International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The paper deals with some aspects of the presentation and application of periodic time-dependent functions in the Fourier analysis. Different approaches for defining and utilising periodic functions are considered. The case when one has only a discrete set of values obtained from measurement and the function itself is not known is also included. In general, the type and the shape of the corresponding frequency distribution is a point of interest and discussion.
The paper presents numerous examples which illustrate the proposed ideas.

For unfolding neutron spectra at physical accelerator facilities in a very wide energy range, Bonner multi-sphere spectrometers are effectively used. Such spectrometers consist of a thermal neutron detector placed in spherical polyethylene moderators of various diameters which are characterized by certain sensitivity functions. The report proposes an approach to optimizing the choice of the number and size of spheres for conducting rational measurements and subsequent unfolding of neutron spectra using Tikhonov’s regularization method. Our approach is based on the use of weighting factors in the regularization functional, built on the condition numbers of the Gram matrix of the set of sensitivity functions. The effectiveness of the approach is demonstrated using the spectral unfolding of reference neutron fields of the JINR Phasotron.

In this work we study numerically the generation of intense terahertz radiation in the interaction of two-color circularly polarized laser pulses of optical or infrared wavelength range with argon. The terahertz pulses obtained in such a scheme can be used to generate strong slowly changing electric and magnetic fields of a given configuration. To investigate the terahertz emission by a plasma source arising from the ionization of a gas medium by femtosecond laser field with a peak intensity of 10¹⁴-10¹⁵ W/cm² a fully kinetic plasma model consisting of the Vlasov equations for the plasma distribution function and the Maxwell equations for the self-consistent electromagnetic field has been used. Our numerical code is based on the particle-in-cell method and employs state-of-the-art widely used algorithms, such as finite difference time domain method for modeling the electromagnetic fields, Boris pusher to update the particle positions and velocities, and the charge conservation scheme to satisfy the continuity equation. The field ionization is implemented using the tunneling ionization rate formula. Our simulations have shown that at a sufficiently small interaction volume the plasma oscillations excited by asymmetric ionization are almost homogeneous in space and lead to an efficient conversion of electron energy into the energy of emitted terahertz radiation.

This paper focuses on the simulation aspects of Bayesian hypothesis testing applied on ophthalmic data. Bayesian statistical analysis often relies on Markov Chain Monte Carlo (MCMC) methods for estimation, when analytical solutions are not possible. We highlight the key aspects of MCMC including model specification, details on the simulation, MCMC diagnostics as well as its limitations and advantages. The simulations are done using R and JAGS.

Oil and gas accumulations located in the porous spaces of the formation exist as a single hydraulically connected system and are factors of many physico-chemical processes that occur, depending on the different conditions that develop in the layer. The study of fluid filtration in porous media, their type, the condition in which the flow occurs and its geometric form, are the main key in which the testing of a well begins and then the determination of various hydrodynamic parameters. In reservoir engineering, the stages of filtration that develop and the changes that occur in the phase state of the fluid are closely related to the changes that occur in the pressure of the reservoir, which characterizes the energy of the layer for the production of fluids on the surface. Radial flow is used in many practical applications in solving various problems encountered in reservoir engineering and precisely the main objective of this paper, is to present a solution of the average pressure of the reservoir in the case of radial flow using a mathematical approach.

Research, optimization and practical implementation of small hydroelectric power plants as a source of clean electricity presents one of the topical tasks in current energetics, which is virtually impossible to solve without powerful computer support due to the strongly nonlinear nature of such systems. The article presents a complete model of a small hydropower plant, modelling its individual subsystems and verifying its dynamic properties in basic operating modes. Also an influence of a major external fault, caused by a drop in the power grid frequency, was investigated. Full Small-Hydropower Plant (SHPP) model properties were verified using MATLAB software package using real parameters of a micro hydro power plant in Dobšina (Slovakia). The obtained results confirmed correctness of the proposed SHPP model, which can be used for design of its control.

Partial differential equations (PDEs) are differential equations in which there is more than one independent variable. They arise in the modelling of a wide-range of physical phenomena including electromagnetism, fluid flow, elasticity, quantum mechanics and heat conduction. The wave equation serves as a fundamental model for understanding various wave phenomena in physics and engineering. In this paper, we explore the application of Sturm-Liouville problems to solve the wave equation. The results of our investigations not only showcase the accuracy and computational advantages of the Sturm-Liouville method but also shed light on the physical interpretations of the obtained eigenfunctions and eigenvalues. In conclusion, this paper contributes to the body of knowledge regarding the application of SturmLiouville problems in wave equation modeling and analysis. It offers a valuable perspective for researchers, scientists, and engineers seeking efficient and insightful solutions to wave-related challenges. The versatility and effectiveness of the Sturm-Liouville approach make it a compelling tool for gaining deeper insights into wave phenomena and their practical applications.

Inverse problems in atmospheric optics, for example, the reconstruction of the optical and microphysical properties of aerosols and clouds, operational algorithms based on measurements or calculations of solar radiation are used. In this work the patterns of formation of the field of reflected solar radiation in a cloudless atmosphere that were obtained during statistical modeling for various opticalgeometric parameters of the observation scheme are discussed. In addition, statistical data processing, the main goal of which was to construct a basic parametric model of solar haze brightness, was performed and analyzed.

In this paper more theory and examples about the infinite numbers and functions that were introduced in a previous paper is presented. These numbers and functions apply in modeling physical and mathematical systems and processes, where infinity somehow appears, i.e. series of numbers, limits calculation, kinematics problems, infinite expansion of certain universe geometric shapes. By strictly applying the theory of limits of functions, more properties of the infinite numbers which are limits of complex functions tending to infinity, are defined. The mirror infinite numbers and some properties of them are also demonstrated and presented. Furthermore, infinite geometric shapes whose sides are infinite numbers, as triangles, circles, spheres and ellipsoids are defined and used in modeling theoretical and technological problems.

This article considers non-parametric models based on feature space modeling in the context of machine learning. The main machine learning models, their advantages and disadvantages are analyzed. The term “non-parametric feature space modeling model” has been considered in detail and compared with other machine learning models. The advantages of these models are justified in comparison with other approaches. The paper contains an analysis that confirms the advantages of using non-parametric feature space modeling models in machine learning tasks.

Obtaining source functions in Fourier transform (FT) on the base of some knowing frequency distributions are presented. The proposed approach allows to study the properties of the obtained results. This technique is used for calculation of some improper integrals as well.

The article presents the results of researches that are a continuation of analyzes of the correlation properties of generating functions intended for the formation of derivatives of Walsh functions. The derivatives of the Walsh functions are designed to obtain pseudorandom sequences (PRS) used in the formation of noise-like signals in multichannel data transmission systems with channel division according to the shape (code) of the signal. The analysis performed showed that the correlation properties of the derivatives of the Walsh functions depend on the type of generating functions, which were the modified Barker codes – direct and inverse composite Barker codes and de Bruijn sequences. It was justified the advantage of using these signals in the development of CDMA systems in order to reduce the interference level of multiple access and to protect against unauthorized access.