The question of electromobility is greatly discussed theme of the present especially in connection with the reduction of greenhouse gas emissions. In order to fulfill decarbonization targets, incentives of many countries lead to the support of electromobility. In this paper we ask to which extend are Visegrád Group countries prepared for the widespread utilization of electric cars and define a new coefficient K called the infrastructural country electromobility coefficient. Its computing is covered by appropriate analysis and calculations done previously. Several indices that keep particular information about the state of preparation for electromobility are defined and debated here, as well. Their product forms the coefficient K. Obtained results include outcomes and discussion regarding the level of infrastructural electromobility preparedness for the chosen states, among which we extra focus on the position of Slovakia compared to the European Union average and European electromobility leaders. Based on the data obtained, we found out that the stage of preparation of Slovakia for electromobility among Visegrad Group countries is rather good, although it is far behind the European Union leaders. We realized that there was a rapid growth of electromobility infrastructure in Slovak Republic in the last five years as its infrastructural country electromobility coefficient grew 334 times.

In this case study, the medium-sized enterprise is looking for ways to achieve sustainable development. Following the Industry 4.0 trend could get the enterprise closer. The rate of information technology usage is very low in the enterprise. The enterprise’s problem is the long production of orders. The orders had to be rejected many times because the customer’s time limit could not be met. The major cause seems to be two environmentally insufficient and obsolete machines in the blast cleaning operation. These machines are replaced in the production by one new wheel blast machine. However, the production process must be redesigned and the layout changed to use this machine effectively. This redesign is difficult to verify and evaluate in the pilot plant experiment. Simulation is the most suitable tool to do it quickly and relatively easily. The ExtendSim simulation program creates a real production process model and then applies the redesign of this process in the model. The model must be thoroughly verified concerning the real production process to not distort the results. The result of the redesign of the production process is the reduction of the production duration by almost 50% and elimination of two environmentally insufficient and obsolete machines. Improved machine blast cleaning has also significantly reduced the utilization of blast cleaning. Spared capacities can be used for pre-production or otherwise for the profit-making of the enterprise. However, a new bottleneck appeared elsewhere in the production process by removing the previous one. The innovation passed through barriers, and Slovak small and medium enterprises started building sustainable development. The enterprise still must focus on further innovation, and more investment will be needed to achieve the final sustainable development goal.

Oriented graphs belong to a part of Mathematics - Combinatorics called Graph Theory. One of the fundamental terms here is a tree. The tree structures have widespread use not only in Mathematics. They can be used in Decision Theory as data mining tools as well. In the present paper we point out to the use of decision trees as models for financial services, namely, by credit scoring, fraud and churn detection. We also underline the important role of Decision Theory in engineering education.

Discussiones Mathematicae Graph Theory