Analytical Dependences Research Articles

Modelling the parameters of accelerated move-ment of passenger cars in coordinated traffic

Problem. In order to fine-tune the coordination plan to the specific traffic conditions on the road network segment selected for coordination, it is necessary to determine the time for vehicles to travel between synchronized traffic lights. Such models should be based on accelerated rather than uniform moving, and a parameter estimation method should be developed to form them. Goal. Development of a new method for estimating the parameters of a linear model of decreasing acceleration, which allows estimating them in specific driving conditions based on knowledge of two quantities: the length of the link and the random time of its overcoming in free driving conditions. Methodology. Using the functional relationships between travel time, acceleration, speed, and distance, known from kinematics, we have moved to a new sequence of actions to select the type and estimate the parameters of the model that relates the acceleration and speed of a car. For this purpose, using the obtained analytical dependence between time and distance travelled, which contains unknown model parameters, it is possible to find the values of these coefficients by minimising the sum of squares of the difference between the calculated and actual lengths of the link. Results. Based on the search for the minimum square of deviations between the actual and calculated values of the link length, the method of estimating the parameters of the model of accelerated movement of cars at a start from a standstill, based on the results of observations in Kharkiv and Vinnitsa, led to coefficients similar to existing models. The average steady-state speed is estimated at 53.14 km/h. Originality. The presented methodology contains the new transition method from actual times of link passing to parameters of linearly decreasing acceleration model. Practical value. The developed method allows fine-tuning the offsets of the traffic light cycles in the coordination plan to the specific traffic conditions on the road network segment selected for coordination based on actual times of link passing.

Forecasting of financial risks of decline in profit and profitability of companies in the retail industry on the basis of correlation and regression analysis of macroeconomic factors

Aim. Development and realization of the innovative approach to forecasting of financial risks of profit and profitability decrease of retail industry companies on the basis of correlation and regression analysis of macroeconomic factors.Tasks. To identify and substantiate the macroeconomic risk factors of decrease in the retail trade turnover of the Russian companies of the retail industry; to develop a methodology of construction and build regression dependence of the total turnover of the companies of the retail trade industry in the Russian Federation (RF) on the macroeconomic factors; to define parameters of the analytical dependence of the retail trade turnover of the leading Russian retailers on the macroeconomic factors; to reveal and argue the position concerning the restrictions of application of correlation and regression analysis.Methods. The authors applied a systematic approach, providing a comprehensive study of the impact of macroeconomic factors on financial risks of profit and profitability reduction, as well as the correlation and regression analysis, methods of mathematical statistics and econometrics.Results. The methodology of estimation and forecasting of financial risks of profit and profitability decrease of the retail industry companies under the influence of external macroeconomic risk factors based on the use of the regression dependence of the retail industry companies turnover on the selected and grounded macroeconomic factors built in the present article is offered.Conclusions. The methodology of building regression dependences of retail turnover on external macroeconomic factors and the methodology of assessing the impact of these factors on the financial risks of reduced profit and profitability indicators proposed in the study are a methodological basis for forecasting changes in the results and efficiency of economic activities of companies in the retail industry and developing preventive measures aimed at reducing the financial risks of such companies. The quantitative assessments of the impact of macroeconomic factors on the retail turnover of leading Russian retailers obtained in the work allow to identify the most significant external macroeconomic risk factors for each of the companies and give a reasonable forecast of changes in retail turnover, profit and profitability indicators of these companies under the influence of macroeconomic factors.

Justification of the method for determining the reliability of the operator of a mobile fire fighting installation

The object of research is the operator of a mobile fire installation; the subject of research is the operator’s characteristics, particularly his reliability. The method of determining the reliability of a mobile fire installation operator as a functional element of a dynamic system is substantiated. Operator failure is interpreted as the output of its frequency characteristics beyond permissible limits. Analytical dependences for variations of the operator’s frequency characteristics on variations of its parameters – transmission coefficient, delay time, and time constant are constructed. The amplitude and phase reliability of the operator of a mobile fire installation are determined using the Laplace functions, the arguments of which are the permissible values of variations in the frequency characteristics of the operator and variations of its parameters. Determination of variations of operator parameters is carried out by the instrumental method using the operator’s activity monitoring system. The test effect on the operator of a mobile fire installation is carried out in the form of a rectangular pulse that formalizes the change in the position of the combustion cell at a priori a given distance over a priori predetermined time. A signal characterizing the operator’s response to the test impact is determined using the Laplace integral transform. Measuring the parameters of this signal allows you to determine the variations in operator parameters that are used to determine its reliability. It is shown that for variations of operator parameters, the values of which are 10.0 % with RMS deviations of 3.3 %, with a probability of 0.8715 the amplitude-frequency and phase-frequency characteristics at the time of its control will not differ from their nominal values by more than 5.0 %. The requirements regarding the reliability of the operator’s activity control system are determined

Обоснование параметров расчета валковой дробилки с учетом применения шпальтовых просеивающих поверхностей

Introduction. The paper considers a method for calculating the parameters of a roller crusher developed on the basis of established analytical dependencies: the theoretical and technical productivity of spalt sieves from the share of the total volume of rock mass, as well as the productivity of a roller crusher when overlapping spalt sieves with metal sheets. Purpose of the work: development of a methodology for calculating the parameters of a roller crusher. Methods and Materials. To achieve the goal of developing a methodology for calculating the parameters of a roller crusher, a search and analysis of materials on this topic was carried out. Research. The resulting method of calculating roller crushers allows you to evaluate the proposed equipment and, if necessary, select a control scheme for its main technical characteristics. Discussion. In the calculation method of a roller crusher, first of all, it is necessary to determine its main parameters, namely its technical performance, to identify the compliance of the obtained parameters with the requirements of further technological links. After determining the main parameters of the crusher, the design is adjusted and its parameters are adjusted, the technical characteristics of roller crushers have high values and various variants of the overlap schemes of the trellis sieves and the roll of the crusher are recommended to reduce the productivity of roller crushers. Conclusion. Studies have shown that the proposed method is suitable for calculating the technical characteristics of roller crushers. Summary. With successful testing and obtaining positive results of the method of calculating the parameters of the roller crusher, it can be successfully applied to the selection of equipment for the development of new enrichment systems. Also, studies have shown that roller crushers require the use of overlapping schemes of trellis sieves and roll.

RESEARCH AND DETERMINATION OF BASIC PARAMETERS OF VIBROSHOCK MODE OF PRODUCTION OF FUNDAMENTAL BLOCKS

The construction of vibrofluidizer shaping of fundamental blocks is offered in shock-oscillation office hours with formwork and removal of the finished product after completion of process of his compression. The regularities of the movement of vibro-impact units, taking into account the influence of the dynamic parameters of the mixture with a product height of 0.6 m, were revealed, and analytical dependen-cies were obtained to ensure the stabilization of the dynamic parameters of the vibrating machine, which works in the resonance mode with purposeful consideration of the internal oscillatory properties of the vibrat-ing system. The calculation and mathematical model of setting is certain. Worked out equations of motion and the areas of stability are investigational. An algorithm and method of calculation of basic parameters of the shock-oscillation setting is developed. The main provisions for the creation of vibro-impact machines for the formation of foundation blocks have been formulated. Numerical values of the dynamic parameters of the working body and the environment were obtained, which can be used in the design of similar vibro-impact systems.

ОПРЕДЕЛЕНИЕ ОСТАТОЧНЫХ ПРОГИБОВ ИЗГИБАЕМЫХ ЖЕЛЕЗОБЕТОННЫХ ЭЛЕМЕНТОВ НА ОСНОВЕ НЕЛИНЕЙНОЙ ДЕФОРМАЦИОННОЙ МОДЕЛИ

The purpose of this work is to numerically implement the determination of residual deflections of reinforced concrete elements based on a nonlinear deformation model. To solve the equations in a physically nonlinear formulation, the iteration method is used in combination with Microsoft Excel and VBA. Most of the existing engineering methods for the verification calculation and reinforcement of bent elements are based on approaches based on the determination of integral stiffness characteristics of the section by simplified methods. This problem acquires new relevance when using the current norms, when it is necessary to take into account the features of nonlinear deformation of materials, loading mode, and the background of the structure. The article considers the application of a nonlinear deformation model in the calculation of residual deflections. To solve this problem, the bent element is divided into separate sections, on each of which stiffness is calculated based on a nonlinear deformation model. When solving systems of equilibrium equations of a nonlinear deformation model, the iteration method is used. In areas with cracks, the stresses in the reinforcement are adjusted by a coefficient that takes into account the unevenness of their distribution in the section with the crack and between them. After determining the stiffness coefficients in each section, the displacement is determined by integrating the values in the sections of unit moments and the calculated curvature by the numerical method of trapezoids. A load-deflection graph is constructed and approximated by a square polynomial with the derivation of an analytical dependence to determine the residual deflections as well as the stress-strain state of the bent elements as a whole. The analysis and comparison of the results with the normative methodology is given. Numerical example of calculation of good convergence with the normative methodology

Selection of the analytical dependency for assessment of slipping of the Kirovets K-7 wheeled agricultural tractor

BACKGROUND: The accuracy of prediction of towing properties is related to selection of the analytical dependency for assessment of slipping in the process of development or modernization of agricultural tractor in order to define the correct configuration of a machine-tractor unit. The relevance of the study lies in justification of the dependency describing slipping of wheels of modern high-powered 4K4b tractors and needed for study of tractors towing properties. AIMS: Justification of the analytical formula of slipping for better accuracy of towing properties prediction at development stages and modernization of 4K4b tractors and units conjugated to them. METHODS: Known analytical dependencies of slipping were analyzed in the study in order to compare the theoretical assessment results with the results of field-testing at harvest field carried out at machine testing stations according to common method. The theoretical and experimental results were obtained for the Kirovets K-7 series agricultural wheeled tractors. The experimental data of the Kirovets K-7 series tractors was approximated in order to find new dependencies for analytical determination of slipping at harvest field. The approximation coefficient was taken as the criterion for assessment of accuracy of experimental data description by the dependencies. RESULTS: Among the considered analytical dependencies for prediction of slipping coefficient value, the equations which describe the experimental data of towing testing of the Kirovets K-7 series tractors the most satisfactorily were outlined. Based on approximated experimental data, the equations of slipping depending on specific towing force were obtained. There is the equation common for all tested tractors and there are separate equations for tractors with 32-inch and 38-inch tires. These equations provide with the best approximation of description of tractors. Values of specific towing force correlating to maximal towing efficiency and acceptable slipping coefficient of 16% for the Kirovets K-7 series tractors were obtained. CONCLUSIONS: Some existing and new proposed in the article equations can be used for prediction of values of slipping coefficient at creating of potential towing characteristic for high-powered 4K4b tractors.

Design of centrifugal radial fans using regression analysis methods

With the development of scientific and technological progress in agriculture, the use of operational and mathematical modelling for effective solution of problems and resource conservation in the field of agricultural engineering is relevant. Therefore, the purpose of the study was to determine the optimal parameters of the centrifugal radial fan of a pneumatic precision seed drill by constructing a new mathematical model of the process of its operation. This was achieved by applying mathematical modelling methods when planning multi-factor experiments. As a result, a complex of automated experiments has been defined, which leads to a significant increase in the productivity of scientific work. A statistical representation of the experiment is established, which allows moving to a multi-factor active experiment, in which it is possible to separate the influence of factors from the noise background and make a transition to statistical methods for analysing the results. This allowed predicting the optimal characteristics of the centrifugal radial fan of the precision seed drill. In the course of this study, a new regression equation was compiled in the form of a first-degree polynomial, which determines the influence of each of the factors on the magnitude and value of the response. The coefficients of the polynomial are determined, the significance of the coefficients is estimated, and the adequacy of the proposed model is checked. After obtaining the regression equation, it became possible to graphically construct the dependence of the response function on impact factors. A fractional factor experiment was also performed, which determined the values of the parameters of the object’s state for all possible combinations of levels of variation of the factors Xi. Based on the established functional relationship between the output parameter of the fan, a regression equation of the following form is obtained: Pv=Pv(n, ß1, ß2, z). This predicted the receipt of the total pressure Pv (Pa), when setting different values of independent quantities n, ß1, ß2 and z. The application of the obtained analytical dependencies significantly simplified the determination of optimal design parameters of pneumatic systems for the development and construction of modern technical seed drills

Searching for the relationship between the temperature and humidity of tailings material by processing digital photographs of laboratory experiments and color models

Relevance. Tailings beach surface dries and deflates, which intensifies the dusting process, results in ecosystems disruption on the adjacent territories, and adversely impacts health of population. The use of digital photographs, including those obtained with the help of unmanned aerial vehicles, seems to be promising in terms of reagents application simplification and dusting minimization. Research objective is to determine the quantitative relationship between the temperature and humidity of tailings materials by analyzing the digital photographs of laboratory experiments using RGB and Lab methods. Methods of research. Standard equipment was used to perform a laboratory experiment to determine the temperature and humidity of tailing dump surface layer samples. Digital photographs were taken in natural light and UV light. At the first stage, the images were processed to obtain the values of the components of two color models, RGB (redness and saturation indices were calculated) and Lab (the color difference index was calculated, two standards of black and white were used). At the second stage, as a “zero” approximation, the simplest (linear) analytical dependence between temperature and humidity was studied. Results and analysis. The coefficients of calculated linear dependences are compared with the corresponding coefficients of direct experimental data processing. It is shown that in natural light: the smallest deviations for the dependence of temperature on humidity correspond to the redness index in the RGB method and the black standard in the Lab method; the smallest deviations for the dependence of humidity on temperature correspond to the saturation index in the RGB method and the black standard in the Lab method. It is shown that in UV light: the smallest deviations for the dependence of temperature on humidity correspond to the saturation index in the RGB method and the black standard in the Lab method; the smallest deviations of the dependence of humidity on temperature correspond to the redness index in the RGB method and the white standard in the Lab method. Conclusions and scope. The mentioned indices and colors of standards can be recommended when processing similar laboratory experiments and natural studies directly on the dusting site.

Solving the Lamé problem in the quasi-brittle setting to substantiate the solution scheme for rock breaking by the blast-hole method

Introduction. The blast-hole method of mining and preparing rocks for excavation has been used by mankind since ancient times. However, there are no generally accepted and generally recognized design and calculation methods for this process, which was established in the review part of this work. Research objective is to develop a basic analytical model for hard rock quasi-brittle materials breaking by a blast-hole method using static thrusts. Methods of research. A detailed analysis of the breaking mechanism through the transition state from the rock material continuity to its separation is the methodological basis of the developed quasi-static model for calculating the energy-power indicators of the process of separating volumes (pieces) of rock into separate parts. It makes it possible to justify and determine: the irreversible energy of rupture through the energy constant rock material in relation to the process energy efficiency, critical load resulting in local breaking, the size and number of the primordial tension cracks, as well as the number of through cracks. Result. The obtained indicators and parameters formed the body of the energy balance equation of the irreversible energy of rupture of rock pieces. The developed methodology for setting and solving the problem of the limiting state of quasi-brittle materials rupture in the form of a thickwalled cylinder (the Lamé problem) that simulates a certain solid volume deformed by a uniformly distributed blast-hole pressure of thrusts, is universal and can serve as a base for assessing a set of issues related to mining. The resulting interrelation of indicators made it possible to derive an equation for the energy balance of the rock volumes rupture. Due to the solution for this equation, the critical value of the blast-hole pressure that results in local breaking, the size of primordial cracks, and the corresponding limiting burst pressure were obtained for the first time. Theoretical novelty. Within the framework of the general approach of the quasi-brittle materials breaking linear theory, based on the developed methodology, the problem of the limiting state of the rock in the form of natural joint loaded with a static thrust through a single blast-hole, was correctly stated and solved by the energy method for the first time. As a result of the research, an analytical dependence of the rock static breaking energy intensity was obtained, which includes both the volumetric specific energy of potential deformation and the specific surface energy

Probability of simultaneous multiple leakages at sections of water networks in the process of localization of hidden water leaks

Hidden leaks from water supply networks account for 50% to 90% of total leakage losses. The presence of two or more simultaneous leaks in a section of the water supply network significantly reduces the accuracy of locating hidden leaks. The method of independent Poisson events and the hypothesis of stationarity, absence of consequences, and ordinariness of leaks are used for the probabilistic description of the problem of multi-leakage in water supply networks. The analytical dependence of the probability of multiple leakages on the specific annual emergency rate of the site, its length and the duration of the localization and repair period is obtained. A generalized semi-empirical equation was obtained for estimating the maximum permissible duration of the localization and repair period depending on the annual emergency rate of the site for a given multi-leakage probability.

РОЗРАХУНОК ПЕРЕТВОРЮВАЧІВ ПОСТІЙНОЇ НАПРУГИ В РЕЖИМАХ ПЕРЕРИВЧАСТОЇ ПРОВІДНОСТІ З ВИКОРИСТАННЯМ МЕТОДА УСЕРЕДНЕННЯ НА ОСНОВІ ТЕОРЕМ ЛАГРАНЖА

The features of calculation of output voltage ripple in dc converters with discontinuous conduction modes are considered. It is shown that the use of behaviors of charge-discharge processes of the output capacitor makes it possible to determine the parameters of voltage pulsation on it, using a mathematical model of the converter with variables averaged using Lagrange's theorems. The specified approach contributes to the significant simplification of calculations and reduction of their labor intensity. Analytical and graphical dependences of the ripple value and the ripple coefficient of output voltage of main circuits of the converters in the mode of discontinuous conduction - buck, boost and buck-boost types - were obtained. The developed analytical dependencies make it possible to effectively calculate the parameters of the converters and investigate their properties at the stage of their design, using available methods of mathematical analysis. The reliability of the obtained analytical ratios and calculation results was confirmed by simulation of converters using the PSim package. References 14, figures 4, tables 3.

Settlement of a Foundation on an Unsaturated Sandy Base Taking Vibrocreep into Account

Dynamic loading causes (1) a substantial change in the strength and deformation parameters of sandy soil and (2) excessive viscoplastic deformation. The goal of this study is to create a new analytical solution to the problem of the settlement of (1) the foundation that is the source of dynamic loading, and (2) a nearby foundation, taking into account the rheological properties of sandy soil subjected to vibration, given that these rheological properties depend on shear stresses. The proposed solution allows the progress of deformation over time to be described. The present paper states and provides an analytical solution for the problem of evaluating the settlement of a single foundation that transmits static and dynamic harmonic pressure to the base. The authors also analyze the settlement of another foundation located at some distance from the transmitting foundation. The second foundation transmits static pressure to the base. The dependence of the viscosity coefficient on the shear stress intensity and vibration intensity, as well as the vibrocreep decay over time, are based on the exponential and homographic dependencies previously identified by two of the authors (A.Z. Ter-Martirosyan and E.S. Sobolev). The solution to the problem is obtained by numerical integration in the Mathcad program of an analytical expression for nonlinear viscoplastic deformations. As a result of the research, the authors have found that the dynamic viscoplastic component makes the greatest contribution to foundation settlement. The settlement of the transmitting foundation increases along with increasing static and dynamic pressure transmitted to the base. The settlement of the nearby foundation increases when the pressure increases under the foundation, but it reduces when static pressure from the transmitting foundation, the depth of the foundation, and the distance between the foundations increase. General analytical dependencies obtained by the authors comply with the results of laboratory and field experiments performed by other researchers. These dependencies can be used to predict the settlement of foundations in whose unsaturated sandy bases mechanical vibrations propagate.

Justification of the Design Parameters of a Small-sized Potato Digger

The results of studies on the optimization of the parameters of oscillatory-separating mechanisms of a small-sized potato digger are presented. An analytical dependence in the form of a regression equation is obtained, which makes it possible to determine the optimal parameters of the vibration separating mechanism to improve separation in the tuber soil mixture.

FREQUENCY ANALYSIS OF AN ARM OF MACPHERSON SUSPENSION ON A PASSENGER CAR

The smoothness, ride comfort, safety and handling of the car depends on the manner of suspension design and its corresponding details. One of main functions of the arm and the rubber bushings mounted on it is to reduce the vibrations and the noise transferred from the road to the passenger car components. This article presents the results of a frequency analysis of an arm of the MacPherson front independent suspension. For this purpose, three-dimensional geometric models of the arm and rubber bushings are created via finite element analysis (FEA) software SolidWorks, where Skoda Octavia passenger car was used as a prototype. The axial, radial and torsional stiffness of the rubber bushings were determined through analytical dependences and FEА. The obtained results had been used for calculation of the natural frequencies and mode shapes of the arm which were compared with experimentally obtained data.

Method for Forecasting the Remaining Useful Life of a Furnace Transformer Based on Online Monitoring Data

Implementing the concept of a “smart furnace transformer” should stipulate its information support throughout its life cycle. This requires improving techniques for estimating the transformer’s health and forecasting its remaining useful life (RUL). A brief review of the problem being solved has shown that the known RUL estimation techniques include processing the results of measuring the facility state parameters using various mathematical methods. Data processing techniques (deep learning, SOLA, etc.) are used, but there is no information on their application in online monitoring systems. Herewith, fast (shock) changes in the resource caused by the failures and subsequent recoveries of the facility’s health have not been considered. This reduces the RUL forecasting accuracy for the repairable equipment, including transformers. It is especially relevant to consider the impact of sudden state changes when it comes to furnace transformers due to a cumulative wear effect determined by their frequent connections to the grid (up to 100 times a day). The proposed approach is based on calculating the RUL by analytical dependencies, considering the failures and recoveries of the facility state. For the first time, an engineering RUL forecasting technique has been developed, based on the online diagnostic monitoring data results provided in the form of time series. The equipment’s relative failure tolerance index, calculated with analytical dependencies, has first been used in RUL forecasting. As a generalized indicator, a relative failure tolerance index considering the facility’s state change dynamics has been proposed. The application of the RUL forecasting technique based on the results of dissolved gas analysis of a ladle furnace unit’s transformer is demonstrated. The changes in the transformer state during the operation period from 2014 to 2022 have been studied. The RUL was calculated in the intensive aging interval; the winding dismantling results were demonstrated, which confirmed developing destructive processes in the insulation. The key practical result of the study is reducing accidents and increasing the service life of the arc and ladle furnace transformers. The techno-economic effect aims to ensure process continuity and increase the metallurgical enterprise’s output (we cannot quantify this effect since it depends on the performance of a particular enterprise). It is recommended to use the technique to forecast the RUL of repairable facilities equipped with online monitoring systems.

Modeling of thermal power plants in the study of reliability of power supply and energy security

RELEVANCE. Maintaining the required level of energy security (ES) and reliability of fuel and energy supply is one of the priority tasks in the management of the energy sector. In the functioning of the fuel and energy complex various threats are possible, which can lead to the violation of the reliability of fuel and energy supply and the emergence of shortages ofvarious types of energy resources. To assess the level of energy security, approaches are considered to form a mathematical model of the FEC, which combines all sectors of the energy sector. Despite the trends of transition to low-carbon energy sources associated with energy transformation, thermal power plants remain one of the main sources of heat and electricity.Due to the ability to generate large amounts of heat only thermal power plants can be a source of centralized energy supply of large territories. In this regard, when modeling the fuel and energy complex, it is necessary to develop mathematical models of TPPs, which will correctly reflect the technological processes that affect the reliability of energy supply. OBJECT. Development of mathematical models of interaction of electric power, heat supply and fuel systems within the framework of thermal power plants designed to study energy security and reliability of fuel and energy supply. METHODS. Mathematical modeling of fuel consumption dependences on electrical and thermal load at thermal power plants is used as methods. To obtain analytical dependencies, the least squares approximation of the consumption characteristics of thermal power plants was carried out. RESULTS. As part of the work, analytical dependences of fuel consumption on thermal and electrical load for various types of thermal units were obtained. For all considered steam turbines, linear dependences of theamount of heat supplied to the turbine on its load (electrical and / or heating depending on the type of turbine) were obtained. For boilers, an approximation of the dependence of efficiency on thermal load was carried out. According to the results of the approximation, a linear dependence is assumed. For gas turbine installations, an approximation of the dependence of the efficiency on the load was carried out, according to the results of which a second-order polynomial was obtained. CONCLUSION. The paper investigates the problem of mathematical modeling of the interconnected operation of fuel, heat and power and electric power systems within the framework of the functioning of the energy sector. Analytical dependences are obtained for different types of generating equipment, including boilers, steam turbines and gas turbine installations. The obtained dependences are necessary for the analysis of energy security and reliability offuel and energy supply. The models of thermal power plants presented in the paper are the most suitable for the analysis of energy security and reliability of fuel and power supply, as they provide the necessary accuracy of calculations and take into account the specifics of various generating equipment, without dropping to the level of microparameters.

Investigation of Bulk Material Transportation by Screw Conveyer with Hinge-Pan Operating Device

The article presents a new design of a hinged and sectional working body and substantiates its optimal parameters for ensuring the movement of loose materials along curvilinear routes. Analytical dependencies have been derived to determine the rational design and power parameters of the hinged-sectional working body, and the functional dependencies of the minimum permissible radius of curvature of the RC technological highway on the angular rotation of adjacent sections and their design parameters have been established. The axial speed and power of cargo transportation by the articulated-sectional working body of the screw conveyor along a curved route have been determined. Experimental studies have been conducted to determine the influence of the number of revolutions, the height of material lifting and the radius of curvature of the flexible helical sectional working body RC on the torque T, as well as the determination of the influence of the number of revolutions n, the filling factor of the main line ψ and the diameter of the main line D on the performance Q when transporting loose materials.

Microscopy with heralded Fock states.

We consider a microscopy setting where quantum light is used for illumination. Spontaneous parametric down conversion (SPDC) is used as a source of a heralded single photon, which is quantum light prepared in a Fock state. We present analytical formulas for the spatial mode tracking along with the heralded and non-heralded mode widths. The obtained analytical results are supported by numerical calculations and the following discussion taking into account realistic setup parameters such as finite-size optics and finite-size single-photon detectors. This allows us to observe that the diffraction limit can be approached with simultaneous alleviation of the photon loss leading to increased signal-to-noise ratio - a factor limiting practical applications of quantum light. Additionally, it is shown that the spatial resolution can be manipulated by carefully preparing the amplitude and phase of the spatial mode profile of the single photon at the input to the microscope objective. Here, the spatial entanglement of the biphoton wavefunction or adaptive optics can be applied for spatial mode shaping. Analytical dependencies between the incident and focused spatial mode profiles parameters are provided.

Optimization of Water Pipe Network and Formulation of Pumping Rate

Minimizing water delivery costs and increasing water supply dependability are the two key objectives in designing and operating of water distribution systems. An analytical solution for the best pipe diameters of a water distribution pipe network was created in this study. The raw water was collected from a water canal and transported to a treatment plant (WTP). The cleansed water was pushed into the water distribution network via the pumping station. The derivative approach was used in the optimization process, and the cost functions incorporating the various capital and operating expenses were used. The initial diameters were adjusted to reach the least-cost diameters. The study shows that the optimum design of a pipe network (PNW) achieves saving a total cost of about 12.3% after utilizing our unique method. The optimal pumping rate in the PNW can also be determined using an analytical approach that considers the optimum value that occurs when the minor and friction losses in the entire network are at their lowest. The analytical solution for the optimum pumping rate shows a rigid value of optimum pumping rate (Qopt) which is 5296.32 m3/day. On comparative estimates, this figure is very close to that of 5,300 m3/day interpreted from the graphical solution, with negligible deviation. The total cost and optimum pumping rate results for the analyzed PNW example demonstrate the correctness of the analytical solutions, reliability, and dependability of the assumptions.