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The derivation of asymptotic equations describing the processes of heat and mass transfer in axisymmetric swirling laminar flows of a viscous incompressible fluid. Self-similar solutions of these equations are obtained, on the basis of which steady hydrodynamic fields (velocities, pressures) and a temperature field in swirling jets are constructed. The plane and axisymmetric heat and mass transfer problems for unsteady laminar layered flows of a viscous incompressible fluid in channels are also considered. [ABSTRACT FROM AUTHOR]

The mathematical models of the mechanical systems "pipeline – pressure sensor" are considered. These systems are designed to measure the pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. Based on the proposed models described by systems of differential equations, the joint dynamics of the sensitive element of the pressure sensor and the working medium in the pipeline is investigated. To describe the dynamics, both linear and nonlinear models of the mechanics of a solid deformable body and the mechanics of fluid and gas are used under various assumptions about the physical model of the working medium: incompressible ideal, compressible ideal. Analytical and numerical methods for solving the indicated initial-boundary value problems are developed. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate weighted time-varying causal graphs based on daily log-return and realized volatility time series of the S&P500 stocks. In order to construct causal graphs for each quarter between Q1 2005 and Q2 2020, we compute cross-correlations between series and conduct pairwise Granger Causality tests for lead-lag relationships. We take individual stocks as nodes and significant causal relationships as weighted edges. Our analysis is based on a comparison of network topology and properties for different periods, including the 2007-2010 subprime crisis, the European sovereign debt crisis, and the coronavirus pandemic, as well as tranquil periods. In addition to edge weights, our study also takes into account the estimated lag of the causal interactions and uses network level measures to identify meaningful patterns over time. We also conduct an analysis of the industrial sectors interconnectedness via smaller graphs derived from the stock-level causality graphs. The results of the work reveal that network topology changes during periods of market stress and crisis and this can be captured by using convenient network construction methods and measures. Our results also show that the patterns of network topology transformation and magnitude of spillovers transmission during the coronavirus crisis and accompanying events differs from previous crisis periods. [ABSTRACT FROM AUTHOR]

For one class of nonlinear wave equations with a small parameter, an initial-boundary value problem with zero boundary conditions is considered. The solution of such a problem is constructed with using series with recurrently calculated coefficients in two ways. In the first case, the method of special series is considered, which is based on the choice of some functions (basic functions), by the powers of these functions the solution of the original problem is presented into a series with recurrently calculated coefficients. In the other case to represent solutions of the problem a combination of Fourier and small parameter methods is used. It is shown that both proposed constructions of series with recurrently calculated coefficients converge to the solution of the initial- boundary value problem on a finite time interval. [ABSTRACT FROM AUTHOR]

This article is deduction of the necessary and sufficient condition for geometric synthesis of involute cylindrical gears with asymmetric profile of the teeth by the classic approach. The necessary condition is presented for slack-free engagement of the corresponding involutes along the initial circles and the crossing of the lines of engagement along the inter-center straight line, which is a new interpretation of the Willis's basic law of the flat engagement. [ABSTRACT FROM AUTHOR]

Periodontal disease may lead to progressive loosen teeth and even to bone loss. Appropriate treatment is splinting the teeth in order to redistribute the loads. The aim of the study is to compare stress distribution between splinted and non-splinted teeth. A 3D model was made based on computed tomography of mandible and six anterior teeth. In order to make the 3D mesh the model was exported in CAD software and merged with the splint. The materials of the teeth and the splint were assigned according to CT density. The calculations were done in ANSYS using Finite Element Analysis where different directions of loads were applied. As engineers our role of the process is creating a 3D models from CT of a patient and a model of a splint. Then via ANSYS software to apply different loads on the teeth. The final pictures of von Mises stress distribution in all cases will give the dentists accurate results. The dentist as medical authorized people will make the decision about the treatment afterwards. [ABSTRACT FROM AUTHOR]

Innovations of the modern neurosurgery and tissue engineering also has led to development of methodology for designing, manufacturing and integration of spinal personalized implants. The purpose of these personalized implants is to perfectly match the needs and anatomical features of the particular patient and therefore it is a way to create better conditions for functional recovery, and overall improve treatment. In the whole process from MRI scanning to designing, developing and integrating the implant were involved a group of specialists-engineers and neurosurgeons. First step of the process is to make a 3D model from the CT file of the spine using MIMICS Medical software. The next step is to design a model of the personalized implant in 3D matching to the person's spine, which could be done in 3-Matic. Another step is adjusting the implant to the personal case. The development of the implant is the next step although every case is different and requires unique decisions about the size and the form of the implant. Various biocompatible materials and shapes of implants exist. The final step is the implementation of the implant by neurosurgeons. The aim of the innovations is to inculcate the methodology and moreover to make the process more precise. The innovations will find direct application in the field of modern neurosurgery and will achieve not only treatment of the disease but also improvement of the quality of life of the patient. Achieving this goal will provide access to this type of high-tech treatment for a broad group of patients. [ABSTRACT FROM AUTHOR]

This study is based on prior research and aims to improve stream wheel performance based on virtual prototyping. Examined stream wheel structure is developed in several vairants concerning its blades number, geometry and dimensions. Final result shows nearly 50% power output increase for some load cases. The research presents another advantage of virtual prototyping – for design variants evaluation without need for expensive physical prototyping and testing. [ABSTRACT FROM AUTHOR]

The increasing complexity of the cyber-physical products used nowadays along with the ever-expanding firmware and electronics and the connectivity aspects of the industrial environment, require thinking beyond the traditional engineering structures and related design stages. The development and evolution of today's virtual and physical prototypes to the digital twin approach requires high levels of accuracy of the simulation models, covering a wide range of multiphysical areas, as well as different levels of scale and reliability of the model - depending on life cycle applications. This high levels of accuracy in the use of engineering decision-making models can only be achieved in an integrated environment closely linked to the digital and physical worlds. The aim of this study is to define the Digital Twin concept based on Virtual Prototypes and create virtual prototypes for an existing uninterruptible power supply system with a kinetic battery accumulator. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to present an approximation method for solving two-dimensional Hammerstein- Volterra fuzzy integral equations with partial integrals (2D-HVFIEPI). The proposed approach is based on homotopy analysis method (HAM). We transform this equation to Hammerstein-Volterra fuzzy integral equations with partial integrals to crisp case. The convergence analysis for the proposed methods is proved and error estimate between the exact and the approximate solution is find. We give numerical application to show efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

The social sustainability is one of the three pillars of the sustainable development. In the article the respective domain ontology is developed as a part of the existing ontological metamodel of the sustainable development. A methodology for the ontology building is proposed including concept exploration, controlled vocabulary and thesaurus creating; ontology formalization, verification, querying and publication. The main concepts of the ontology are extracted from a text corpus covering well-established and authoritative sources, approved articles, standards and commonly accepted regulations of United Nations. For the purpose, manual selection and automatic text mining by the language processing toolkit GATE is performed. The ontology is formalized by OWL in Protégé environment and after verification its code in GitHub is published. [ABSTRACT FROM AUTHOR]

In the article the problems related to the analysis and measurement of competitiveness at the firm level are explored. An original methodology is proposed on the base of detailed literature review in the area including investigation of the known theoretical studies and the practical achievements. A special attention to the definitions and terminology is paid. The methodology is on the base of existing methods and own algorithms. It proposes an innovative information model of firm competitiveness using ontology engineering for creating metamodel, statistical methods for identifying firm competitiveness criteria and indicators and web technologies for prototype online information system building. A regression analysis is applied revealing the mutual dependency between the firm and the product competitiveness for identifying firm competitiveness criteria and indicators. Based on the methodology a prototype online information system is developed intended for firm competitiveness index calculation and analysis. The proposed information model and the prototype online system fill a gap in the firm competitiveness research and analysis tools. It is expected that their application in the practice would improve awareness of firm managers about positions of their organizations and increase the conclusion quality of the business analysts. [ABSTRACT FROM AUTHOR]

The purpose of this study is to determine analytically what and how acceleration from paralleling execution of a task depends. It is reasonable if level of parallelism is increased, the costs of synchronization will also be increased and upon reaching a certain degree of granulation acceleration of multi-program execution starts to decrease. It is shown that there is a limit to the possibilities for parallelization of activities, taking into account real restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of derivation in product (direct product) of additively idempotent semirings. These semirings are useful and important tools in diverse areas such as design of switching circuits, automata theory, information systems, dynamic programming and decision theory. We study hereditary derivations, inner derivations and obtain a representation of an arbitrary derivations which are zero on the multipliers. [ABSTRACT FROM AUTHOR]

The purpose of this article is to describe parametrically all nontrivial solutions of the diophantine equation in the title. One parameter family of elliptic curves is naturally associated with the equation, for which family we apply "complete 2-descend" algorithm to obtain a parametric description of all possible values of parameter k ∈ ℤ, for which nontrivial solutions exist. The article is a natural continuation of [1]. [ABSTRACT FROM AUTHOR]

Ulam type stability concepts for non-instantaneous impulsive difference equations are introduced and studied. Sufficient conditions for Ulam-Hyers stability, generalized Ulam-Hyers-Rassias stability and Ulam- Hyers-Rassias stability are obtained. Also some conditions for instability are provided. Some of the obtained results are illustrated on examples. These examples are computer realized by coding the corresponding algorithms for calculating the values of the solution for each step. [ABSTRACT FROM AUTHOR]

In this article are considered a new type of subsemirings – the subsemirings of the endomorphism semiring of the interval [0, 1]. [ABSTRACT FROM AUTHOR]

The article gives a simulation model of a warehouse and logistics department of a medium-sized company. Based on the pre-specified workload, the following characteristics of the department are established, such as the load of the warehouses, the size of the queues for import / export of goods and the waiting time in them, the volume of the warehouse and the number of service personnel (warehouse workers). The model can be easily changed for various similar situations. [ABSTRACT FROM AUTHOR]

In the modern world it is necessary to use various IT technologies for effective and high-quality work of the company. Today, the competitiveness and survival of the company in the market depends on this. Various applications and chat bots are very important means to achieve company's goals. The article provides statistics on the popularity of programming languages for 2020. Based on the results of statistical data review, several programming languages are selected for comparative analysis as the most convenient means for writing a chatbot in the Telegram messenger. [ABSTRACT FROM AUTHOR]

This article deals with the use of Blockchain technology and game approach in the context of the educational process in high education institutions. Application of new information technologies and the educational sector general digital transformation in conjunction with Blockchain technology and game mechanics allow, on the one hand, to increase information systems reliability and, on the other hand, to increase the efficiency of learning the information by students. Based on the materials described, the model is developed that can be used for own educational software products elaboration. [ABSTRACT FROM AUTHOR]

In the current research a model simulating a system consisting of DC-DC converter with fuel cell and supercapacitor is presented. The model is realized in MATLAB/Simulink environment. For energy storage device a supercapacitor is used. On the base of the developed model and the control system of the energy flows, a researches related with the necessary value of the supercapacitor with the basic purpose provision of the aforetime set load profile are realized. Another essential problem of the control system of the power converter is to provide operation mode with maximal efficiency of the power source – fuel cell. This research is useful for determination of the optimal value of the energy storage device, which has significantly meaning for economically efficiency of the system for decentralized production of the electrical energy. [ABSTRACT FROM AUTHOR]

Supercapacitors as any other capacitors also have tolerance in their capacitance. That brings difficulties when charging a series connected cells because the voltage of each cell changes with different rate. This problem had a solution called voltage balancing. Nowadays the most popular is an active voltage balancing. This paper presents a modification of an algorithm for an active voltage balancing system. These algorithms are applicable to any energy storage systems, made of supercapacitor sell connected in series. The benefits of the new algorithm are mentioned. Lowering the installed power and lower torque power of the additional DC-DC converters is achieved in the proposed algorithm. The equalization algorithm is verified by software simulation in LTSpice by using the obtained equations. The calculation procedure considers limitations related to some parameters of the energy storage elements like current and voltage. Simulations results showing the operability of the algorithm are presented. [ABSTRACT FROM AUTHOR]

The paper discusses the exchange of information between energy storage systems. Variants of information exchange between Power Distribution Units are simulated. The advantages and disadvantages of different options for information protection are shown. Experimental data for PDUs have been used and can be multiplied for energy storage systems. The options for visibility and information protection are illustrated. [ABSTRACT FROM AUTHOR]

The apparatus of the Generalized Nets (GN) is applied to describe the LPF-algorithm for modeling a conflict-free schedule for packet crossbar switch. Throughput calculation results for a switch node with the LPF- algorithm computer simulation with a family of load traffic patterns are presented. Studies show that the execution time depends on the degree of dimension O(n exp(4,7)). The necessary computations have been implemented on AVITOHOL supercomputer, location – Sofia, IICT-BAS, BG. [ABSTRACT FROM AUTHOR]

The problem of reconstructing the origin-destination matrix for transport following fixed routes is studied. Estimates are based on statistics on passengers entering and leaving at each stop. Various models for estimating of origin-destination matrices are analyzed, including the entropy model and the generalized gravitational model. The properties of correspondences of duplicating and complementary routes are taken into account for comparing the models. [ABSTRACT FROM AUTHOR]

In 2018 Bulgaria was the number 74 economy in the world in terms of GDP (constant 2011 international USD), the number 63 in total exports, the number 60 in total imports, and the number 47 most complex economy according to the Economic Complexity Index (ECI). Given the importance of imports for Bulgaria's economic development, and the ensuing implications, the central aim of this paper is to examine the dependence of imports on consumption, investment and exports in Bulgaria, using time series data for the period 2004-2018. This study examines the dependence of Bulgarian imports, using vector error correction model (VECM) and to examined the causal relationships among the four factors on the obtained model. The results indicated that, no matter in the short term or long term, consumption and export fluctuation is the reason why import change, while the investment fluctuation is not the reason for the growth of import. The consumption and export impact will produce great influence on import in the short term, but, in the long term, the influence will tend to be gentle. [ABSTRACT FROM AUTHOR]

In the current research modeling and simulation of a hybrid electric vehicle (HEV) in PSIM environment is presented. A review of the frequently used structure of for realization of the HEVs are proposed. Consistently, the individual stages of modeling are presented including the choice of electric motor, power electronic converters and energy storage devices. The simulation results of the most important electrical and mechanical parameters which characterized the HEVs are presented. This modeling method is very useful and suitable for the purposes of the training of the power and automotive electronics. [ABSTRACT FROM AUTHOR]

Energy storage systems use electrical converters for charging and discharging. In order to obtain higher power of the converters, parallel operation of units is used. Often these converters are resonant converters operating on a common load and with dephased controls - multiphase systems. The processes in a multi-unit system are complex and model-based design can be used for the design. The paper presents basic steps for model-based design. A model of a multiphase converter is presented, suitable for model-based design. Simulation results of the operation of the model are shown. [ABSTRACT FROM AUTHOR]

The paper considers the possibility of improving the characteristics of power electronic converters by using model-based optimization. To show the validity of the approach, a specific example of a single-transistor resonant converter with direct mode detection is considered. This type of converter is characterized by the absence of a transient process and in order to improve the energy performance it is chosen to optimize the operating mode in order to obtain the maximum value of the first harmonic of the current through the resonant inductance. The obtained results are also useful in expanding the use of the power circuit as a DC-DC converter in this case a transformer is used and it is of particular importance to reduce the losses in it. Thus, with the used optimization, on the one hand, greater efficiency is achieved, and on the other hand, the production of products with reduced weight and size indicators and improved characteristics. [ABSTRACT FROM AUTHOR]

The present work deals with the influence of the geometry of the central part of the kinetic battery on the amount of accumulated energy and the level of sound pressure emitted by it. The study was realized with a 3D structural- acoustic model in the environment of COMSOL Multiphysics®. The model explores the possibilities of reducing the sound pressure level at keeping and/or increasing the kinetic battery energy while maintaining the initial mass of the object. On the basis of the amount of energy stored and the sound pressure level emitted by the kinetic battery, geometric shapes with the best performance in terms of these parameters are determined. An experiment was performed aiming to verify the results of the numerical study with COMSOL Multiphysics®. The results of the study are analyzed. [ABSTRACT FROM AUTHOR]

The goal of this project is the development of a Simplified Simulator for Student Training for one of the nuclear power plant's main equipment, namely the steam generator. The TRIPLE S simulator is designed for basic understanding of undergraduate students in nuclear engineering educational programs. Scilab is used to implement a simulation model and to develop a graphical user interface and it run on a personal computer. [ABSTRACT FROM AUTHOR]

This paper investigates the change in the acoustic characteristics of the Sonic Crystal acoustic barrier as the number of rows on the barrier changes. The study was implemented with a 2D model of Sonic Crystal acoustic barrier with cylindrical profiles of base elements in COMSOL Multiphysics® environment. The effect of increasing the row number of the Sonic Crystal acoustic barrier with vertical cylindrical profiles on the change in the acoustic characteristics of the barrier is investigated. The rows increase with a constant and/or variable distance. An experiment was conducted to verify the results of the numerical study with COMSOL Multiphysics®. The results of the study are analysed and will be used in the design of Sonic Crystal acoustic barriers. [ABSTRACT FROM AUTHOR]

The paper discusses a methodology for model-based synthesis of power electron converter control using the MATLAB/ Simulink software environment. To illustrate the procedure, a specific example with synthesis of a Buck DC- DC converter controller is considered. The individual stages of the process and their respective implementation are indicated. A comparison of results obtained using a linearized and nonlinearized model is performed, thus proving the adequacy of the used model-based approach for control synthesis. Another advantage of the proposed methodology is that when working with it is not necessary to use complex mathematical formulas and in-depth knowledge of the theory of automatic control, which is largely a barrier to the training of students in power electronics. On the other hand, the approach allows the application of not only classical but also modern methods for control of power electronic converters based on artificial intelligence, neural networks, fuzzy logic and others. [ABSTRACT FROM AUTHOR]

The paper represents practical method for calculation and simulation of loop control part of peak current mode buck converter. It's useful for initial design in very early stage of product development. The presented research is useful from the point of view of the synthesis of control of power electronic converters, where it is of special importance to guarantee the output parameters, with a number of destabilizing factors such as: input, output, environment, tolerances of circuit elements. A significant advantage of the proposed approach is that its implementation does not require in-depth knowledge of both the theory of automatic control and mathematics. In this aspect, the synthesis of a controller emphasizes the use of specialized mathematical software. [ABSTRACT FROM AUTHOR]

In this paper, a path following controller for nonholonomic unicycle-type mobile robots is presented. First, a kinematic model in error coordinates appropriate for path following applications is developed. Using the classical linear control theory, a feedback path control based on distance-only measurements is proposed. The stability of the closed-loop system is analyzed and the performance of the control system is studied for rectilinear and circular path with unknown curvature. Numerical simulations and experiments are conducted to validate the synthesized feedback path following control scheme. [ABSTRACT FROM AUTHOR]

The paper presents validation results for multi-1D thermal-hydraulic models with RELAP/SCDAPSIM mod3.5 used for pseudo-3D reactor vessel simulation. The main objective is to test the capabilities and limitations of such calculation models to represent the vessel mixing phenomena in a VVER-1000. The test case is from Phase 2 of the OECD/NEA VVER-1000 coolant transient benchmark (V1000CT-2) and includes the calculation of an asymmetric vessel thermal-hydraulic transient caused by a steam generator isolation leading to heat-up of the disturbed loop. The considered 3D thermal-hydraulic transient in the reactor vessel is relevant to the initial part of VVER-1000 main steam line break scenarios from hot full power. The task is to solve a reactor vessel boundary condition problem with given initial and boundary thermal-hydraulic conditions and to calculate the fuel assembly inlet temperatures in the final state, the formation of the disturbed sector at the core inlet, the angular shift of the loop flows in the final state and the reactor vessel outlet parameters during the transient. Plant data from flow mixing experiments conducted during the commissioning of Kozloduy-6 are available for comparison. Two calculation models with different detail of vessel discretization and cross-flow junctions were tested: a 12-azimuth sector vessel model without radial discretization and a 24-sector model with radial discretization. The predicted integral parameters are in generally good agreement with the reference plant data. The preliminary results from the 24-sector model show some improvement in the predicted peripheral azimuthal and radial transition zones of the disturbed core inlet sector compared to the 12-sector ones but indicate a need for further mesh refinement studies. An integrated uncertainty analysis for input parameters used as vessel boundary conditions was carried out with RELAP/SCDAPSIM for the 12-sector model simulation. The benchmark calculation results illustrate the applicability of such models to asymmetric vessel transients involving thermal mixing and azimuthal flow rotation. [ABSTRACT FROM AUTHOR]

On the basis of thermodynamic analysis, new mathematical models of the combustion process (thermal theory) and vibrational combustion are constructed. A global inhomogeneity of the system can be described as an inhomogeneous distribu- tion of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (Q, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corresponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive com- ponent velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up. [ABSTRACT FROM AUTHOR]

Since the end of 2019, with the outbreak of the new virus COVID-19, the world changed entirely in many aspects, with the pandemia affecting the economies, healthcare systems and the global socium. As a result from this pandemic, scientists from many countries across the globe united in their efforts to study the virsus's behavior and are attempting to predict mathematically its infection model in order to limit its impact and developing new methods and models to achieve this goal. In this paper we explore a time-depended SEIR model, in which the dynamics of the infection in four groups from a selected target group (population), divided according to the infection, are modeled by a system of nonlinear ordinary differential equations. Several basic parameters are involved in the model: coefficients of infection rate, incubation rate, recovery rate. The coefficients are adaptable to each specific infection, for each individual country, and depend on the measures to limit the spread of the infection and the effectiveness of the methods of treatment of the infected people in the respective country. If such coefficients are known, solving the nonlinear system is possible to be able to make some hypotheses for the development of the epidemic. This is the reason for using Bulgarian COVID-19 data to first of all, solve the so-called "inverse problem" and to find the parameters of the current situation. Reverse logic is initially used to determine the parameters of the model as a function of time, followed by computer solution of the problem. Namely, this means predicting the future behavior of these parameters, and finding (and as a consequence applying mass-scale measures, e.g., distancing, disinfection, limitation of public events), a suitable scenario for the change in the proportion of the numbers of the four studied groups in the future. In fact, based on these results we model the COVID-19 transmission dynamics in Bulgaria and make a two-week forecast for the numbers of new cases per day, active cases and recovered individuals. Such model, as we show, has been successful for prediction analysis in the Bulgarian situation. We also provide multiple examples of numerical experiments with visualization of the results. [ABSTRACT FROM AUTHOR]

The problem of the layered plates throwing in the conditions of incomplete dispersal of detonation products (DP) is devoted to quite a lot of work, but this problem is usually solved either by various numerical methods, which in practice are not applicable due to the significant difficulties for calculations, or in one-dimensional form, that does not allows for the correct determination of pressure in DP and turn angles after the impact of the plates. This paper provides a mathematical model of multi-layered throwing calculation using fairly simple analytical equations to determine the above parameters when solving various applications for explosive processing of materials by a sliding detonation wave. [ABSTRACT FROM AUTHOR]

Forecasting is a special scientific study, the subject of which is the perspective for the development of the phenomenon. It is of great importance for many scientific and applied fields. This article presents a stochastic model for microgrid load forecasting. Statistical and stochastic methods are used for forecasting. [ABSTRACT FROM AUTHOR]

In this article is proposed a method for forecasting vehicle traffic intensity in urban conditions and provides an estimate of the forecasting error. For input data in this study are used: the number of vehicles that have passed through a location of the road, based on data collected by observations; meteorological conditions; the day of the week; the season. For this purpose, database processing methods, statistical and stochastic methods are used. [ABSTRACT FROM AUTHOR]

In this article, a stochastic model for prediction of microgrid photovoltaic power generation, using statistical and stochastic methods is presented. The study is performed in the following steps: Processing of a large database of historical data (Data Mining); Construction of a stochastic forecasting model; Reporting a symmetric mean absolute percentage error in forecasting. [ABSTRACT FROM AUTHOR]

This article offers estimation of the error in forecasting the consumption of the natural gas of the freight schedule per subscriber according to the seasons. Statistical and stochastic methods are used for the analysis and forecasts. [ABSTRACT FROM AUTHOR]

The problems of two types of dynamic optimization of flow around solids are described in general form. The features of these problems are analyzed from the point of view of the optimal control theory, the difficulties caused by such features, and ways to overcome them. The problem solving schemes developed for the applied engineer are briefly described, the idea of the mathematical justification of one of them is presented. [ABSTRACT FROM AUTHOR]

Traffic flows determine the hierarchy of transport network elements. More loaded arcs and vertices are more important for the entire network. It is obvious that the traffic flow on any element depends on the network design and the origin-destination matrix of network vertices. Therefore, any change in the origin-destination matrix changes to the hierarchy of network elements. In this study, we consider the origin–destination-based betweenness centrality with the origin-destination matrix obtained from the gravity model. We investigate the network elements hierarchy generated by the betweenness centrality. For such hierarchy we establish some features. In particular, we obtain conditions for the parameters of the gravity model under which the hierarchical ranks of the network element satisfy given properties. We also investigate the dependence of the element hierarchy on the the parameters of the origin-destination matrix for the highway network of a certain region. [ABSTRACT FROM AUTHOR]

One of the possible improvements of the classical Black–Scholes option pricing model is to incorporate the stochastic nature of the short rate dynamics in option valuation. In this paper, we present the numerical scheme, based on the discontinuous Galerkin method, for European option pricing when the short rate follows the Merton model. The pricing function satisfies a partial differential equation with two underlying variables — stock price and short rate value. With a localization to a bounded spatial domain, including setting the proper boundary conditions, the governing equation is discretized by the discontinuous Galerkin method over a finite element grid and Crank-Nicolson time integration is applied, consequently. As a result the numerical scheme is represented by a sequence of linear algebraic systems with sparse matrices. Moreover, the numerical simulations reflect the capability of the scheme presented. [ABSTRACT FROM AUTHOR]

The paper presents a 2D model of a system for contactless inductive energy transmission. Graphical dependences for the inductance of the transmission coil on the frequency, on the magnetic permeability of the concentrators and on the distance between the coils are obtained. In addition, results for the power of the transmitting coil and the dependence of the induced voltage in the receiving coil on the frequency of the power supply are shown. An analytical model of an air transformer is used to explain the numerical results. [ABSTRACT FROM AUTHOR]

The model is a subdiffusion-type fractional degenerate parabolic equation. We consider two inverse source problems with power vertical diffusion coefficients, including the well-known Monin-Obukhov atmospheric model. Final-time over-determination condition is posed. Solutions to both problems are expressed in series expansion. Numerical examples are discussed. [ABSTRACT FROM AUTHOR]

Algorithm for the exact solution of the problem of estimating the parameters of linear regression models by the least absolute deviations method is described. It is based on the descent through the nodal straight lines. This algorithm significantly outperforms other well-known methods of solving the problem and it can be effectively used in practice. The computational complexity of the descent algorithm through the nodal straight lines is assessed. [ABSTRACT FROM AUTHOR]

The reliability analysis and the estimate of preventive maintenance indicators appear a key factor for the devices used in automotive industry. The increasingly successful entry of electronic systems into that sector, in particular in electric vehicles, requires the exploration of reliability analysis methods and tools, as well as the proposal of solutions and recommendations for improving reliability. The present paper considers a complex reliability analysis of wireless electrical vehicles charging station, starting by determining the elements and blocks of lowest reliability in the charging station and pointing out their significance and effect on the overall reliability of the charging station. The next stage is to define the probability states by means of which we determine the state the charging station will be in - operability, failure, protection, maintenance or repair. This analysis allows us to define parameters such as availability, total down time and number of expected failures. The last step is to determine the maintenance time and the interval reliability after carrying out maintenance for a given period of operation. By using this complex analysis, we could identify the weak units in the systems, define how long before maintenance and repair can be done, and give recommendations for improving their reliability. [ABSTRACT FROM AUTHOR]