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Introduction

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## Publications

Publications (27)

ECMI Conference in Sicily in 2000.

The gyrotron is a microwave source whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. Powerful gyrotrons can be used to heat nuclear fusion plasma. In addition, they have found a wide utility in plasma diagnostics, plasma chemistry, radars, extra-high-resolution spectroscopy, high-tem...

Gyrotrons are microwave sources whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. This process is described by the system of two complex differential equations: nonlinear first order ordinary differential equation with parameter (averaged equation of electron motion) and second order...

There are considered some aspects for numerical solving of problem with Robin's boundary conditions arising in the gyrotron theory. The single mode case is carefully investigated. The obtained observations make possible to offer the suitable strategy for the numerical solving of the problem for general system of nonstationary gyrotron oscillations.

A stationary problem with the integral boundary condition arising in the mathematical modelling of a gyrotron is numerically investigated. The Chebyshev's polynomials of the second kind are used as the tool of calculations. The main result with physical meaning is the possibility to determine the maximal value of electrons efficiency.
First publis...

Numerical aspects for solving of certain problem arising in gyrotron theory are discussed. Particularly, finite-difference
schemes using quasistationarization and method of lines were applied and the relevant results analyzed.

There are considered some aspects for numerical solving of problem with Robin's boundary conditions arising in the gyrotron theory. The single mode case is carefully investigated. The obtained observations make possible to offer the suitable strategy for the numerical solving of the problem for general system of nonstationary gyrotron oscillations....

The mathematical model which describes the web drying in the papermaking machine has been carried out in the collaboration between our institute and joint-stock company “Paper Mill ‘Ligatne’” engineers. The general principles of this develpopment were underlined in the report [zz00]. Under some simplifying assumptions this model can be reduced to t...

A mathematical model for sawn timber drying based on detailed transport phenomena considering both heat and moisture transfer is proposed. The finite difference scheme derived by the method of finite volumes is applied for the numerical approximation of the obtained mathematical model. The model allows to manage the experimental drying process of s...

A mathematical model of wood or paper drying based on a detailed consideration of both heat and moisture transport phenomena is proposed. By averaging we express the model as a sequence of initial value problems for systems of two first order nonlinear ordinary differential equations. This mathematical model makes it possible to efficiently investi...

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffus...

The mathematical model of wood drying based on a detailed transport phenomena considering both heat and moisture transfer have been offered in the article [5]. We apply this model to quickly moving paper sheet. The range of the moisture content correspond to the period of drying and only vapor movement in the web is possible. By averaging we have o...

The mathematical model of wood drying based on a detailed transport phenomena considering both heat and moisture transfer have been offered by S. Pang [Wood and Fiber Science 29, 48-67 (1997)]. We apply this model to quickly moving paper sheet. The range of the moisture content correspond to the period of drying and only vapor movement in the web i...

The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations....

The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations.

„Qualitative investigations of boundary value problem for self‐similar second order system which arises from modeling of surface chemical reactions" Mathematical Modelling Analysis, 2(1), p. 41-47
First Published Online: 14 Oct 2010

There is considered the full mathematical model of chemical reactions on the surface of glass fibre material that was imbedded in the flow of acid solution and was pulled longitudionally. Self-similar forms of this model are obtained and their approximations by monotone schemes of differences are proposed. Some special cases which make possible to...

Influence of the source function contained in the system of differential equations to mutual disposition of the lower and upper solutions and solvability of the Neumann problem is shown.

The boundary value problems modeling distribution of products concentration in a spherical particle which acts in a biochemical reactor have been investigated. A reaction kinetics expression supplemented by an additional multiplier is shown to cause multiplicity of the problem solutions.

Technological processes determined by chemical reactions on the surface of the uniformly moving glass fibre material taking into account the effect of gravitation are considered. There is carried out a mathematical model which under some assumptions is reduced to a boundary value problem for a selfsimilar system of ordinary differential equations.

Multiplicity of solutions for the boundary value problem x '' +1-p+q tx ' -pq t 2 x+bt r x t p n =0, x(0)=0,x(t 0 )=x 0 ,b,t 0 ,x 0 ∈(0,+∞), is investigated by phase analysis method as long as the values of the parameters are permissible.