Introduction/purpose: Molodtsov introduced the concept of soft sets as a new mathematical tool for dealing with problems containing uncertainties. In the literature, different kinds of operations of soft sets are defined and used in theory and applications. Methods: This study is based on the paper "A New Operation on Soft Sets: Extended Difference of Soft Sets" by Sezgin, Ahmad and Mehmood [Journal of New Theory 27 (2019) 33-42]. Results: In this paper, we define a new operation on soft sets, called extended symmetric difference and investigate its relationship between extended symmetric difference and restricted symmetric difference and some other operations of soft sets. Conclusion: The author believes that the obtained results represent a significant improvement of many known results in the existing literature.

In this paper, tiling a plane with equilateral semi-regular convex polygons is considered, and, that is, tiling with equilateral polygons of the same type. Tiling a plane with semi-regular polygons depends not only on the type of a semi-regular polygon, but also on its interior angles that join at a node. In relation to the interior angles, semi-regular equilateral polygons with the same or different interior angles can be joined in the nodes. Here, we shall first consider tiling a plane with semi-regular equilateral polygons with 2m-sides. The analysis is performed by determining the set of all integer solutions of the corresponding Diophantine equation in the form of , whereare the non-negative integers which are not equal to zero at the same time, and are the interior angles of a semi-regular equilateral polygon from the characteristic angle. It is shown that of all semi-regular equilateral polygons with 2m-sides, a plane can be tiled only with the semi-regular equilateral quadrilaterals and semi-regular equilateral hexagons. Then, the problem of tiling a plane with semi-regular equilateral quadrilaterals is analyzed in detail, and then the one with semi-regular equilateral hexagons. For these semi-regular polygons, all possible solutions of the corresponding Diophantine equations were analyzed and all nodes were determined, and then the problem for different values of characteristic elements was observed. For some of the observed cases of tiling a plane with these semi-regular polygons, some graphical presentations of tiling constructions are also given.

Globally, when accessing and driving in public transport vehicles, women have a problem with fear, experiences of sexual harassment and violence. Women's daily trips are very different from those made by men. These factors make a woman more vulnerable, as standard public transport companies do not consider these characteristics enough. The safe public transport option also helps increase the number of women in economic activities. The way of traveling determines the type of work or shift that the woman will accept. Mobility provides women with financial strength and independence, and currently access to safe public transport, both in Sarajevo Canton and throughout Bosnia and Herzegovina, and it can be said that it is not at a satisfactory level in the region, so urgent actions need to be taken. The concept for the implementation of gender equality within the Erasmus + TRAFSAF project, modeled on EU projects, is that all project partners, both those coming from the segment of higher education and NGOs, keep gender statistics and that measures to promote enrollment must be provided. female populations at all levels of study. It is also a requirement for project participants to increase the participation of women as trainers, as well as to enhance the presence of women in trainings related to traffic safety during the project. These activities should continue after the completion of the project, bearing in mind that it is necessary to integrate gender equality in the segment of traffic safety.

The influence of light and temperature stress conditions and oxygen availability on the chemical composition of Satureja montana and Lavandula angustifolia essential oils is reported. Photostability and thermal stability were evaluated by gas chromatography-mass spectrometry (GC‑MS) analysis, comparing composition before and after the applied regimes. In Satureja montana essential oil, the amount of thymol (13.0-11.9%) and carvacrol (10.3-9.4%) decreased at elevated temperature and in the presence of air, with a simultaneous increase of p-cymene (24.2‑26.2%) while in an inert atmosphere the composition remained the same as in fresh oil. Light caused a dehydrogenation of α-terpinene (2.1-0.9%) and γ-terpinene (5.6‑4.7%) to p-cymene (24.2-25.9%) and decrease of trans-caryophyllene (5.1-4.3%). In Lavandula angustifolia essential oil, compounds sensitive to elevated temperature and the presence of oxygen were cis‑ocimene (2.8-2.2%) and trans‑ocimene (2.6-2.0%), alloocimene (3.0-2.3%), trans‑caryophyllene (4.3-3.6%) and β-farnesene (1.7-1.2%). Irradiated samples showed a decrease in the content of cis-ocimene (2.8-1.9%), alloocimene (3.0‑2.0%), crypton (0.6-0.1%), cuminal (0.3-0.0%), trans‑caryophyllene (4.3-3.5%), β-farnesene (1.7-1.1%) and germacrene-D (0.5-0.1%) and an increase of trans-ocimene (2.6-3.5%), β-bourbonene (0.0-0.2%) and several unidentified peaks. Both oils showed an individual response to light and temperature stress. The absence of oxygen and light is the only storage regime under which the initial composition can be preserved.

Monitoring programs should generate high-quality data on the concentrations of substances and other pollutants in the aquatic environment to enable reliable risk assessment. Furthermore, the need for comparability over space and time is critical for analysis of trends and evaluation of restoration of natural environment

Abstract This paper is concerned with a recently introduced graph invariant, namely the Sombor index. Some bounds on the Sombor index are derived, and then utilized to establish additional bounds by making use of the existing results. One of the direct consequences of one of the obtained bounds is that the cycle graph Cn attains the minimum Sombor index among all connected unicyclic graphs of a fixed order n ≥ 4. Graphs having the maximum Sombor index are also characterized from the classes of all connected unicyclic, bicyclic, tricyclic, tetracyclic, and pentacyclic graphs of a fixed order, and a conjecture concerning the maximum Sombor index of graphs of higher cyclicity is stated. A structural result is derived for graphs with integer values of Sombor index. Several possible directions for future work are also indicated.

It is well known that the Golden Section plays an important role in the geometry of several polygons and polyhedra; the best known example is the length of a diagonal in the regular pentagon with unit side. In this contribution we show how the Golden Section appears as the solution of an enumerative problem connected with heptagons, more precisely, with heptagonal tilings of the hyperbolic plane. The results are then generalized by investigating whether it also appears in other types of hyperbolic tilings.

The Sombor index is a recently introduced graph-theoretical invariant of the bond-additive type. It is known that it takes integer values for bipartite semi-regular graphs whose degrees appear as two smaller elements in a Pythagorean triple. In this note, we show that it can have integer values also for graphs with more complicated structure and construct infinite families of graphs with integer Sombor indices.