced small parameter – the ratio of fluid layer thickness to cylinder radius. This fact allows applying of asymptotic methods and helps to derive a simplified equation on the film thickness. The obtained equation is a non-linear partial-derivative equation and  cannot be solved analytically in general form. Perturbation theory is applied for the subsequent analysis. Linear stability analysis for uniform film on the vertical cylinder surface is carried out. Response to time-periodic perturbation of the cylinder tilt is studied. Main Results. In the case of strictly vertical cylinder, capillary forces imply instability of axisymmetric perturbations with a wavelength exceeding critical value. The obtained critical wavelength value is proportional to the cylinder radius. It is shown that when a cylinder axis oscillates around the vertical, non-uniform fluid layer appears with diametrically opposite thickening and thinning. In the case when the axis oscillation frequency is equal to the rotation frequency, a resonance appears.Practical Relevance. The obtained results might be used for better understanding and further improvement of existing manufacturing processes.

 Subject of Research.The paper considers a spectral problem for chains of weakly coupled ball-shaped resonators under the action of an external magnetic field. Two basic geometries are studied composed of identical resonators: the chain with a single kink and the one with symmetric branching. The vector of magnetic field induction is assumed to be perpendicular to the plane including the centers of resonators that are forming the chain. The delta-like potentials with the same intensity are applied to all contact points. Method. The mathematical model of the chain consisting of identical resonators interacting with each other via a single point is constructed in the framework of the theory of self-adjoint extensions of symmetric operators. The modification of Neumann formulas was used for adjoint operator description. Both systems have a periodicity in parts and the model itself is constructed in such way that it becomes possible to use the transfer matrix approach to obtain the spectrum of the model Hamiltonian. Main Results. The structure of the spectrum for both chains is analytically described; namely, all equations and inequalities are obtained, which give the possibility to find the bands of the continuous spectrum, as well as the energy values ​​related to the discrete spectrum. Numerical simulation clearly demonstrates the structure of the continuous spectrum of the systems depending on the model parameters. Practical Relevance. Since the model has different variable parameters, it can be used to construct real systems that have certain spectral properties. The geometries considered in this paper are the basic elements for the construction of more complex systems.

 Subject of Study. Modern standards specifying competencies and learning outcomes have been analyzed. The model of an educational program has been developed providing building a correct educational program based on the prerequisites and planned outcomes analysis. A creation concept has been specified for a learning management system of new generation that allows forming individual learning trajectories based on analysis of student’s achievements, wishes and peculiarities. Method. The rules of creating a correct educational program were defined, which, together with prerequisites, planned outcomes, achievements, wishes and functional state analysis, lead to automatic individual trajectory analysis. Main Results. The analysis of modern educational standards has been performed; models and rules of forming educational module sets used for learning trajectory creation have been developed; models that analyze students' achievements during the learning trajectory formation have been developed; method of student’s functional state analysis has been developed aimed at creating adaptive educational environment. Practical Relevance. Forming individual learning trajectories based on student’s achievements and functional state analysis provides the possibility to build educational process automatically that will be suitable for a specific student and satisfy the requirements of the educational program.

 Subject of Research. We propose educational platform created on the basis of the automated production in the Industry 4.0 concept. The interaction of automated production area components is described.  The paper describes the process of new components integration into a standardized architectural model. Method. While creating an automated production area, a modern service-oriented architectural model is used, which describes the production process both from the life cycle side and at different levels of the hierarchy, as well as the interaction levels of the components of this production. The basis of the production is a single-board Raspberry Pi computer with a server being started on it for data exchange between the database and the engraving site. Main Results. A model was designed for the next stage of production supplementing by a set of 3D printers. Interfaces between the components of the automated production were also identified. Practical Relevance. The created production area gives the possibility to get acquainted with the basis of the Industry 4.0 concept. The developed model will be implemented for training students to work with modern industrial automation. In addition, the architecture of the created production area provides an opportunity to develop new automation programs, introduce additional production components, and study their interaction with existing ones.