Step-constrained self-avoiding walks on finite grids

The study of self-avoiding walks (SAWs) on integer lattices has been an area of active research for several decades. In this paper, we investigate the number of SAWs between two diagonally opposite corners in a finite rectangular subgraph of the integer lattice, subject to certain constraints. In the two-dimensional case, we provide an explicit formula for the number of SAWs of a prescribed length, restricted to three-step directions. In addition, we develop an algorithm that produces faster computational results than the explicit formula. For some special cases, we present detailed counts of the SAWs in question. For rectangular grid graphs of higher dimensions, we provide a formula to count the number of SAWs that are exactly two steps longer than the shortest walks

Structural elucidation, biological significance and computational approach of Copper(ii), Nickel(ii) and Cobalt(ii) with bidentate schiff base of N-(Napthalene-1-ylmethylene)isonicotinohydrazide

The increasing prevalence of antibiotic-resistant bacteria and oxidative stress-related diseases underscores the need for novel therapeutic agents with potential dual functionality. In this research, a schiff base ligand, N-(Napthalene-1-ylmethylene)isonicotinohydrazide, was synthesized and complexed with Copper(II), Nickel(II), and Cobalt(II) ions. Characterization of the compounds using various spectroscopic and analytical techniques confirmed successful complex formation and structural stability. Antibacterial testing through the disc diffusion method revealed that the Ni(II) complex exhibited the highest antibacterial activity, with significant inhibition against Staphylococcus aureus , Bacillus subtilis , Escherichia coli , and Shigella flexneri . The antioxidant activity, evaluated via DPPH radical scavenging, showed that the Cu(II) complex was the most effective with an IC 50 value of 187.81 ± 1.42 µg/mL. Molecular docking studies against DNA gyrase (PDB ID: 7P2M) predicted the Ni(II) complex as the best binder (–9.9 kcal/mol), suggesting strong initial affinity. Complementary molecular dynamic simulations further demonstrated that Cu(II) and Co(II) complexes maintained the most stable protein-ligand interactions under dynamic conditions, highlighting their potential as robust inhibitors. ADMET predictions indicated favorable pharmacokinetic and toxicity profiles, though recognized as preliminary. DFT calculations confirmed stable geometries and showed a reduction of the HOMO–LUMO energy gap from 4.21 eV (ligand) to 2.85 eV (Ni complex), consistent with enhanced reactivity and biological activity. Mapping of electron density and atomic charge analysis identified potential nucleophilic attack sites, reinforcing the complexes’ therapeutic potential in combating bacterial infections and oxidative stress

Population genetic insights for climate-adaptive oak management: Results from a large-scale study of Turkey oak populations

Human-assisted translocation of oak reproductive material as part of climate-adaptive oak management has long been a key consideration in Central Europe. In this study, we conducted population genetic analysis of 32 Turkey oak (Quercus cerris L.) populations from Central and Southeast Europe, using ddRAD-seq genotyping, to support forestry adaptation measures. Our results revealed multiple genetic groups within the sampled range, suggesting that long-distance transfers of reproductive material could lead to the admixture of genetically distinct groups. We also detected a diversity cline, with genetic diversity increasing from the southwest and southeast toward the northwest. The highest diversity was observed in the Carpathian Basin, which is the most continental part of the sampled range and includes many populations near the species’ drought limit. In this region, the surplus of genetic diversity may play a crucial role in local adaptation. Our findings further suggest that transferring reproductive material from Southeast Europe to the Carpathian Basin should be approached with caution, as this direction runs counter to the observed diversity gradient. Furthermore, loci under selection and their genotype-environment associations indicate that Turkey oak is primarily challenged by temperature fluctuations and extremes, rather than by water availability, as previously observed in co-occurring sessile oak (Q. petraea (Matt.) Liebl.). These results provide valuable support for a detailed assessment of Turkey oak’s adaptive capacity, improving the efficiency of provenance selection for climate-adaptive forest management

From crisis to crisis: Assessment of financial performance of SMEs in the healthcare sector in Visegrad Countries

The living standards of the population in Visegrad Countries (V4) have long been below the EU and OECD averages, and the increase of negative impacts and crisis phenomena may be detected in their health systems, too. Our study examines the similarities and differences of the SMEs of healthcare sector in Visegrad Countries and their characteristics and common hallmarks of the overburdened healthcare system in which they are integrated. The aim of our research is to explore the similarities the financial indicators (liquidity, profitability, indebtedness, and efficiency) of SMEs in the healthcare sector of the four Visegrad Countries and to identify the possible clusters with similar financial typology. The research covers two crisis periods – from the 2008 financial and capital market crisis to the 2020 Covid-19 health crisis – and analyses the relationship and patterns in the financial performance of healthcare SMEs using correlation and cluster analysis. Based on our primary research results we found that the financial typology of SMEs in the healthcare sector in the Visegrad Countries shows similar characteristics in terms of liquidity – profitability – indebtedness – efficiency. Financial indicators of indebtedness and efficiency were significantly similar for all four countries. In addition, three relatively homogeneous groups could be formed according to the typical financial characteristics of each country

Site variability in chemical compositions and color parameters of black locust (Robinia Pseudoacacia L.) wood

Robinia pseudoacacia L. has a valuable wood due to its natural durability and resistance to decay and external environments. This durability is attributed to its high content of extractives and the amount of tyloses in earlywood vessels. Given the widespread occurrence of black locust across Hungary, the wood chemical components may differ depending on site growth conditions. This research investigated the chemical extractives and color parameters of wood from Robinia pseudoacacia L. from different counties and growth conditions in Hungary. The relationship between chemical extractives and color based on the CIElab system was also analysed. The results indicated that both counties and growth conditions showed significant variations in chemical extractives and color parameters. The counties of Vas and Győr-Moson-Sopron exhibited the highest total contents of extractives, polyphenol, antioxidant capacity and intense lightness. Compatible outcomes were recorded under poor growth condition mixed species. Lightness was significantly associated with extractives from methanol-water and total phenol contents with lightness. While the extractive from the cyclohexane-ethanol solvent system was linked with all color parameters. Subsequent research will investigate the impact of extractives on wood durability under different locations and growth conditions

Insights into EU Sustainability Regulations Promoting Wood as a Climate-Smart Construction Material

In response to the growing challenges of climate change and environmental degradation, the European Union announced the Green Deal on 11 December 2019, aiming for climate neutrality by 2050. To achieve this, a series of regulatory measures have been introduced to promote sustainability in the construction sector. This paper examines key EU regulations that, while not explicitly mandating wood, create conditions favorable to timber and wood-based products due to their low-carbon and renewable properties. The Carbon Removal Certification Framework (CRCF) encourages timber adoption through voluntary carbon removal incentives, whereas the new Construction Products Regulation (CPR) represents a mandatory intervention, embedding environmental and climate criteria directly into market standards. Additional regulations, including the Ecodesign for Sustainable Products Regulation (ESPR), the Energy Performance of Buildings Directive (EPBD), the Carbon Border Adjustment Mechanism (CBAM), the Nature Restoration Law (NRL), and the Regulation on Deforestation-Free Products (EUDR), further support wood by promoting resource efficiency, responsible sourcing, energy performance, and long-term carbon storage. Together, these measures form a multi-layered framework in which voluntary and binding instruments interact, indirectly supporting sustainable construction practices. Given its ability to store carbon over extended periods and achieve a net negative footprint in life cycle assessments, wood emerges as a strategic material for advancing the EU’s climate objectives

Turkish hazel (Corylus colurna L.) in Hungary: A case study on its forestry potential

This study investigates the structure and growth of a 73-year-old Turkish hazel (Corylus colurna L.) plantation in Hungary. The stand had a tree density of 290 per ha, mean height of 18.2 m, quadratic mean diameter of 34.2 cm, and a basal area of 26.7 m² ha⁻¹. The slenderness ratio of 0.55 indicates moderate stability. Diameter distribution was normal (22–53 cm). Crown structure parameters showed moderate correlations with diameter (R² = 0.59 for crown diameter; R² = 0.53 for crown projection area), emphasizing the role of crown traits in yield modelling. An optimal planting density of 434 trees ha⁻¹ was estimated based on the average crown projection area (23 m2). Turkish hazel, with its drought resilience and valuable wood, is a promising species for afforestation in semi-arid climates. However, further research is needed on its management and genetic improvement to support wider application. This study can be considered gap-filling both in a Hungarian and, to some extent, an international context

Structural characteristics mediate forest mitigation potential against climate change and biodiversity loss

European forests play an important role for climate change mitigation and biodiversity conservation. As they have been shaped by silviculture for centuries, it is important to understand how management practices affect forest structure and in turn influence the role of forests in achieving both goals. We analyzed data on a wide range of temperate European forests encompassing the most widespread management regimes to understand the interplay of forest structure, aboveground carbon stocks, and the richness of several taxonomic groups. Using structural equation modeling, we identified the forest structural characteristics that are positively correlated with both carbon stocks and species richness. We found that stand age and tree species richness are related to other forest structural characteristics, which had positive links to carbon stocks in deadwood. Increasing stand age was associated with an increase in deadwood carbon stocks. There were no direct negative relationships between stand age or tree species richness and the richness of different taxonomic groups. An increasing richness of deadwood types had positive links with the species richness of birds, saproxylic beetles, and saproxylic fungi, as with deadwood carbon stocks. However, increases in the species richness of birds and understory vascular plants were negatively related to increasing carbon stocks in living wood, while beetle species richness was positively related to this carbon stock. Birds' species richness was directly and positively associated with increasing mean tree diameter. Conversely, a higher richness of tree species was indirectly linked to lower carbon stocks in living wood. Additionally, an increase in mean tree diameter was indirectly correlated with a decrease in bird and vascular plant species richness. Our findings highlight potential trade‐offs between carbon stocks in living wood and the species richness of several taxonomic groups in European forests, while the species richness of some taxonomic groups was positively correlated to deadwood carbon stocks. Policies focused on increasing living biomass may not target both the climate and biodiversity crises. Instead, the diversity of deadwood emerges as a key factor in explaining the relationship between carbon storage and biodiversity, and should hence play a prominent role in forest management strategies and related policies