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Current research studies devoted to cutting forces in drilling are oriented toward predictive model development, however, in the case of mechanistic models, the material effect on the drilling process itself is mostly not considered. This research study aims to experimentally analyze how the machined material affects the feed force (Ff) during drilling, alongside developing predictive mathematical–statistical models to understand the main effects and interactions of the considered technological and tool factors on Ff. By conducting experiments involving six factors (feed, cutting speed, drill diameter, point angle, lip relief angle, and helix angle) at five levels, the drilling process of stainless steel AISI1045 and case-hardened steel 16MnCr5 is executed to validate the numerical accuracy of the established prediction models (AdjR = 99.600% for C45 and AdjR = 97.912% for 16MnCr5). The statistical evaluation (ANOVA, RSM, and Lack of Fit) of the data proves that the drilled material affects the Ff value at the level of 17.600% (p < 0.000). The effect of feed represents 44.867% in C45 and 34.087% in 16MnCr5; the cutting speed is significant when machining C45 steel only (9.109%). When machining 16MnCr5 compared to C45 steel, the influence of the point angle (lip relief angle) is lower by 49.198% (by 22.509%). The effect of the helix angle is 163.060% higher when machining 16MnCr5.

In the current digital transformation to Industry 4.0, the demands on the ability of countries to react responsibly and effectively to threats in the field of cyber security (CS) are increasing. Cyber safety is one of the pillars and concepts of Industry 4.0, as digitization brings convergence and integration of information technologies (IT) and operational technologies (OT), IT/OT systems, and data. Collecting and connecting a large amount of data in smart factories and cities poses risks, in a broader context for the entire state. The authors focus attention on the issue of CS, where, despite all digitization, the human factor plays a key role—an actor of risk as well as strengthening the sustainability and resilience of CS. It is obvious that in accordance with how the individuals (decision-makers) perceive the risk, thus they subsequently evaluate the situation and countermeasures. Perceiving cyber threats/risks in their complexity as a part of hybrid threats (HT) helps decision-makers prevent and manage them. Due to the growing trend of HT, the need for research focused on the perception of threats by individuals and companies is increasing. Moreover, the literature review points out a lack of methodology and evaluation strategy. This study presents the results of the research aimed at the mathematical modelling of risk perception of threats to the state and industry through the disruption of CS. The authors provide the developed factor model of cyber security (FMCS), i.e., the model of CS threat risk perception. When creating the FMCS, the researchers applied SEM (structural equation modelling) and confirmatory factor analysis to the data obtained by the implementation of the research tool (a questionnaire designed by the authors). The pillars and sub-pillars of CS defined within the questionnaire enable quantification in the perception of the level of risk of CS as well as differentiation and comparison between the analyzed groups of respondents (students of considered universities in SK and CZ). The convergent and discriminant validity of the research instrument is verified, and its reliability is confirmed (Cronbach’s alpha = 0.95047). The influence of the individual pillars is demonstrated as significant at the significance level of α = 5%. For the entire research set N = 964, the highest share of risk perception of CS threats is achieved by the DISRIT pillar (disruption or reduction of the resistance of IT infrastructure).

During 2020, factors such as the global pandemic, financial uncertainty and the US election saw an increase in the correlation between bitcoin and gold and the stock market. Both bitcoins and gold rose sharply during 2020, thanks to the relentless press of fiat money by governments and central banks that intend to keep their economies afloat as a result of the coronavirus pandemic. As digital gold, BTC appeals to the cashless Internet economy largely for its features, which include continuous price transparency and a lack of restrictions, disruptions or third-party oversight. The paper focuses on the analysis and identification of the relationship between the value of basic cryptocurrencies and gold price movements, as well as the research hypothesis that the value of the most known and used cryptocurrency bitcoin (BTC) increases with the rising price of gold - a special commodity that serves several functions of the world economy. This issue is currently gaining more and more attention also in context of risk management which is the identification, evaluation, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability or impact of unfortunate events or to maximize the realization of opportunities and mobile commerce in the aspect of the impact of modern technologies and mobile communication platforms on consumer behavior and consumer preferences. Innovatively, we have made our observations of the price of bitcoin in relation to price fluctuations in the gold markets in order to develop a predictive model for simulating the development of the price of bitcoin. The mathematical model was developed on the basis of statistical analysis of the observed data.

The article is aimed at the mathematical and optimization modeling of technological processes of surface treatments, specifically the zincing process. In surface engineering, it is necessary to eliminate the risk that the resulting product quality will not be in line with the reliability requirements or needs of customers. To date, a number of research studies deal with the applications of mathematical modeling and optimization methods to control technological processes and eliminate uncertainties in the technological response variables. The situation is somewhat different with the acid zinc plating process, and we perceive their lack more. This article reacts to the specific requirements from practice for the prescribed thickness and quality of the zinc layer deposited in the acid electrolyte, which stimulated our interest in creating a statistical nonlinear model predicting the thickness of the resulting zinc coating (ZC). The determination of optimal process conditions for acid galvanizing is a complex problem; therefore, we propose an effective solving strategy based on the (i) experiment performed by using the design of experiments (DOE) approach; (ii) exploratory and confirmatory statistical analysis of experimentally obtained data; (iii) nonlinear regression model development; (iv) implementation of nonlinear programming (NLP) methods by the usage of MATLAB toolboxes. The main goal is achieved—regression model for eight input variables, including their interactions, is developed (the coefficient of determination reaches the value of R2 = 0.959403); the optimal values of the factors acting during the zincing process to achieve the maximum thickness of the resulting protective zinc layer (the achieved optimum value th* = 12.7036 μm), are determined.

Legalization of the proceeds of crime represents a worldwide problem with serious economic and social consequences. Information technologies in conjunction with advanced computer techniques are important tools in the fight against money laundering (ML), financial crime (FC) and terrorism financing (TF). Nowadays, the applied literature on ML/FC/TF uses much more mathematical modelling as a solving strategy to estimate illicit money flows. However, we perceive that there is preference of linear models of economical dependences and sometimes lack of acceptance of nonlinearity of such investigated economic systems. To characterize the risk of legalization of crime proceeds in a certain country, the scientific researchers use the Basel anti-money laundering (AML) index. To better understand how the global indicators (WCI, CPI, EFI, GII, SEDA, DBI, GSCI, HDI, VATGAP, GDP per capita) affect the level of risk of ML/TF in the countries of EU, the authors use a unique data set of 24 destination countries of EU over the period 2012–2019. The article deals with two main research goals: to develop a nonlinear model and optimize the ML/TF risk by implementation of nonlinear optimization methods. The authors contribute: (i) providing the cross-country statistical analysis; (ii) creating the new nonlinear mathematical-statistical computational model (MSCM); and (iii) describing the observed dependent variable (Basel AML index). This study deepens previous knowledge in this research field and, in addition to the panel regression analysis, also applies nonlinear regression analysis to model the behavior of the investigated system (with nonlinearity). Our results point out the differences between the estimates of the investigated system behavior when using panel and nonlinear regression analysis. Based on the developed MSC model, the optimization procedure is conducted by applying an interior point method and MATLAB toolboxes and the second goal is achieved: the statement that such values of input variables at which the risk of legalization of income from criminal activity will be minimal.

Although the application of mathematical optimization methods for controlling machining processes has been the subject of much research, the situation is different for µ-WEDM. This fact has prompted us to fill the gap in this field in conjunction with investigating µ-WEDM’s very low productivity and overall process efficiency, since the current trend is oriented towards achieving high quality of the machined area at a high manufacturing productivity. This paper discusses in detail the application of non-linear programming (NLP) methods using MATLAB to maximize the process performance of µ-WEDM maraging steel MS1 sintered using direct metal laser sintering (DMLS) technology. The novelty of the solution lies mainly in the selection of efficient approaches to determine the optimization maximum on the basis of a solution strategy based on multi-factor analysis. The main contribution of this paper is the obtained mathematical-statistical computational (MSC) model for predicting high productivity and quality of the machined area with respect to the the optimal efficiency of the electrical discharge process in the µ-WEDM of maraging steel MS1 material. During the experimental research and subsequent statistical processing of the measured data, a local maximum of 0.159 mm3·min−1 for the MRR parameter and a local minimum of 1.051 µm for the Rz parameter were identified simultaneously during µ-WEDM maraging steel MS1, which was in the range of the predicted optimal settings of the main technological parameters (MTP).

Ordered semigroups are understood through their subsets. The aim of this article is to study ordered semigroups through some new substructures. In this regard, quasi-filters and (m,n)-quasi-filters of ordered semigroups are introduced as new types of filters. Some properties of the new concepts are investigated, different examples are constructed, and the relations between quasi-filters and quasi-ideals as well as between (m,n)-quasi-filters and (m,n)-quasi-ideals are discussed.

Engineering optimization is the subject of interest for many scientific research teams on a global scale; it is a part of today’s mathematical modelling and control of processes and systems. The attention in this article is focused on optimization modelling of technological processes of surface treatment. To date, a multitude of articles are devoted to the applications of mathematical optimization methods to control technological processes, but the situation is different for surface treatment processes, especially for anodizing. We perceive their lack more, so this state has stimulated our interest, and the article contributes to filling the gap in scientific research in this area. The article deals with the application of non-linear programming (NLP) methods to optimise the process of anodic oxidation of aluminium using MATLAB toolboxes. The implementation of optimization methods is illustrated by solving a specific problem from engineering practice. The novelty of this article lies in the selection of effective approaches to the statement of optimal process conditions for anodizing. To solve this complex problem, a solving strategy based on the design of experiments approach (for five factors), exploratory data analysis, confirmatory analysis, and optimization modelling is proposed. The original results have been obtained through the experiment (performed by using the DOE approach), statistical analysis, and optimization procedure. The main contribution of this study is the developed mathematical-statistical computational (MSC) model predicting the thickness of the resulting aluminium anodic oxide layer (AOL). Based on the MSC model, the main goal has been achieved—the statement of optimal values of factors acting during the anodizing process to achieve the thickness of the protective layer required by clients, namely, for 5, 7, 10, and 15 [μm].

The system of the quasilinear differential first order equations with the antisymetric matrix and the same element f (t,x(t)) on the main diagonal have the property that r'(t) = f (t,x(t))r(t), where r(t) ≥ 0 is the po- lar function of the system. In special cases, when values f (t,x(t)) and g (t,x(t)) are only dependent on r^2 (t), t ∈ Jo we can find the general solution of the system (1) explicitly.

This paper presents an energy management strategy for secondary energy sources and their optimization in the context of the tax gap on mineral oils represented by the tax gap on petrol and diesel. Energy companies face drastic economic and environmental challenges; therefore, this area necessarily requires the setting up of transparent economic instruments and, of course, production. The tax gap in VAT collection represents the gap between how much the state could potentially collect from VAT in accordance with the law and how much VAT really comes into the state coffers. The loss of tax revenues is caused by unpaid and undeclared tax liability. The Estimation of the Gap on Corporate Tax in Slovakia is a pilot project of the International Monetary Fund (IMF) in cooperation with the Institute for Financial Policy (IFP). The results present the estimation of the tax gap within a two-year delay. It is necessary to consider the estimation of the tax gap in the last two years as preliminary due to possible revisions of the national accounts data. Estimations of the tax gap from 2010 to 2017 indicate a decreasing trend. The significant part of the tax gap decrease can be observed from 2014. The main factor, which determines this decrease, is the improving condition of the Slovak economy. From the point of view of the tax gap, the volume of losses is decreasing and the volume of profit, from which the tax is paid, is increasing.

The paper deals with the comparison of usage of three basic types of neural units in order to create the most suitable model predicting determining the final thickness of the alumina layer formed at surface with current density of 1 A∙dm−2. In addition, the reliability of obtained prediction models, depending on the amount of training data, has been monitored. With properly selected range of training data it is possible to create prediction models with reliability greater than 95 % with achieved toleration 2×10−6 mm.

Austenitic stainless steel belongs to the best oxidation-resistant alloys, which must function effectively and reliably when used in a corrosion environment. Their attractive combination of properties ensures their stable position in the steel industry. They belong to a group of difficult-to-cut materials, and the abrasive water jet cutting technology is often used for their processing. Samples made of stainless steel AISI 304 has been used as the experimental material. Data generated during experiments were used to study the effects of AWJ process parameters (high-pressure water volume flow rate, the diameter of the abrasive nozzle, the distance of the nozzle from the material surface, cutting head feed rate, abrasive mass flow, and material thickness) on surface roughness. Based on the analysis and interpretation of all data, a prediction model was created. The main goal of the long-term research was to create the simplest and most usable prediction model for the group of austenitic steels, based on the evaluation of the practical results obtained in the company Watting Ltd. (Budovateľská 3598/38, Prešov, Slovakia) during 20 years of operation and cooperation with customers from industrial practice. Based on specific customer requirements from practice, the publication also contains specific recommendations for practice and a proposal for the classification of the predicted cut quality.

In this research, the authors set out to propose a new method of predicting and adjusting the main cutting parameters of chip machining, namely spraying on the substrate. In the experiments, a total of 28 turning cuts on a Stellite 6 coating layer were realized. The base materials of the Stellite 6 layers were EN S235JRG1 and carbide WC-Co. This work aimed to find out and optimize the influence of different combinations of cutting parameters. Due to the coating solution, the work is focused on the evaluation of the roughness Ra (μm) of the turned substrate, the grain size Dgr (μm) of the spraying, the normal stress σrz (MPa), the residual stress σrez (MPa), the specific cutting force Fc (N), the quality of adhesion to the substrate Adhmp (MPa) and other parameters. For the sake of a comprehensive solution to the problem, several new predictive equations and subsequent suggestions for solutions have been derived from this research topic based on the newly obtained experimental results. The proposed models and procedures make it possible to get new results and insights into coating technologies.

The aim of the paper was to examine the influence of cutting conditions on the roughness of surfaces machined by longitudinal turning, namely of surfaces coated with Stellite 6 prepared by high-velocity oxygen fuel (HVOF) technology and applied onto a standard structural steel substrate. From the results of measurements of the cutting parameters, a prediction model of the roughness parameters was created using mathematical and statistical methods. Based on a more detailed analysis and data comparison, a new method for prediction of parameters of longitudinal turning technology was obtained. The main aim of the paper was to identify the mutual discrete relationships between the substrate roughness and the machining parameters. These were the feed rate vc (m·min−1), in the case of turning and milling, and the feed rate f (mm·rev−1) and the depth of cut ap (mm). The paper compared and verified two approaches of this method, namely the mathematical statistical approach, the analytical approach and measured dates. From the evaluated and interpreted results, new equations were formulated, enabling prediction of the material parameters of the workpiece, the technological parameters and the parameters of surface quality.

This paper shows an influence of chemical composition of used electrolyte, such as amount of sulphuric acid in electrolyte, amount of aluminium cations in electrolyte and amount of oxalic acid in electrolyte, and operating parameters of process of anodic oxidation of aluminium such as the temperature of electrolyte, anodizing time, and voltage applied during anodizing process. The paper shows the influence of those parameters on the resulting thickness of aluminium oxide layer. The impact of these variables is shown by using central composite design of experiment for six factors (amount of sulphuric acid, amount of oxalic acid, amount of aluminium cations, electrolyte temperature, anodizing time, and applied voltage) and by usage of the cubic neural unit with Levenberg-Marquardt algorithm during the results evaluation. The paper also deals with current densities of 1 A·dm−2 and 3 A·dm−2 for creating aluminium oxide layer.

The paper investigates the influence of the chemical composition and temperature of electrolyte, the oxidation time, voltage, and the current density on Vickers microhardness of aluminium oxide layers, at the same time. The layers were generated in the electrolytes with different concentrations of sulphuric and oxalic acids and surface current densities 1 A·dm−2, 3 A·dm−2, and 5 A·dm−2. The electrolyte temperature varied from −1.78°C to 45.78°C. The results have showed that while increasing the electrolyte temperature at the current density of 1 A·dm−2, the increase in the layer microhardness values is approximately by 66%. While simultaneously increasing the molar concentration of H2SO4 in the electrolyte, the growth rate of the microhardness value decreases. At the current density of 3 A·dm−2, by increasing the electrolyte temperature, a reduction in the microhardness of the generated layer occurs with the anodic oxidation time less than 25 min. The electrolyte temperature is not significant with the changing values of the layer microhardness at voltages less than 10.5 V.

With the aim to improve the mechanical properties of the layer deposited by anodic oxidation of aluminum on material EN AW-1050 A-H24, in this paper was investigated the microhardness of generated layer as a function of physical and chemical factors acting in the process of anodic oxidation at constant current density JA = 3 A.dm-2 in electrolyte, constituted by sulfuric acid and oxalic acid, with the emphasis on physical factors: the electrolyte temperature, time and applied anodizing voltage. The model of studied dependence was compiled based on mathematical and statistical analysis of matrix of obtained experimental data from experiment composite rotation plan with five independent variables factors. The experiment was carried out on 44 separate attempts with the current change of values of the separate factors under defined levels in each implementation.

In this paper we introduce Cayley digraphs associated to finitely generated polygroups, where the vertices correspond to finite products of the generators of polygroups and the edges to multiplication by vertices and generators. We investigate some properties of the Cayley digraphs, emphasizing connectivity and existence of cycles for each vertex of the Cayley digraphs. Particularly, we identify Cayley digraphs on polygroups derived from conjugate classes of dihedral groups. Moreover, we examine some fundamental illustrative examples of Cayley digraphs through the class of gmg-polygroups.