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A kisiskolás gyerekek térszemléletének fejlesztése az oktatási folyamat fontos feladata, különös tekin-tettel a megszerzett kompetenciák gyakorlati alkalmazása a valós életben. A tanulmányban röviden bemutatjuk a 11-12 éves tanulók térszemlélet fejlesztésére fókuszáló projektünkben alkalmazott fejlesztő feladatokat, melyek a matematika órákon valósultak meg. A tanulók olyan feladatokat oldottak meg, amelyek a sík és térbeli tárgyakkal való problémamegoldásra, a sík vagy térbeli helyzetek elemzésére és a tárgyakkal való manipulálására összpontosítottak.

Creation in space and perception of spatial relations are important workplace skills that can be successfully developed in public education through the cooperation of art education, mathematics, and technology, the STEAM model that has been successfully employed in higher education. In a longitudinal school-based experiment, we enhanced the spatial skills of preadolescents through a STEAM-based educational programme. To design our methods of intervention in mathematics, visual arts, and information technology, we used the structure of spatial skills identified in previous studies. Developmental methods involved two- and three-dimensional visualisation tasks in real-life and virtual learning environments. We employed a pre- and post-hoc assessment design using a spatial ability task sequence standardised in Hungary that proved to be valid for assessing Slovak students as well. Authentic assessment tasks included real-life situations when visualisations of spatial relations were used for orientation and creation. Pre-test results showed significant differences between school classes: we identified high achievers and middle-to-low achievers. Our developmental programme was aimed at personalised talent development in the high-achieving classes and the general improvement of the performance of low achievers, raising insufficient pre-test results to an average post-test performance.

Application of technical developments in biology and vice versa or biological samples in technology led to the development of new types of functional, so-called “biohybrid” materials. These types of materials can be created at any level of the biological organization from molecules through tissues and organs to the individuals. Macromolecules and/or molecular complexes, membranes in biology, are inherently good representatives of nanosystems since they fall in the range usually called “nano.” Nanohybrid materials provide the possibility to create functional bionanohybrid complexes which also led to new discipline called “nanobionics” in the literature and are considered as materials for the future. In this publication, the special characteristics of photosynthetic reaction center proteins, which are “nature’s solar batteries,” will be discussed in terms of their possible applications for creating functional molecular biohybrid materials.

The feasibility of the application of the Photo-Fenton process in the treatment of aqueous solution contaminated by Tylosin antibiotic was evaluated. The Response Surface Methodology (RSM) based on Central Composite Design (CCD) was used to evaluate and optimize the effect of hydrogen peroxide, ferrous ion concentration and initial pH as independent variables on the total organic carbon (TOC) removal as the response function. The interaction effects and optimal parameters were obtained by using MODDE software. The significance of the independent variables and their interactions was tested by means of analysis of variance (ANOVA) with a 95% confidence level. Results show that the concentration of the ferrous ion and pH were the main parameters affecting TOC removal, while peroxide concentration had a slight effect on the reaction. The optimum operating conditions to achieve maximum TOC removal were determined. The model prediction for maximum TOC removal was compared to the experimental result at optimal operating conditions. A good agreement between the model prediction and experimental results confirms the soundness of the developed model.

We show that any graph of maximum degree at most $3$ has a two-coloring, such that one color-class is an independent set while the other color induces monochromatic components of order at most $189$. On the other hand for any constant $C$ we exhibit a $4$-regular graph, such that the deletion of any independent set leaves at least one component of order greater than $C$. Similar results are obtained for coloring graphs of given maximum degree with $k+ \ell$ colors such that $k$ parts form an independent set and $\ell$ parts span components of order bounded by a constant. A lot of interesting questions remain open.