## MODELING OF LIQUID SPREADING IN RANDOMLY PACKED METAL PALL RINGS

Mathematical Modeling, Vol. 1 (2017), Issue 4, pg(s) 174-177

The present work compares two different approaches, Computational Fluid Dynamics (CFD) and dispersion model, for liquid distribution modeling with experimental data for liquid spreading in randomly packed metal Pall rings. The used experimental data are obtained in a semi-industrial column with a 0.6m diameter for several packing heights and liquid loads. It is shown that the appropriate choice of dispersion model parameters is essential for prediction of liquid distribution. In both models some parameters are determined by fitting with experimental data, the remainder are calculated or taken from literature. Comparison of the two model liquid distributions with experimental data shows that both CFD and dispersion model are in good agreement with the experiment especially for higher packing bed, when the wall flow is fully developed.

## A MATHEMATICAL MODEL OF VISCOUS LIQUID MIXTURE MOTION THROUGH A VERTICAL CYLINDRICAL PIPE

Mathematical Modeling, Vol. 1 (2017), Issue 4, pg(s) 178-179

In the paper a mathematical model of the non-stationary motion of a viscous liquid mixture through the vertical straight pipe of the circular cross section is proposed. During the model construction weak compressibility of the mixture is considered. The Navier-Stokes equations system is taken as a basis. Such model can be used in the description of oil motion in a vertical well.

## STATISTICAL METHODS FOR THE ANALYSIS OF THE MONTE CARLO SIMULATION RESULTS IN VISION SYSTEMS

Mathematical Modeling, Vol. 1 (2017), Issue 4, pg(s) 171-173

In this paper, we present some results of statistical processing of the results of numerical simulation of the characteristics of vision systems through the atmosphere obtained with the help of a special software package created by us (Gendrina I.Yu., Kvach A.S.).

## COMPARISON OF THE RESULTS OBTAINED BY PSEUDO RANDOM NUMBER GENERATOR BASED ON IRRATIONAL NUMBERS

Mathematical Modeling, Vol. 1 (2017), Issue 4, pg(s) 167-170

Pseudo-random number generators (PRNG) based on irrational numbers are proposed elsewhere. They generate random numbers using digits of real numbers which decimal expansions neither terminate nor become periodic and practically their decimal expansion has infinite period. Using that algorithm, we generate sequences of random numbers and then we check their randomness with statistical tests from Diehard battery. Our main idea is to check is there a difference in the randomness of the generated sequences if digits of any irrational non- transcendental number (like √2, √3,√5, … ) are used versus the case when digits of a transcendental number (like π or e) are used. In our experiments we use about 3·107 digits of a given non-periodic irrational or transcendental number. Many experiments were done and all generated sequences by proposed PRNG based on irrational numbers passed the Diehard tests very well. We may conclude that there is not a significant difference in the randomness of the generated sequences in the both cases (irrational nontranscendental versus irrational transcendental number).

## ABOUT THE PROBLEM OF DATA LOSSES IN REAL-TIME IOT BASED MONITORING SYSTEMS

Mathematical Modeling, Vol. 1 (2017), Issue 3, pg(s) 121-122

Fast growing market of IoT devices revealed a number of complex problems. Among these problems, there is a problem of data losses caused by data package losses or delays while its transition from sensor to server. As anticipated, there are a number of businesses relying on easy opportunity to build real-time monitoring systems using modern software and IoT hardware solutions. Although the growing reliability of contemporary communication networks one can find the problem of making decision about lost or delayed data packages. Current research is dedicated to building an algorithm for compensation of gaps in data series to support real-time monitoring systems with appropriate artificially generated values. Cases of applicability of the algorithm were also studied and discussed.

## PARAMETRIC INDUCED INSTABILITIES OF BOSONS IN MAGNETAR’S CRUST

Mathematical Modeling, Vol. 1 (2017), Issue 3, pg(s) 123-126

In the present work, we are discussing the Klein–Gordon equation describing relativistic spinless particles evolving in the (stationary) magnetar’s crust. With the wave function expressed in terms of Mathieu’s functions, we compute first-order transition amplitudes, pointing out the role of the strong magnetic induction in transitions to states which may be characterized by values of the model’s parameters in instability bands.

## ON THE USE OF CONFORMING AND NONCONFORMING RECTANGULAR FINITE ELEMENTS FOR EIGENVALUE APPROXIMATIONS

Mathematical Modeling, Vol. 1 (2017), Issue 3, pg(s) 127-130

The paper deals with some combinations of conforming and nonconforming rectangular finite elements in order to obtain twosided bounds of eigenvalues, applied to second-order elliptic opertor. The aim is to use the lowest possible order finite elements. Namely, the combination of serendipity conforming and rotated bilinear nonconforming elements is considered in details. This work continues some recent researches of the authors concerning eigenvalue approximations. Computational aspects of the used algorithm are also discussed. Finally, results from numerical experiments are presented.

## EVOLUTIONARY MATHEMATICAL MODELS WITH DISTRIBUTED PARAMETERS ON THE NET AND NETLIKE DOMAIN

Mathematical Modeling, Vol. 1 (2017), Issue 2, pg(s) 72-74

Mathematical models of evolutionary processes on the network and setepodobnoj area. The method, which applies to many tasks of optimal control of differential systems, the status of which is defined by the weak solutions of evolutionary equations of mathematical physics on networks and setepodobnyh areas. This method is very common and is applicable to a wide class of linear tasks that have an interesting analogy with also multi-phase tasks of mechanics (in particular, the theory of plasticity). The results obtained in this manner for a specific equation with distributed parameters in the setepodobnoj area, serve not only to demonstrate the method, but also of interest to applications.

## FUNDAMENTALS OF THE KINETIC THEORY OF MULTICOMPONENT EMULSIONS

Mathematical Modeling, Vol. 1 (2017), Issue 2, pg(s) 75-79

The paper proposes a mathematical model for describing the dynamics of multicomponent emulsions, based on ideas and methods of the kinetic theory of gases. The methodological basis of the proposed theory is the ideas and methods of the theory of integral kinetic equations.

## CONCEPTUAL CYBERNETIC MODEL OF TEACHING AND LEARNING

Mathematical Modeling, Vol. 1 (2017), Issue 2, pg(s) 80-83

The article describes conceptual models of learning and teaching as a managed cybernetic system to achieve the knowledge and skills required by the standards. In the article, the learning process is examined as a system for building a knowledge system of a learner actively which is managed and directed by the tutor or teacher to achieve specified learning goal. The information received by the learner has a multimedia nature. The recipient receives the information through various channels (sensors), sight, hearing, smell, taste and touch. The received information arrives in the short-term memory where it is processed – confronted with the previous knowledge in long-term memory of the individual. New information and knowledge can reinforce and extend the recipient’s long-term knowledge system if they are consistent logically. If there is a conflict between new information and old knowledge and information – the conflict needs to be solved. The solution can be the clarification of the knowledge system, correction of misconceptions so they are in line with objective reality and relevant knowledge about the subject of learning. It means, learning is not a constant storage of isolated information and information units in memory, but their transformation into active knowledge which is connected to logical structures and forms the knowledge system of the learner. The actual knowledge system enables an individual to solve non-standard problems not only in everyday life but also in science and technology and in various research areas from which the necessary, suitable and useable knowledge (expert) system is built.