The aim of this research is to analyze new proposals for the organization of traffic in the intersection model with rational solutions to increase its performance. The intersection represents a traffic node on a major European corridor and can be classified as highly loaded with frequent traffic jams. The signal-controlled intersection does not currently provide a suitable solution for traffic jams. Using Aimsun version 8 software, a detailed model of the intersection was developed, where the current situation and nine alternative scenarios (an optimization of the signal plan, an addition of a fourth signal phase, a widening of the connecting lane and the construction of an overpass) were tested. The simulation results were compared with the results of calculations according to the applicable technical regulations. The performance was evaluated based on delay time, travel time, queue length, and vehicle speed. The results showed that the overpass is the most effective solution, significantly reducing delay times and improving traffic flow. While other solutions offered local improvements, the overpass provided the most significant overall performance increase.

The aspects of inquiry based learning (IBL) are vigorously and frequently in the focus of recent studies. With the use of inquiry in mathematics in the daily school practice, some further questions are arising there: What kind of problems can be useful for an analysis of students' competencies in the field of IBL and how to assess the performed level of competencies? In this paper, the Mathematics B-day contest assignment is introduced as a mean to assess the students' performance in mathematical inquiry skills. Some new rubrics with didactical variables were designed as a tool for assessing students' competencies. The statistical implicative analysis was used to investigate 29 solutions of Mathematics B-day 2017: Arrow clocks. We identified the key subtasks solutions directly related to the level of the IBL competencies performed in the final mathematical investigation. The subtask which required actually high level of algebraic thinking influenced the level of the final mathematical investigation the most.

Rail transport is the basis for the proper functioning of a transport system that is sustainable for future generations. It is safe and environmentally friendly; moreover, it is suitable for carrying a large number of passengers. Train connections should be operated following the requirements of the traveling public, as well as with the potential to reach those who have hitherto preferred individual car transport. The study aimed to identify the needs of current as well as potential rail users and to propose measures for improving service provision and supporting more sustainable transport possibilities. Given the ecological nature of rail transport and the high numbers of tourists using individual car transport in the summer and winter seasons, the study sought solutions to shift transport from road to rail infrastructure. Visitors to the area were approached directly during their visit as part of a transport–sociological survey conducted during periods of peak visitation, specifically in the summer and winter seasons. Drawing on findings from previous studies and the results of the transport–sociological survey, four universal variants were developed. The study applies to the method of practical permeability indicators. It evaluates variants of measures involving timetable adjustments, line modifications, and construction of new stations. It assesses their impact on reducing travel times and proper timetable management. The result of the study is to propose building a station on the railway infrastructure, which brings fundamental changes in increasing the practical capacity of the line and meets the goal of sustainability concerning increasing the number of connections and thus increasing the number of public service opportunities. The study addresses the growing pressure of individual car transport in a protected natural area and the need to shift demand towards more sustainable rail transport.

The aim of this paper is to develop a case study of the recent situation of a bike-sharing service in a chosen small urban area. Žilina is situated in northern Slovakia, with a population exceeding 80,000 and an area of 80.03 km². This study represents a complex analysis of the available data on a bike-sharing service, as well as data on bicycle rentals from a local provider. Both were processed by the QGIS software. First, the number of rentals and the attractiveness of the bicycle stations were evaluated, taking into account the seasons from 2019 to the end of the 2023 season. Spatial analysis, based on marking the availability of the isochrones of the 32 bike-sharing stations at the end of the season 2024, was conducted considering the map’s characteristics. The analysis was supplemented with a questionnaire survey of bike-sharing service users. This study provides an overall view of the recent situation of a bike-sharing service operating for five years in a small urban area with the intention of identifying deficiencies and improving the service for future system expansion. The originality of this paper lies in the processing of a wide dataset with an extensive set of control variables and the connection of spatial and non-spatial analyses. The approaches and results can serve as proposals for introducing or designing bike-sharing services in other small urban areas for researchers.