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Постійне посилання колекціїhttps://dspace.nuft.edu.ua/handle/123456789/7522
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Документ Improving the efficiency of mass-exchange between liquid and steam in rectification columns of cyclic action(2021) Buliy, Yuri; Kuts, Anatoly; Yuryk, Ivan; Forsyuk, AndriyThe purpose of the work was to determine the optimal time of residence of the liquid on the plates, the grade of extraction and concentration ratio of volatile impurities of alcohol and the specific consumption of heating steam in rectification columns of cyclic action. The studies were carried out in a rectification column, equipped with flaky plates with a variable free cross-section. Concentration of alcohol volatile impurities was determined by chromatographic method, the grade of their extraction and concentration ratio – by calculation method, other indicators – by commonly known methods. The maximum extraction of volatile impurities was being achieved in a rectification column, equipped with flaky plates containing turnaround sections connected to drive mechanisms, the action of which is occurred according to a given algorithm. The optimal parameters of operating the column were: vapor velocity in the orifices of the flakes during the period of liquid retention on the plates 12-14 m/s; during liquid pouring 1-1.5 m/s; time of residence of the liquid on the plates 40 s, pouring time 1.7 s; pressure in the lower part of the column 12 kPa; the concentration of ethyl alcohol in the still liquid 3-4% vol. In order to provide the cycles, the free sectional area of the plates must change instantaneously from 5.5 to 51.7%. This technical solution allows to provide complete disposal of ethers, methyl acetate and isopropyl alcohol, to increase the grade of extraction of higher alcohols of sivush oil and methanol by 38%, the concentration ratio of aldehydes by 25%, higher alcohols by 38%, methanol by 37%, and to reduce specific consumption of heating steam by 40% compared to a typical column operating in stationary mode.Документ On exact solutions of nonlinear equation(2021) Yuryk, IvanA method for construction of exact solutions to nonlinear equation ut = (F(u)ux)x + G(u)ux + H(u) which is based on ansatz p(x) = ω1(t) φ(u) + ω2(t) is proposed. The function p(x) here is a solution of equation (p')2 = Ap2 + B, and the functions ω1(t), ω2(t) and φ(u) can be found from the condition that this ansatz reduces the nonlinear equation to a system of two ordinary differential equations with unknown functions ω1(t) and ω2(t). Запропоновано метод побудови точних розв’язків нелінійного рівняння т ut = (F(u)ux)x + G(u)ux + H(u), який ґрунтується на використанні підстановки p(x) = ω1(t) φ(u) + ω2(t), де функція p(x) є розв’язком рівняння (p')2 = Ap2 + B, а функції ω1(t), ω2(t) та φ(u) знаходяться з умови, що дана підстановка редукує рівняння до системи двох звичайних диференціальних рівнянь з невідомими функціями ω1(t) та ω2(t).Документ Unitary representations of Poincare group P(1;n) in SO(1, n)-basis(2021) Ostrowska, Olga; Yuryk, IvanThis paper concerns the problem of reduction of unitary irreducible representations of the Poincare group P(1;n) with respect to representations of its subgroup SO(1, n). Basing on the generalization of the Wigner--Eckart theorem matrix elements of the shift operators in the SO(1, n)-basis are obtained. Стаття присвячена проблемам редукції незвідних зображень групи Пуанкаре P(1;n) по зображенням її підгрупи SO(1, n). На основі теореми Вігнера-Еккарта отримані матричні елементи операторів трансляції в SO(1, n)-базисі.Документ On exact solutions of the nonlinear heat equation(2019) Barannyk, Anatoliy; Yuryk, IvanA method for construction of exact solutions to nonlinear heat equation ut = (F(u)ux)x + G(u)ux + H(u) which is based on ansatz p(x) = ω1(t) φ(u) + ω2(t) is proposed. The function p(x) here is a solution of equation (p')2 = Ap2 + B, and the functions ω1(t), ω2(t) and φ(u) can be found from the condition that this ansatz reduces the nonlinear heat equation to a system of two ordinary differential equations with unknown functions ω1(t) and ω2(t). Запропоновано метод побудови точних розв’язків нелінійного рівняння теплопровідності ut = (F(u)ux)x + G(u)ux + H(u), який ґрунтується на використанні підстановки p(x) = ω1(t) φ(u) + ω2(t), де функція p(x) є розв’язком рівняння (p')2 = Ap2 + B, а функції ω1(t), ω2(t) та φ(u) знаходяться з умови, що дана підстановка редукує рівняння до системи двох звичайних диференціальних рівнянь з невідомими.Документ Partial solutions of a system of Euler equations(2019) Yuryk, IvanGroup-theoretical methods are applied to find particular solutions to differential systems in hydrodynamics.Obtained solutions that satisfy the Rankine-Hugoniot conditions .Документ Exact solutions to nonlinear equation of utt=a(t)uuxx+b(t)u2x+c(t)u(2018) Barannyk, Anatoliy; Barannyk, Tatiana; Yuryk, IvanДокумент Invariant solutions of a system of Euler equations that satisfy the Rankine–Hugoniot conditions(2018) Yuryk, IvanWe consider equations of hydrodynamics with certain additional constraints. Group-theoretical methods are applied to find invariant solutions of a system of Euler equations that satisfy the Rankine–Hugoniot conditions. Ми розглядаємо рівняння гідродинаміки з певними додатковими обмеженнями. Теоретико-групові методи застосовуються для пошуку інваріантних рішень системи рівнянь Ейлера, що задовольняють умовам Ренкіна-Гюгоніо.Документ Application of group-theoretical methods to point explosion problem in incompressible liquid(2015) Yuryk, IvanGroup-theoretical methods are applied to find particular solutions to differential systems in hydrodynamics. Obtained solutions that satisfy the Rankine-Hugoniot conditions is used to describe a point explosion in incompressible liquid.Документ On hidden symmetries and solutions of the nonlinear d’Alembert equation(2013) Barannyk, Anatoliy; Barannyk, Tatiana; Yuryk, IvanNon-Lie symmetries of nonlinear d’Alembert equation in the pseudo-Euclidean space R2;2 are studied and new classes of exact solutions are constructed. Вивчаються неліївські симетрії нелінійного рівняння Даламбера в псевдо-евклідовім просторі R2; 2Документ Generalized separation of variables for nonlinear equationutt = F(u)uxx + aF′(u)u2х(2013) Yuryk, IvanWhere F(u), a#0 are an arbitrary function and constant, correspondingly. The problem is studied for which functions F(u) it admits ans¨atz t = w1(x)d(u) + w2(x), which reduces this equation to a system of two ordinary differential equations with unknown functions w1(x) and w2(x). For these equations classes of exact solutions with generalized separation of variables are constructed, which can not be obtained by the method of classical group analysis.
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