# П. Ф. ЖукNational Aviation University · applied mathematics

П. Ф. Жук

17.43

·

PhD; Dr.Sci

## About

57

Publications

2,613

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

225

Citations

Introduction

Research Experience

April 2004 - present

**National Aviation University**

Position

- Professor

January 1979 - August 1979

**National Academy of Sciences of Ukraine**

Position

- Researcher

Description

- mathematical modeling of water purification processes

## Publications

Publications (57)

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...

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 this article provides a definition and been hypothesized regarding the criterion of the adequacy of the mathematical model of the kinetics of chemical reactions in terms of stable matrices.

HOMOGENEOUS WATER OXIDATION CATALYZED BY CO-BASED POLYOXOMETALATES

Считается, что в состоянии термодинамического равновесия прямая и обратная скорость каждой стадии химической реакции всегда должны быть равны, т.е. реакция должна подчиняться принципу детального баланса. Этому принципу предоставлен высший приоритет, поскольку с его помощью удается обосновать запрет на осуществление циклических процессов, чего нельз...

Tutorial regulatory discipline "Mathematical Methods in
aerodynamics "is designed for high school students who
studying the direction of 6.040301 "Applied Mathematics" specialty
8 / 7.04030101 "Applied mathematics". Handbook covers all
thematic modules curriculum subjects, prepared in accordance with
educational standards.

An all-inorganic, oxidatively and thermally stable, homogeneous WOC based on redox-active (vanadate(V)-centered) POM ligands, Na10[Co4(H2O)2(VW9O34)2]∙35H2O (Na101-V2, sodium salt of the polyanion 1-V2), was synthesized, thoroughly characterized and shown to catalyze water oxidation in dark and visible-light-driven conditions. This synthetic cataly...

We present the definition and study the dependence on the initial approximation of the asymptotic rate of convergence of a two-layer symmetrizable iterative method of the variational type. The explicit expression is obtained for the substantial (with respect to the Lebesgue measure) range of its values. Its domain of continuity is described.

Hydrogen sulfate salts of [Ru(1)2]2+ where 1 = 4′-(4-pyridyl)-2,2′:6′,2′′-terpyridine and four N-alkylated derivatives [Ru(L)2]4+ were used as photosensitizers (λmax 510 nm) for water oxidation in light driven reactions with peroxydisulfate as a sacrificial electron acceptor and Na10[Co4(H2O)2(α-PW9O34)2] (Co4POM) as the catalyst in sodium borate b...

A mathematical model of intracellular calcium homeostasis in smooth muscle cells has been investigated by computer modelling method. The results of calculations showed that for the plasma membrane calcium pump (PMCA) the limiting rate (V(mPM)) increasing or the Michaelis constant (K(mPM)) decreasing result in a lowering of the Ca2+ concentration in...

We construct and investigate a mathematical model of a cascade of sorption apparatus for the intradiffusion process of sorption in granules of a homogeneously porous sorbent (known examples of these sorbents are KAD, AG-3, and SKT activated carbons).

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 visible-light-driven react...

A mathematical model describing kinetics of transmembrane calcium transport in a smooth muscular cell has been elaborated and investigated taking into account that the change of calcium cations concentration within a cell is determinated by four processes: calcium entry in cytosol through the calcium channels of plasma membrane (increasing of carry...

It is proposed to use the constant of inhibitory effect QI for the comparison of reversible inhibitor
actions on enzymatic reactions with a productive enzyme-inhibitor-substrate complex. This constant
does not depend on the substrate dissociation constant and the inhibitor and substrate concentra-
tions, but it involves only parameters which are de...

A mathematical model, which describes kinetics of transmembrane calcium transport in a smooth muscular cell, has been elaborated and investigated taking into account that the change of calcium cations concentration within a cell is determined by two mutually opposite processes: an increase of a carrying capacity of calcium channels of plasma membra...

On the example of the Rayleigh functional a new approach is developed to the study of the asymptotic behavior of the -step method, based on the proof of the existence of limit iteration parameters of the method in even (odd) iterations. This approach may be used to analyze the asymptotic behavior of the -step method in the optimization of arbitrary...

A conjecture of Forsythe on the asymptotic behavior of the s-step method of steepest descent for a quadratic functional is confirmed for the two-step method, and the essential range of the asymptotic rate of convergence is found. Conditions are determined for the eigenvalues of the matrix to be in the asymptotic spectrum of the method. Devices for...

The asymptotic behavior of sequences of vector functions ak and ck (k = 1, 2, ...) that constitute a solution to a linear mathematical model of a train of serially connected cycling sorption columns is examined. The sequences are shown to exponentially converge along certain asymptotic directions to their limits a∞ and c ∞, which describe steady-st...

We obtain exact (unimprovable) estimates for the rate of convergence of the s-step method of steepest descent for finding the least (greatest) eigenvalue of a linear bounded self-adjoint operator in
a Hilbert space.

Simulation has been used to derive all the observed relationships between the differential heat of adsorption and the degree of filling for an inhomogeneous surface bearing three types of center, for which the adsorption is described by Langmuir isotherms with differing b0; this is based solely on the adsorbate-adsorbent interaction and does not in...

The existence of limiting iterational parameters of the s-step method of steepest descent for minimizing a quadratic functional F(u)=0·5(Au,u)-(f,u) in Hilbert space is proved. The asymptotic behaviour of the method is investigated; in particular, analogues of the results in finite-dimensional spaces established by H. Akaike [Ann. Inst. Statist. Ma...

The adsorption of molecules from the gaseous phase on a nonhomogeneous surface consisting of two types of centers with different heats of absorption was studied by computer modeling. It was shown that the two types of centers contribute to the heat of absorption irrespective of the degree of surface coverage, as a result of which the experimentally...

An implicit finite-difference scheme is constructed for solving a nonlinear initial-boundary-value problem for a nonlinear homogeneous parabolic equation of second order with a nonlinear boundary condition that contains the time derivative of the sought function. The results are used for numerical solution of the mathematical model of internal-diff...

Methods are proposed for determining the diffusion coefficients of adsorbed molecules and the adsorption isotherms from given concentrations of the solutes in the external solution. The methods are based on a comparison of experimental data with the numerical results produced by a mathematical model of internal-diffusion kinetics of adsorption from...

A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation of the second kind which arises in the study of the mathematical model of internal-diffusion kinetics of adsorption of a substance from an aqueous solution of constant and bounded volume. The efficiency of the method is demonstrated using prototype exa...

The method of lines is constructed and proved for numerical solution of a nonlinear initial-boundary-value problem of parabolic type describing the adsorption of a substance from an aqueous solution of bounded volume by a spherical adsorbent. The method is developed under natural assumptions on the smoothness of the solution of the original problem...

We consider the finite-difference eigenvalue problem u
xx
–
+ u=0, u0= un+1=0 on a nonuniform grid =xii=0,1,...,n+1, x0=0, xn+1=1. In connection with the issue of existence of exact-spectrum schemes for second-derivative operators, we examine the extremal properties of functions fn(v, h)=1
v(h)+ ...+n
v(h), v R. We prove that the maximum of fn(–1,...

Iterative methods for solving linear equations in Hilbert space, which generalize the s-step methods of steepest descent, minimal residuals, α-processes and the two-level gradient descent method, are proposed. Estimates are obtained for their mean rates of convergence.

A solution to the equations for the unsteady mass transfer of a multicomponent mixture in a porous material that includes the matrices of the diffusivities and the reaction rate constants is obtained. A method for determining these matrices is developed. The matrix elements for the kinetic coefficients for the case of adsorbing a gas mixture on an...

The theory of multi-stage adsorption in a series of fixed-bed units is discussed, and a model of the process is derived, showing that a steady state of repetitive cycles can be attained. Experimental data are in good agreement with the theory.

Series of porous polymeric sorbents are compared for adsorption of phenol from aqueous solutions. The best sorbents was Chromosorb 105. A theoretical model of the nonequilibrium dynamics of adsorption for this sorbents was used to calculate the volume to breakthrough as a function of the phenol concentration and depth of the sorbent layer. The depe...

Experience in the use of adsorption processes in the technology of removal of organic impurities from water and waste water shows that it is most feasible to remove organics in multistage adsorbers with serial connection of the adsorbers. The paper examines the principle of operation of an adsorption system consisting of three adsorbers, each of wh...

A mathematical model is examined of the sorption dynamics of dissolved substances in a cascade of dense bed devices and a method is presented for calculation of multistage adsorbers. The present paper is concerned with an analysis of the operation of a cascade of adsorbers in the removal of dissolved substances for the case of convex and concave so...

In the majority of cases, waste water adsorption treatment technology involves absorption and separation of a multicomponent mixture. Equipment of various types is used for this purpose. Recently a trend has been observed toward use of continuous processes of absorption of organics from aqueous solutions by activated carbon in a series of agitator...

A method of constructing vectors invariant in direction relative to two iterations of the s-step optimal gradient method is described. A sufficient condition is found for Forsythe's hypothesis on the asymptotic behaviour of the s-step optimal gradient method to be valid.

Установлена формула близости итераций, позволяющая оценить погрешность и ускорить метод

WHEN finding the least eigenvalue of a positive definite and self-adjoint finite-dimensional operator by the method of steepest descent, the asymptotic behaviour of the normalized gradients is examined. The results are used to justify devices for accelerating the convergence of the method. A means is outlined for simultaneously finding three eigenv...