Кафедра прикладної математики

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Відповідальний за розділ: Толбатов Євген Юрійович, доцент кафедри Вищої та обчислювальної математики. E-mail: eugene_t@ukr.net

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A brief overview of modern software optimization approaches
(National Aviation University, 2018) Pristavka, P.O.
Approximate solution to abstract differential equations with variable domain
(2010-03) Vasylyk, V.B.
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral for vector-valued functions. This technique translates the initial problem to a system of integral equations. Then the system is approximated with exponential accuracy. The theoretical results are illustrated by examples associated with the heat transfer boundary value problems.
Asymptotic normality of improved weighted empirical distribution functions
(Theory Probab. Math. Stat, 2004) Кубайчук, Оксана Олексіївна; Майборода, Р.Є
Weighted empirical distribution functions are often used to estimate the distributions of components in a mixture. However, weighted empirical distribution functions do not possess some properties of probability distribution functions in the case of negative weight coefficients. We consider a method allowing one to improve weighted empirical distribution functions and obtain an estimator that is a distribution function. We prove that this estimator is asymptotically normal. The limit distribution of the improved weighted empirical distribution function coincides with that of the initial estimator.
Bis(4'-(4-pyridyl)-2,2':6',2"-terpyridine) ruthenium(II) complexes and their N-alkylated derivatives in catalytic light-driven water oxidation
(RSC, 2013) Zhuk, Petro; Hongjin, Lv
Comparison of some methods for solving the internal wave propagation problem in a weakly stratified fluid
(Shpringer Link, 2011) Москальков, М.Н
COMPONENTS OF INFORMATION TECHNOLOGY PROCESSING OF DATA OBTAINED FROM UNMANNED AERIAL VEHICLE
(НАУ, 2012) Приставка, Пилип Олександрович; Ассаул, Андрій; Нічіков, Євген; Рогатюк, Анастасія
The system of automated processing and analysis of digital images and videos obtained from the board of unmanned aerial vehicle offered.
Consideration of the contribution of chemical (non-enzymatic) conversion of substrate in the general mechanism of enzyme
(Інститут біохімії ім. О. В. Палладіна НАН України, 2018) Костерін, Сергій Олексійович; Карахім, Сергій Олександрович; Жук, Петро Федорович; Kosterin, Segiy Oleksiyovych; Karahim, Sergiy Oleksandrovych; Zhuk, Petro Fedorovych
When enzyme-catalyzed reactions are studied, it is necessary to take into account the contribution of the chemical (non-enzymatic) conversion of the substrate to the product, which is carried out together with the enzyme-catalyzed conversion of the substrate. It is generally believed that the difference of the product concentration that was formed in the presence of the enzyme and in its absence (during the same time interval) is the concentration of the product that was formed directly in the enzyme-catalyzed reaction, i.e. that there is additivity of the product concentrations at each time point. In this paper, we have analyzed when there is additivity and how to correctly take into account the contribution of chemical (non-catalytic) substrate conversion when the enzyme-catalyzed reactions are investigated. We have shown that the additivity of productconcentrations and initial rates is observed only for a period when the product concentration increases linearly with time. The longer the reaction proceeds the more the deviation from the additivity. Under equilibrium condition, there is no additivity of equilibrium product concentrations but under conditions of detailed balance the equilibrium product concentration of the overall reaction, including the enzyme-catalyzed and chemical (nonenzymatic) conversion of the substrate, is also at the same time the equilibrium concentration of the product of the enzyme-catalyzed conversion of the substrate.
DIGITAL VIDEO STABILIZATION FOR UNMANNED AERIAL VEHICLE
(НАУ, 2014) Приставка, Пилип Олександрович; Нічіков, Євген
A video stabilization information technology from unmanned aircraft proposed. It allows compensate the impact of macromotions and micromotions of video camera, ie remove the fluctuations of individual video frames and increase their sharpness. The above methods and means can be used for video processing in real time.
Doxygen и Graphviz: документирование проектов на C#
(2006) Пискунов, А.Г.; Горбань, А.С.
Данный документ обсуждает использование open source утилит Doxygen и dot из пакета Graphviz для генерации документации из кодов C#.
Full specle suppression in laser projectors using two Barker code-type diffractive optical elements
(Optical Society of America, 2013) Klymenko, V. O.
Functional moments estimators analysis by the Monte-Carlo method for model of mixture with varying concentrations
(Journal of Advances in Mathematics (JAM)., 2018) Kubaychuk, O
The functional moments estimation by the sample from the mixture with varying concentrations is studied. The problem of efficiency the simple linear estimator with fixed weight against the adaptive or improved estimators with random weight is considered. By the Monte-Carlo method it is shown that simple linear estimator is better for small sample sizes, but for large samples the adaptive and improved estimators are more efficient.
Hypoxic regulation of MYBL1, MEST, TCF3, TCF8, GTF2B, GTF2F2 and SNAI2 genes expression in U87 glioma cells upon ire1 inhibition
(Ukr. Biochem. J., 2016) Kubaychuk, O
We investigated the impact of IRE1/ERN1 (inositol requiring enzyme 1/endoplasmic reticulum to nucleus signaling 1) knockdown on hypoxic regulation of the expression of a subset of proliferation and migration- related genes in U87 glioma cells. It was shown that hypoxia leads to up-regulation of the expression of MEST and SNAI2, to down-regulation – of MYBL1, TCF8 and GTF2F2 genes at the mRNA level in control glioma cells. At the same time hypoxia does not affect the expression of TCF3 and GTF2B transcription factor genes. In turn, inhibition of IRE1 modifies the effect of hypoxia on the expression of all studied genes, except MYBL1 and GTF2B. For instance, IRE1 knockdown decreases sensitivity to hypoxia of the expression of MEST, TCF8 and SNAI2 genes and increases sensitivity to hypoxia of GTF2F2 expression. At the same time IRE1 inhibition introduces sensitivity to hypoxia of the expression of TCF3 gene in glioma cells. The present study demonstrates the inhibition of IRE1 in glioma cells affects the hypoxic regulation of the expression of genes studied. Hypoxic conditions do not abolish the effect of IRE1 inhibition on the expression of respective genes. To the contrary, in case of SNAI2, GTF2F2 and MEST hypoxic conditions magnify the effect of IRE1 inhibition on the expression of respective genes in glioma cells.
Improved estimates for moments by observations from mixtures
(Theory Probab. Math. Stat, 2005) Kubaychuk, O.; Majboroda, R
Abstract. Procedures for improving weighted empirical distribution functions constructed from mixtures with varying concentrations are considered. The procedures are such that the estimators of moments of the mixture components constructed from weighted empirical distribution functions have specified properties (say, estimators of the variance must not be negative). We prove that the moment estimators constructed from improved weighted empirical distribution functions have the same asymptotic behavior as those constructed from the original weighted empirical distribution functions.
Influence of partial hydrolysis on the protein extraction from sunflower meal
(National University of Food Technologies, 2014) Kubaychuk, O.О.; Nosenko, T.T.; Vovkodav, N.I.; Cherstva, A.A.
We investigated the influence of protein hydrolysis degree in the presence of neutral protease from Bacillus subtilis on the process of protein extraction from sunflower meal. Correlation between protein hydrolysis degree and affectivity of protein extraction was analyzed. Materials and methods. The degree of protein hydrolysis was determined as increase of TCA-soluble proteins concentration compared to control samples. Protein concentration in extracts was determined photometrically. Result and discussion. Determination of protein concentration in obtained extracts have shown that main part of soluble proteins was extracted during first 20 min. The protein concentration in extracts obtained in the presence of protease was approximately twice higher than in control samples. The protein hydrolysis degree was sufficiently low and varied from 3,5 % to 5,2 % at moderate enzyme/substrate ratio. When enzyme/substrate ratio increased the degree of hydrolysis was also rising and it reached 9,0-9,5 % during 40- 60 min. Such level of hydrolysis is desirable for improvement of protein functional properties and higher hydrolysis level results in loss of protein functionality. The protein hydrolysis degree was dependent from the enzyme/substrate ratio and the duration of reaction. Nonlinear model was obtained for estimation of the affectivity of protein extraction as function of enzyme/substrate ratio and extraction time. Obtained model explains 92.81% of data variation and approximates well the available data. It was shown also that high correlation (r=0,69) exists between concentration of proteins in extracts and degree of protein hydrolysis. Conclusion. The partial hydrolysis of sunflower meal proteins by neutral protease resulted in increase of protein concentration in extracts. Obtained model could be used in prediction of protein hydrolysis level during protein extraction from sunflower meal in the presence of proteolitic enzymes and their functional properties.
Kinetics simulation of transmembrane transport of ions and molecules through a semipermeable membrane
(Springer Science+Business Media, 2020) Карахім, Сергій Олександрович; Жук, Петро Федорович; Костерін, Сергій Олексійович; Karakhim, Sergiy Oleksandrovych; Zhuk, Petro Fedorovych; Kosterin, Sergiy Oleksiyovych
We have developed a model to study the kinetics of the redistribution of ions and molecules through a semipermeable membrane in complex mixtures of substances penetrating and nonpenetrating through a membrane. It takes into account the degree of dissociation of these substances, their initial concentrations in solutions separated by a membrane, and volumes of these solutions. The model is based on the assumption that only uncharged particles (molecules or ion pairs) diffuse through a membrane (and not ions as in the Donnan model). The developed model makes it possible to calculate the temporal dependencies of concentrations for all processing ions and molecules at system transition from the initial state to equilibrium. Under equilibrium conditions, the ratio of ion concentrations in solutions separated by amembrane obeys the Donnan distribution. The Donnan effect is the result of three factors: equality of equilibrium concentrations of penetrating molecules on each side of a membrane, dissociation of molecules into ions, and Le Chatelier’s principle. It is shown that the Donnan distribution (irregularity of ion distribution) and accordingly absolute value of the Donnan membrane potential increases if: (i) the nonpenetrating salt concentration (in one of the solutions) and its dissociation constant increases, (ii) the total penetrating salt concentration and its dissociation constant decreases, and (iii) the volumes ratio increases (between solutions with and without a nonpenetrating substance). It is shown also that only a slight difference between the degrees of dissociation of two substances can be used for their membrane separation. Ми розробили модель для вивчення кінетики перерозподілу іонів і молекул через напівпроникну мембрану у складних сумішах речовин, що проникають і не проникають через мембрану. При цьому враховується ступінь дисоціація цих речовин, їх початкові концентрації в розчинах, розділених мембраною, та обсягах цих рішення. Модель ґрунтується на припущенні, що тільки a незаряджені частинки (молекули або іонні пари) дифундують через a мембрана (а не іони, як у моделі Доннана). Розроблена модель дає змогу розрахувати часові залежності концентрацій для всіх переробних іонів і молекул при переході системи з вихідного стану в рівноважний. У рівновазі Умови співвідношення концентрацій іонів у розчинах, розділених аммбраною, підпорядковується розподілу Доннана. Доннан ефект є результатом трьох факторів: рівності концентрацій рівноваги проникаючих молекул на кожній стороні мембрани, дисоціація молекул на іони та принцип Ле Шательє. Показано, що розподіл Доннана (нерегулярність іона розподіл) і відповідно абсолютне значення мембранного потенціалу Доннана збільшується, якщо: (i) концентрація солі, що не проникає (В одному з розчинів) та його константа дисоціації зростає; (ii) загальна концентрація проникаючої солі та її концентрація константа дисоціації зменшується, і (iii) збільшується співвідношення обсягів (між розчинами з непроникаючими і без них речовина). Показано також, що можна використовувати лише незначну різницю між ступенями дисоціації двох речовин їх мембранне відділення. Нами разработана модель для изучения кинетики перераспределения ионов и молекул через полупроницаемую мембрану в сложных смесях веществ, проникающих и непроникающих через мембрану. Учитывает степень диссоциация этих веществ, их начальные концентрации в растворах, разделенных мембраной, и объемы этих решения. Модель основана на предположении, что только незаряженные частицы (молекулы или ионные пары) диффундируют через мембрана (а не ионы, как в модели Доннана). Разработанная модель позволяет рассчитать временные зависимости концентраций для всех обрабатывающих ионов и молекул при переходе системы из исходного состояния в равновесное. В равновесии В соответствии с условиями соотношение концентраций ионов в растворах, разделенных мембраной, подчиняется распределению Доннана. Доннан эффект является результатом трех факторов: равенство равновесных концентраций проникающих молекул на каждой стороне мембраны, диссоциация молекул на ионы и принцип Ле Шателье. Показано, что распределение Доннана (нерегулярность иона распределение) и, соответственно, абсолютное значение мембранного потенциала Доннана увеличивается, если: (i) концентрация непроникающей соли (В одном из растворов) и его константа диссоциации увеличивается, (ii) общая концентрация проникающей соли и ее константа диссоциации уменьшается, и (iii) увеличивается объемное соотношение (между растворами с непроникающим и без него вещества). Показано также, что только небольшая разница между степенями диссоциации двух веществ может быть использована для их мембранное разделение.
Markov Chain Model for Stock Market Move Prediction
(Національний авіаційний університет, 2018) Pristavka, P.O.
Mathematical modelling and analysis of the mushroom drying process at the optimal temperature
(Int. Journal of Engineering Research and Applications, 2016-02) Kubaychuk, Oksana; Mazurenko, O; Roman, T
To preserve food is used drying method. It was found experimentally that drying mushroom caps and legs should be conducted at temperatures close to 52,5°C and 55,5°C, accordingly. In this case, we can get the product of the highest quality. Statistically, we proved that the drying processes of mushroom caps are different for fixed levels of temperature (from 40° C to 80° C, by step 10° C). At the same time, at higher temperatures, the nature of the process changes abruptly. Based on the experimental data, the polynomial regression model was built. This model can used for estimating and forecasting a specific evaporation heat at the optimal temperature.
MODELING OF CHAMPIGNON STIPE DRYING PROCESS
(Наукові праці НУХТ., 2015) Kubaychuk, O
The problem of champignons drying has beenn investigated in this article. The optimum temperature for drying is the temperature at which the final product has the best taste and retains the maximal quantity of nutrients. The research was conducted using the method of simultaneous thermal analysis. It was established experimentally that the optimum temperature for the stipes and caps of champignons vary significantly. The models of drying fungi stipes at different fixed temperatures have been developed. The drying process of fungi stipes at optimum temperature has been modeled.
Multi-Electron-Transfer Catalysts Needed for Artificial Photosynthesis
(Materials research society, 2011) Zhuk, Petro; Vickers, James; Hongjin, Chemistry Lv
We report a study on catalytic water oxidation by cobalt in oxygen ligand environments because such systems are as promising as any in the water oxidation component of solar fuel production. We have re - examined the catalytic activity of Co(II) in aqueous solution using either [Ru(bpy) 3 ] 3+ as a stoichiometric oxidant or in visib le - light - driven reactions with persulfate as a sacrificial electron acceptor. In both systems a distinctive induction period is observed. A simple kinetic model is proposed that describes the experimental data well. The presence of an induction period is explained by relatively slow formation of the true catalyst from aquac obalt(II) .
Numerical simulations of dynamics of elastic tubular spirals conveying internal masses of non-homogeneous boiling liquid
(National aviation university, 2019-08) Tolbatov Yevgeniy
The computer simulation problem of the dynamics of elastic tube serpentines with internal flows of boiling liquid is set up. The clots motion model of the non-homogeneous boiling liquid is proposed. The numerical solution technique of the constructed equations based on the use of an algorithm for numerical integration in time and a method of the transfer matrix.

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