Some problems in Wagner spaces with vanishing Douglas tensor

In this paper we consider a two dimensional Wagner space of Douglas type with zero curvature scalar, and we give the main scalar function of this space

Investigation of processing test results based on knowledge similarity

The traditional scoring is based on the difficulty of the task. However, the same total score can be earned with different knowledge, hence it is difficult to create homogenous groups by only relying on the total score. In our work, we aim to present a new scoring method where such knowledge-based groups can be created, as opposed to the previous point-based method. For comparison of the test result done by the students, we utilized different distance measures. The main challenge with finding the similarities between the results is the high dimensionality of the data compared to the total number of observations. First, we used the traditional Minkowski distance with different p values, then we used local similarity hashes and high dimensional embedding techniques designed originally for natural language processing. With these never before used techniques, we were able to identify students with similar skillsets and knowledge. Furthermore, we utilized dimension reduction methods (t-SNE and UMAP) to make a lower dimension representation where we can cluster the data easier. These clusters and pairwise similarities were assessed by oral exam subjective scores. The teacher's subjective scores correlated more with this new metric-based method of scoring than the total test score itself. The presented procedures can not only be used effectively in research but can also help to get a more complete picture of the students' knowledge we teach in everyday practice

Perspective with Six Vanishing Points - an Alternative Method

The purpose of this paper is to describe perspective with six vanishing points. The line opened by axonometry and continued by one, two, three vanishing points and spherical perspectives, one became complete with the sixth vanishing point. Linear perspectives are often used, well known systems. Introducing new vanishing points doubles the represented part of space. The question of representing the half-space, hence the definition of the first five vanishing points can be found in literature. However, there was no useful solution for the representation of the whole space for a long time. This paper introduces a new definition of the sixth vanishing point that resulted a well applicable system. A short historical introduction looks at some of the interactions between mathematics and arts of western culture. Afterwards we formulate the new alternative perspective and give some methods of construction for notable lines and planes. Finally we write about possible applications

Vizualizacije krivulja i ploha u Sol geometriji

The paper makes an attempt to visualize one of the homogeneous geometries, the it Sol geometry, by illustrating first the geodesic curves and spheres then the so-called translation curves and spheres. We\u27ve collected their basic properties, too.Ovaj članak je pokušaj vizualizacije jedne od homogenih geometrija, Sol geometrije. Prvo se ilustriraju geodetske krivulje i sfere, a zatim i tzv. translatirajuće krivulje i sfere. Također su navedena njihova osnovna svojstva

Alternative Method to Determine the Characteristic Polynomial Applying Three-by-Three Matrices

The main aim of this paper is the presentation of the connection between the elements of the classical matrix arithmetic in case of three-by-three arbitrary real matrices. The given formulae can be used as well in case of the topic of stability analysis connected to the characteristic polynomial. The theorems and formulae presented in this article can be used in linear algebra courses or e.g. in three Degrees-of-Freedom mechanical problems, in machine tool bases designing, or in analyzes of earthquake effect on different type of structures

Changes in learning strategy and learning time in the wake of the pandemic

University studies were also significantly affected by the pandemic. The first-year students had already spent the last months of high school, which are especially important for graduation, in distance learning. In Hungary, the graduation procedure was changed due to the epidemic. Education was completely digital in hybrid form: the lectures were held online, and the seminars were attended in-person and from September of 2021 again in-person. Our research team has been monitoring learning time and effectiveness for years using the EduBase online educational platform, which provides a framework for all teaching aids for the calculus subject. In our research, we analysed the learning processes and their effectiveness of mechatronic and energy engineering students who were admitted to BME in 2020. The results were compared with the learning habits of the class of 2018, with whom a detailed study was also performed. It can be stated that the pandemic greatly influenced the learning time: students took advantage of the available practice opportunities to a greater extent in digital education, which did not reduce the practice time during the end-of-semester spurt, thus, learning became more balanced. Considering the high school results, it can be observed that on average, those who took advanced level subjects spent more time practicing, even though they had already mastered some calculus in high school. In addition, test scores also influenced practice time, while students coped successfully even with the more difficult tasks

Gerinchasználattal- és prevencióval kapcsolatos tudás vizsgálata és fejlesztése 6-10 éves gyerekek körében

The study aimed to develop a questionnaire examining back care knowledge and spine disease prevention of children aged 6–10 years and testing its psychometric properties, and examine the effectiveness of an evolved 1-school year child back school program. According to the results, the questionnaire is a reliable tool for the measurement of back care knowledge of 6-10 years old children and the evolved back school program was effective in the improvement of trunk state and back care knowledge of 6-7 years old childre