• ## Development of a small hydropower plant model verified on real parameters

pg(s) 3-6

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.

• ## Application of Sturm Liouville Problem in the Wave Equation

pg(s) 76-79

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.

• ## The parametric model of reflected solar radiation in a cloudless atmosphere

pg(s) 74-75

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.

• ## New concepts about the infinite numbers and functions and their application in modeling technological and mathematical problems

pg(s) 69-73

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.

• ## Feature space modeling in machine learning: a potential for regression and classification tasks

pg(s) 40-44

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.

• ## Dependencies between functions in Fourier transforms

pg(s) 36-39

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.

• ## Peculiarities of the correlation properties of generating functions for Walsh derivative functions used in the formation of noise-like signals

pg(s) 3-7

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.

• ## Classification of Digital Images using topological signatures – A Case Study

pg(s) 106-109

Topological Data Analysis (TDA) is relatively new filed of Applied Mathematics that emerged rapidly last years. The main tool of Topological Data Analysis is Persistent Homology. Persistent Homology provides some topological characteristics of the datasets. In this paper we will discuss classification of digital images using their topological signatures computed with Persistent Homology. We will experiment on the Fashion-MNIST dataset. Using Topological Data Analysis, the classification was improved.

• ## D – optimal plans in the case of a piecewise constant function

pg(s) 103-105

It is known that a large number of algorithms of the Monte Carlo method and experiment planning are based on the choice of a
certain probability distribution ρ.
This probability distribution ρ is given on a measurable space (X, B). And a given measurable space (X, B) has a density ρ(x) = dρ/dν by
some σ-finite measure v on (X,B).
When choosing a probability distribution ρ, the problem of solving the problem of finding the optimal density ρ arises.
As a result of solving the tasks, an explicit form of the Least squares Method of unknown parameters and variance was obtained. The
criterion of D – optimality is considered.
The D-optimal plans considered in this article are well known due to an important class of efficiency functions. To compare plans in terms of
D-optimality, the effectiveness of an arbitrary plan relative to the optimal plan is determined.
constant function.

• ## Procedure for analyzing the quality, structure and subjective rating of distorted images by the Full- Reference technique

pg(s) 100-102

In the present work, we study the regularities of the influence of the type of distorting algorithm on the result of evaluating the image quality by the Full-Reference method in the presence of subjective quality assessments. As an example, we used the TID2013 database with 3000 images distorted by 24 types of algorithms and subjective mean square scores (MOS) quality ratings. An image quality score based on the Weibull distribution model and the usual PSNR similarity measure is applied. It is shown that the applied distorting algorithms are classified into two types – normal, leading to results consistent with the Human Visual System, and “anomalous”, the corresponding quality estimates of which are disordered or chaotic.

• ## Spectral collocation solution of linear singularly perturbed two-point boundary value problems with interior layer

pg(s) 79-81

In this study, we solve linear singularly perturbed two-point boundary value problems applying the collocation method based on mapped Chebyshev polynomials and simply computed collocation points. The proposed approach generates well-conditioned collocation matrices and produces highly accurate results if a suitable mapping function is used. Numerical results for a problem with a steep interior layer are presented.

• ## Infinite numbers and functions applied in modeling technological systems and in solving mathematical problems in which infinity appears

pg(s) 75-78

In this paper, the infinite numbers and functions are introduced and applied in modeling physical and mathematical systems and processes, where infinity somehow appears, i.e. infinite ladder electrical networks and systems instability analysis, series of numbers and limits calculation. Infinite numbers are defined as limits of complex functions that tend to infinity. Using these numbers it is possible to calculate the extended Laplace transform across the whole frequency spectrum as well as the extended bilateral Laplace transform, where the corresponding integral does not converge. Furthermore, the derivatives/integrals of the infinite number functions are determined. Using infinite numbers certain mathematical problems can be analysed and calculated, as well as problems in Physics and Engineering, where infinity appears, can be easily modeled and solved.