We discuss a central concept of nanothermdynamics; the subdivision potential. We explain how it can be measured or calculated for some typical ensembles, as this has been disputed in the literature. We proceed to discuss its meaning for particular systems, and predict scaling laws for three ensembles. The laws depend on the small system geometry in a predictable way for an ideal gas model with surface adsorption. We provide new equations which relate the subdivision potential to experimental investigations, and give expressions for grand canonical ensembles of spheres, cylinders, slit pores and fluids confined in porous media. The subdivision potential is not compatible with the popular Hadwiger theorem in geometry, and can therefore not be described by a Minkowski set of variables. It is equivalent to Gibbs descriptions when shape- and size variables are defined.

In preserving genetic diversity among domestic animal breeds, the strategies emphasizing be-tween-breed diversity may be not optimal by neglecting within-breed variation. The present study aimed to assess the extent of the population subdivision of Mangalica pigs and the contri-bution of migration intensity to their substructure. Genealogy analysis was performed for breeding animals born between 1981 and 2023 examining three colour variations (Blonde, Swal-low-Belly, and Red). The fixation index (FST) was calculated and evaluated by Multidimensional Scaling and Clustering to expose the population substructure. The average FST is 0.04 for the Blonde and 0.05 for the Swallow-Belly and the Red while in the active herds, these parameters are smaller being 0.03 and 0.04, respectively. The migration of individuals affected 61.63% of the Blonde, 75.53% of the Swallow-Belly, and 63.64% of the Red breed herds. No population sub-structure was found in any Mangalica breed which can be explained by the extensive within breed migration among the herds.

The aim of this work is to analyze and investigate the shape preserving properties of ternary 4-point non-stationary interpolating subdivision schemes constructed by Beccari et al. [1] with a tension parameter !k+1 which can reproducing exponential. Moreover, the conditions on the initial control points are developed that allow user to generate shape preserving limit curves after a nite number of subdivision steps and generalize these results in limiting case. Signicance of derived conditions are illustrated through graphs and the whole discussion is followed by examples.

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

Because of hyper complexity, difficulty to define, multiple stakeholders with conflicting perspectives, and lack of clear-cut solutions, wicked problems necessitate innovative and adaptive strategies. Operations Research has been a valuable tool for managers to make informed decisions for years. However, as we face increasingly complex and messy problems, it has become apparent that relying solely on either hard or soft OR approaches is no longer sufficient. We need to explore more innovative methodologies to address these wicked problems effectively. This study has bridged the research gap by proposing a structured process encompassing a subdivision-based problem structuring method for defining the wicked problem, a multi-attribute decision-making (MADM) for prioritizing sub-problems, and a hard OR technique, data envelopment analysis (DEA) for tackling one of the most critical sub-divisions. The proposed methodology, implemented in a case study, focuses on a higher education institution experiencing a decline in student admissions and involves five steps. First, a diverse group of stakeholders is formed to ensure comprehensive consideration of perspectives. Second, the wicked problem is defined, considering long-term consequences, multiple stakeholders, and qualitative stakeholder opinions. Third, a hierarchical structure is created to break down the wicked problem into manageable sub-problems. Fourth, a multi-criteria decision-making (MCDM) method prioritizes sub-problems. Finally, the sub-problems are addressed one by one using a combination of soft and hard OR tools. The findings highlight the benefits of integrating hard and soft OR approaches. The article concludes with reflections on the implications of using a combined OR approach to tackle wicked problems in higher education and beyond.

After reviewing the history of the struggle between human beings and plant diseases, insects and weeds, especially reviewing the thoughts of plant protection in ancient Chinese agricultural books, the target recognition of plant pests and the six types of plant protection methods and 36 subdi-vision measures were summarized. Then the development overview of pesticide application technology was focused and reviewed systematically by combining the development timeline of pesticide application and the key technologies including the performance measurement and the simulation and modeling of pesticide spraying system. And three suggestions for further research were proposed from the perspectives of human-being and environmental health, the sustainable and eco-friendly application medium, and the efficiently application equipment system in plant protection.