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].

In this paper, the following research problem was addressed: Is there a significant economic impact of multidimensional specified competitiveness within the EU (28) countries on the competitive business environment, human development, and sustainable growth? Based on the mentioned research problem, we formulated the aim of paper: To detect the significant interrelations among the assessment of global competitiveness, business environment as well as human development in the EU (28) countries for the period of 2006–2017. To address these problems, the methodology of global multi-criteria indices, namely the global competitiveness index (GCI), doing business index (DBI), and human development index (HDI), as well as panel analysis and non-linear regression analyses with ANOVA, were applied. The panel analysis results suggest that there is a direct linear relationship between the GCI and HDI. Moreover, the impact of the DBI on the change in the GCI score was not confirmed. We identified the main areas of countries’ interest, and important economic and statistical significant relations of competitiveness by creating three models: The GD model (constructed by GCI and DBI scores), GH model (GCI and HDI scores), and GDH model (GCI, DBI and HDI scores). Based on the results, all interrelations were confirmed. However, the highest extent of variability for the explanation of the selected data was recorded in the case of the GDH model (87.12%). We detected the impact of the business environment and human resources as competitive advantages on global macroeconomic competitiveness. As the business sector in EU (28) countries is represented mainly by small and medium-sized enterprises (SMEs), enterprise activities play a key role in the process of sustainable competitive economic development. Moreover, human resources are considered to be another important driver of the internationalization of European SMEs.

Participation in the tax system of the country and tax liability itself are two of the basic characteristics of the functioning of all economically active subjects belonging to national economies. The revenues from taxes represent a substantial part of the resources in each state’s budget, so it is not easy to achieve any form of joint action by all concerned in this area. Within the revenues obtained by taxes, customs, and levies, the issue of taxes is one of the most sensitive areas. Higher efficiency of tax collection is possible to achieve by implementing not only external tools (e.g., tax control, detecting tax fraud, etc.) but also internal ones (e.g., internal motivation of taxpayers). Therefore, it is important to improve the perception of the tax system among the population and thus to influence and create a responsible approach to the collection of taxes and levies. Due to the COVID-19 pandemic, some changes and restrictions have been implemented into the system of tax and customs collection in the Slovak Republic, but very unexpectedly and purposefully. It results in a more complicated and confused system of tax and customs administration. Therefore, our research efforts are aiming to identify and analyze the key significant factors that affect the perception of tax and customs administration in the Slovak Republic from the perspective of its inhabitants, to capture differences in perception of taxpayers. The novelty of this study lies in its approach to identifying and eliminating redundancies and opacities in tax collection processes performed by institutions of tax and customs administration systems in Slovakia, namely the approach from the taxpayer point of view, to promote voluntary compliance with tax duties. Due to the lack of such oriented studies, a survey performed in three regions of Slovakia using the research tool (the questionnaire) developed by authors is presented in this article. To solve this complex problem, a solving strategy based on exploratory analysis (KMO = 0.641) and later confirmatory factor analysis is proposed to extract four key common factors from the items of the research tool (with a total value of 80.623% of the explained variability). The reliability of the used research tool, pre-tested in the pilot study, is demonstrated by the achieved Cronbach coefficient value of 0.827%. In order to evaluate the obtained data, the respondents were divided into groups by gender, residence, and occupation, in accordance with the indications and outputs of the pilot study. Finally, experimentally obtained data were analyzed and compared. The significant differences in the respondents’ perceptions of the extracted factors between selected groups are confirmed by applied analysis, both between men and women and between respondents depending on the place of residence. The main differences are observed in the questionnaire items Q10 “Administrative complexity of the tax and customs agenda”, Q7 “Ease of tax collection”, Q16 “Labor costs for staff dealing with the tax and customs agenda”, and Q5 “Helpfulness and willingness of administrative workers”. Time costs for tax processing are considered critical.

The presented publication is focused on increasing the productivity and efficiency of machine production of precision holes. Considerable attention was paid to the influence of the pre-preparation and drilling technology on the quality of the reamed hole. The material selected for machining was chromium-molybdenum steel 42CrMo4 QT. The cluster analysis is implemented to evaluate the experimental results obtained by measuring the cylindricity and surface roughness of the drilled and reamed holes. The factor of hole pre-preparation technology was selected in two quality levels, and the factor of drilling technology in four quality levels. The constant factors were carefully controlled during the experiment, i.e., other possible influences were excluded or minimised. Under constant cutting conditions, the experiment of the subject machining process was carried out. The cutting process parameters investigated were the cylindricity and the roughness of the machined surface Ra. The novelty and contribution of this research lie in confirming the assumption that drilling technology influences hole quality primarily, whereas hole pre-preparation technology has a secondary effect.

The current practice in the field of anodic oxidation of aluminium and its alloys is based mainly on a set of partial empirical experiences of technologists obtained during surface treatment. The aim of the presented paper is deeper and more complex identification of the influence of chemical and technological factors acting during the anodic oxidation process especially on the thickness of the formed surface layer by the electrolysis method in a sulfuric acid solution. The current density was selected as the basic criterion for verification evaluation and analysis of experimentally obtained data, in accordance with Faraday’s laws. For current densities of 1 to 5 A·dm⁻², the synergy of significant influence factors was identified, and mathematical and statistical models were then developed to predict the thickness of the surface layer with a relative accuracy of up to 10%. The presented paper does not only focus on the observation of the thickness of the surface layer desired by the customer, but also on the monitoring of this thickness in relation to the overall layer thickness of the coating.