Browsing by Subject "mathematical model"
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Item A flow-based model of two-level routing in multiservice network(Видавництво Львівської політехніки, 2010) Lemeshko, Olexandr; Hailan, Ahmad M.; Ali, Ali S.In this paper an approach to the flow-based modeling of two-level routing in multiservice networks is considered. The model supports the source routing. At the low level – the level of edge routers – the routes are directly computed, and at the top level the received decisions are coordinated for excluding overloads of communication channels in a multiservice network.Item About problem of absorption of greenhouse gas by chlorophyilsynthesizing microalgae in the presence of sulfur dioxide(Видавництво Львівської політехніки, 2017-12-23) Dyachok, Vasyl; Katysheva, Viktoriia; Lviv Polytechnic National UniversityThe presence of non-competitive reverse inhibition by sulfur dioxide in the process of photosynthesis based on the Lineweaver-Burk theory was theoretically justified and experimentally proved. The mathematical description of the growth of the cells of the microalgae is given and as a result of processing experimental data the growth rates of the algae at certain values of inhibitor concentration was defined. Based on the obtained values the analytical dependence of growth rate of biomass from the substance of inhibitor was redused. The maximum value of concentration of sulphur dioxide which may occur photosynthesis and biomass growth of microalgae was set.Item About the problem of biological processes complicated by mass transfer(Lviv Politechnic Publishing House, 2017-01-20) Dyachok, Vasyl; Huhlych, Serhiy; Yatchyshyn, Yuri; Zaporochets, Yulia; Katysheva, Viktoriia; Lviv Polytechnic National University; National University of Food TechnologiesПредставлено результати вивчення процесу поглинання вуглекислого газу одноклітинними мікроводо- ростями. З’ясовано стадії перебігу процесу, враховуючи особливості умов культивування, зокрема наявність клі- тинного та міжклітинного середовища. Встановлено константи, які конкретизують математичну модель погли- нання вуглекислого газу з повітря клітинами мікроводоростей. Отримані рішення дають можливість прогнозувати кінетику процесу поглинання вуглекислого газу та проектувати обладнання для здійснення технологічного процесу очищення газових викидів за умов реалізації біотехнології на практиці.Item Activator of carbon dioxide absorption by chlorophyll-synthesizing microalgae(Lviv Politechnic Publishing House, 2019-02-26) Dyachok, Vasil; Mandryk, Solomiia; Huhlych, Serhiy; Lviv Polytechnic National UniversityThe influence of nitrogen oxides on the СО2 uptake rate by chlorophyll-producing microalgae of Chlorella type was investigated. Experimental dependences of microalgae concentration growth over time under certain values of nitrogen oxides concentration in the culture medium were obtained. The mathematical model of microalgae biomass growth depending on nitrogen oxides concentration was developed. Based on the solution of the mathematical model and the obtained experimental data, the concentration of nitrogen oxides for the maximal microalgae growth was determined.Item Adaptive decision support system for estimating financial risks(Видавництво Львівської політехніки, 2015) Kozhukhivska, O.; Bidyuk, P.; Kozhukhivskyi, А.A computer based decision support system is proposed the basic tasks of which are adaptive model constructing and forecasting of financial risks. The DSS development is based on the system analysis principles, i.e. the possibility for taking into consideration of some stochastic and information uncertainties, forming alternatives for models and forecasts, and tracking of the computing procedures correctness during all stages of data processing. A modular architecture is implemented that provides a possibility for the further enhancement and modification of the system functional possibilities with new forecasting and parameter estimation techniques. A high quality of final result is achieved thanks to appropriate tracking of the computing procedures at all stages of data processing during computational experiments: preliminary data processing, model constructing, and forecasts estimation. The tracking is performed with appropriate set of statistical quality parameters. Examples are given for estimation of financial credit. The examples solved show that the system developed has good perspectives for the practical use. It is supposed that the system will find its applications as an extra tool for decision making when developing the strategies for financial companies and enterprises of various types.Item Analysis of Magnetic Field of Electrical Devices Based on Their Circuit Models(Видавництво Львівської політехніки, 2021-05-05) Горячко, Всеволод; Гамола, Орест; Рижий, Тарас; Horyachko, Vsevolod; Hamola, Orest; Ryzhyi, Taras; Lviv Polytechnic National UniversityЗапропоновано аналіз магнітних полів електричних машин і електромагнітних апаратів на підставі їх колових математичних моделей. Магнітні системи електротехнічних пристроїв у цих моделях подано у вигляді планарних нелінійних магнітних кіл зі зосередженими елементами. Параметри цих елементів визначено на підставі геометричних розмірів з врахуванням конструктивних особливостей пристроїв та фізичних параметрів середовища.Item Analysis of overvoltages in transformer windings with considering of distributed parameters(Видавництво Львівської політехніки, 2011) Seheda, Mykhaylo; Mazur, Tetyana; Chutora, IvanThe procedure of mathematical model forming intended for electromagnetic processes analysis in transformers when distributed parameters are taken into account is presented. Problems of calculation of the equivalent circuit parameters and solving of partial differential equations are discussed.Item Analysis of process parameters of wastewater treatment of edible oils production(Видавництво Львівської політехніки, 2017-12-23) Dyachok, Vasyl; Marakhovska, Anastasia; Lviv Polytechnic National UniversityInvestigated the liquid extraction method for possibility to sewage treatment of oils production plants. The mixture of organic solvent (extractant) for selective removal of the main pollutants of wastewater was selected. The resulting equilibrium line and operating line process was obtained. Established transfer steps number. The mathematical model of liquid-extraction wastewater treatment was built. The solution of model allows to predict the kinetics of wastewater extraction for implementing the technology in practice. The equipment to design the flowsheet of liquid extraction method for wastewater treatment of food oils production was matched.Item Analysis of the environmental impact of unsorted cullet(Lviv Politechnic Publishing House, 2019-03-20) Hurets, Larysa; Kotolevets, Anastasiia; Miakaieva, Hanna; Miakaiev, Oleksandr; Sumy State UniversityPrediction of cullet accumulation at municipal solid waste landfills was carried out by linear and multiple regression methods. Over time, the amount of waste at the landfills will increase and the soil condition will deteriorate due to Na+ leaching This is confirmed by the experimental study of leaching of sodium ions from the cullet surface of different fractions with pure water and solutions with pH = 4.8 and pH = 9.2.Item Application of liquid extraction for treatment of wastewater from edible oils production(Lviv Politechnic Publishing House, 2018-01-20) Dyachok, Vasyl; Marakhovska, Anastasia; Marakhovska, Svitlana; Lviv Polytechnic National UniversityДосліджено структуру емульсії, яка утворюється у стічних водах виробництв харчових олій. Встановлено вид емульгатора та запропоновано спосіб руйнування емульсії, що забезпечує в подальшому якісне очищення стічних вод олійних виробництв рідинно- екстракційним методом. Отримана лінія рівноваги та робочі лінії процесу. Встановлено кількість ступеней переносу. Побудовано математичну модель рідинно-екстракційного очищення стічної води. Рішення її дає можливість прогнозувати кінетику процесу екстркційного очищення стічних вод при реалізації технології на практиці. Підібрано обладнання для проектування технологічної схеми очищення стічних вод виробництва харчових олій рідинною екстракцію.Item Application of structural matrices for the simulation of mems devices(Видавництво Львівської політехніки, 2015) Karkulovskyi, B.; Karkulovskyy, V.; Kryvyy, R.; Panchak, R.; Pauchok, O.Розглянуто підхід до моделювання МЕМС пристроїв із використанням методу структурних матриць. Розроблено структуру підсистеми для визначення основних характеристик широкого класу пристроїв. In the article the approach to modeling of MEMS devices using the method of structural matrices is presented. The structure of the subsystem to determine the basic characteristics of a broad class of devices.Item Auxiliary model of parametric sensitivity(Publishing House of Lviv Polytechnic National University, 2012) Tchaban, Vasyl; Kostiuchko, Serhiy; Tchaban, ZoranaThe two-point boundary value problem of the differential equations of parametric sensitivity in addition to solving a two-point boundary value problem of the differential equations of state is solved. A joint monodromy matrix is defined by the product of matrix coefficients of the equations of state and the matrix of so-called auxiliary model of parametric sensitivity as the equations of first variation of the incomplete equations of state. The computational results are presented. Розв’язується доточкова крайова задача для диференціальних рівнянь параметричної чутливости як додаток до розв’язання доточкової крайової задачі для диференціальних рівнянь стану. Матриця монохромії визначається добутком матриці коефіцієнтів диференціальних рівнянь стану і матриці так званої допоміжної моделі параметричних чутливостей як рівнянь першої варіації неповних рівнянь стану. Подаються результати комп’ютерної симуляції.Item Computer-Aided System for Monitoring and Planning of Actions to Increase Machine-Building Enterprises Energy Efficiency(Lviv Politechnic Publishing House, 2019-02-26) Ступницька, Наталія; Stupnytska, Nataliya; Національний університет “Львівська політехніка”; Lviv Polytechnic National UniversityОписана математична модель аналізу ефективності енергетичних витрат машинобудівного підприємства (залежно від типу та обсягу продукції, обсягів споживання окремих видів енергоресурсів в умовах конкретних виробничих процесів тощо). Наведено методологію та математичну модель планування заходів щодо модернізації виробничих процесів промислового виробництва. Запропоновано здійснювати оцінку ефективності енергозберігаючих заходів шляхом розрахунку відношення зниження вартості енергоспо- живання до вартості будівельно-монтажних робіт та матеріалів, пов’язаних з впровадженням цих заходів. Розглянуто проблемно-орієнтовану класифікацію енергоспоживчих виробничих процесів та альтернативних заходів, спрямованих на зменшення витрат паливно-енергетичних ресурсів машинобудівного виробництва. Запропоновано алгоритм та програмну реалізацію автоматизованої системи моніторингу та планування заходів з підвищення енергоефективності машинобудівних підприємств.Item Construction of a mathematical model of an unbalanced vibrating separator on a spring suspension(Видавництво Львівської політехніки, 2023-02-28) Topilnytskyy, Volodymyr; Vyshatytskyy, Volodymyr; Lviv Polytechnic National UniversityIn the article, a mathematical model of the oscillating motion of a vibrating separator is constructed. The methods of nonlinear mechanics and the calculation scheme of the vibration separator with an eccentric and a spring suspension, which is presented in the form of a flat mechanical system with four degrees of freedom, were used for its construction. The amplitude of oscillations of the vibration separator capacities in the vertical plane is greater than the amplitude of its oscillations in the horizontal plane. It is believed that the containers of the vibroseparator move only in the vertical plane, that is, they are in planar motion. The obtained mathematical model makes it possible to investigate the influence of the separator parameters with their arbitrary combination on the productivity of its work with the aim of its optimization.Item Determining of volume of natural gas losses caused by damages of distribution networks(Lviv Polytechnic Publishing House, 2015) Dzhyhyrei, Viktor; Matiko, Fedir; Klymkovskyi, Dmytro; Lviv Polytechnic National UniversityThe algorithm of calculation of gas volume losses caused by damages of above-grounded pipelines is proposed in this paper. The mathematical model of natural gas movement in the pipeline is developed for the implementation of the algorithm. The model is used to determine the parameters of the gas flow at the leakage point. The equation for calculation gas flowrate through the holes in the pipeline wall is developed on the basis of the formula of Saint-Venant-Wentzel. The equation is valid for subcritical and critical regime of gas flow. The equation for determining discharge coefficient of the holes in the pipeline wall for gas pressure up to 1.2 MPa is proposed.Item Development of mathematical model of controlled plant using the obtained experimental data(Lviv Polytechnic Publishing House, 2016) Fedoryshyn, Roman; Klos, Sviatoslav; Savytskyi, Volodymyr; Lviv Polytechnic National UniversityThe results of the experimental study of the dynamical and static properties of an electric oven as a controlled plant are presented in the paper. Up-to-date microprocessor instruments were applied during the experiments. Mathematical model of the electric oven was developed on the basis of the experimental data. The adequacy of the model was verified.Item Development of model f integral fire riskmanagement by correlation-registration analysis(Lviv Politechnic Publishing House, 2018-02-10) Kravtsiv, S.; Sobol, O.; National University of Civil Defence of UkraineThis work is devoted to the construction of a mathematical model for controlling integral fire risk using correlation-regression analysis. On the basis of previous work, work is ongoing on developing a risk management method. For this purpose, the second cluster, which includes the Kharkiv region, was analyzed. In the field of initial data, included statistics for 2010–2017 on parameters such as the number of victims of fire in a year, the time of flight of fire and rescue units to the place of fire, the time of their localization of fire, the time of elimination of the fire and the number of people living in the study area. Using statistical data, the risk of death from a fire in a year was mathematically calculated and entered into the field of output data as a parameter to be investigated. The study cluster includes 9 areas, therefore 63 events were received and analyzed. As a result, a regression equation was obtained, which makes it possible to predict a risk with a 95 % confidence. For example, the Kharkiv region conducted a forecast of the corresponding risk, with the actual result close to the forecasted, and lies within the permissible limits with a deviation of 5 %, which indicates the reliability of the developed mathematical model.Item Development the methods of optimum placement undirected planar objects with piecewise non-linear boundaries in the multiply area(Commission of Motorization and Energetics in Agriculture, 2016) Chaplya, Yu.; Sobol, O.In this paper the statement of the problem is formulated and the mathematical model of optimization the placement of the undirected planar geometrical objects with piecewise non-linear boundaries in the multiply area is developed. It is shown the geometrical interpretation and derived the estimate of the number of restrictions in the model. On the basis of a mathematical model for finding the global extremum of the objective function was proposed modified method of branches and boundaries. It is also shown the solutions tree that takes into account the problems of optimal placement of undirected planar geometrical object with piecewise non-linear boundaries in the multiply area, and received the complexity of this method. For locally optimal solutions of the problem modified simulated annealing method has been developed. Thus the analytical expressions for the function of energy system were received, the function, that describes the decrease of temperature over time, function that forms a new state of system. The method of formation the new state of the system was investigated in more detail, which is based on a random permutation of numbers the pair of the objects, it is also based on a consistent placement of objects according to reshuffle their numbers and determining the probability of transition to a new state. It is shown the example of determining permissible points of placement the local coordinate system of the specific geometrical object. The conclusion is that to solve practical optimization problems of placement of the undirected planar geometrical objects with piecewise non-linear boundaries in the multiply area should be used the modified simulated annealing method.Item Diesel generator sets with pulse-width excitation control(Lviv Polytechnic Publishing House, 2016) Semeniuk, Mykola; Leskiv, Ihor; Lviv Polytechnic National UniversityThe article analyzes the processes of diesel generator sets with pulse-width excitation current control with automatic relay controller obtained by mathematical modeling.Item Dynamic simulation of a load system driven by two identical PMDC motors(Видавництво Львівської політехніки, 2013) Atalay, Ahmet Kubilay; Kocabas, Derya Ahmet; Basdogan, SedaIn this study, dynamic simulation of a load system driven by two identical permanent magnet direct current (PMDC) motor is performed by MATLAB / SIMULINK. In the dynamic simulation, two equivalent motors are tandem operated both at same voltage and different voltages in order to drive a mechanical load. The current of each motor, total induced torque and steady state speed of the entire drive system are obtained. It is seen that, when the motors are supplied by the same voltage they share the load equally. On the other hand, if they are operated with different voltages, the motor which is supplied with lower voltage always operates as a generator and the motor which is supplied with higher voltage is overloaded in order to supply the other one and drive the mechanical load.