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In this paper, we extend our investigation about the generalized comaximal graph introduced in Biswas et al. (Discrete Math Algorithms Appl 11(1):1950013, 2019a). The generalized comaximal graph is defined as follows: given a finite commutative ring R, the generalized comaximal graph G(R) is an undirected graph with its vertex set comprising elements of R and two distinct vertices u, v are adjacent if and only if there exists a non-zero idempotent e ∈ R such that u R + v R = e R . In this study, we focus on identifying the rings R for which the graph G(R) exhibits planarity. Moreover, we provide a characterization of the class of ring for which G(R) is toroidal, denoted by γ (G (R)) = 1 . Furthermore, we also evaluate the energy of the graph G(R). Finally, we demonstrate that the graph G(R) is always Hamiltonian for any finite commutative ring R. [ABSTRACT FROM AUTHOR]

In this paper, we describe an activity that involves economics and mathematics. It is included in the planning of orientation paths towards university studies within the Mathematical High School Project and is dedicated to students in the last years of high school. In particular, this research will deal with the issue of solving an economic problem using not only real analysis instruments but also geometrical topics concerning Euclidean geometry and topology. Mathematics becomes a language to understand and explain a real life problem, such as determining the optimal position of an airport, a nuclear reactor and so on. Some activities made use of dynamic geometry software and computer simulations. [ABSTRACT FROM AUTHOR]

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation theorem concerning the fuzzy rate of convergence of these operators. Furthermore, through an example, we illustrate that our summability- based Korovin type theorem has an advantage over the fuzzy Korovkin type theorem proved in the seminal paper by Anastassiou (Stud. Univ. Babeş-Bolyai Math L(4):3–10, 2005) [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with 1. In Biswas et al. (Disc Math Algorithms Appl 11(1):1950013, 2019), we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if a R + b R = e R for some nonzero idempotent e in R. Let G ′ (R) be the subgraph of G(R) generated by the non-units of R. In this paper, we characterize those rings R for which the graph G ′ (R) is connected and Eulerian. Also we characterize those rings R for which genus of the graph G ′ (R) is ≤ 2 . Finally, we show that the graph G ′ (R) is a line graph of some graph if and only if R is either a regular ring or a local ring. [ABSTRACT FROM AUTHOR]

Solovyov (Fuzzy Sets Syst 159:2567–2585, 2008) introduced the notion of stratified Q-topological spaces, which in turn gives rise to the category Str-Q-TOP of stratified Q-topological spaces (where Q is a fixed member of a fixed variety of Ω -algebras). Singh and Srivastava (Ann. Fuzzy Math. Inform. 12:539–546, 2016) introduced the Q-topological space (Q , ⟨ { i d Q } ∪ { q ̲ ∣ q ∈ Q } ⟩) which is a Sierpinski object in the category Str-Q-TOP. In this paper, motivated by Singh (Fuzzy Sets Syst 159:2611–2615, 2008), we determine the coreflective hull of (Q , ⟨ { i d Q } ∪ { q ̲ ∣ q ∈ Q } ⟩) in the category Str-Q-TOP. We also determine the coreflective hulls of the categories Str-Dis-Q-TOP of discrete Q-topological spaces and Str-Ind-Q-TOP of stratified indiscrete Q-topological spaces, in the category Str-Q-TOP, motivated by Hoffmann (Arch Math 33:258–262, 1979) and Singh and Srivastava (Quaest. Math. 36: 167–179, 2013) [ABSTRACT FROM AUTHOR]

In a society that has to reconcile two areas which are conceptually very distant from each other, such as interdisciplinarity and specialization, the education for young people is essential to form a thought to understand complexity, thanks also to the stimuli deriving from increasingly powerful and interconnected technological and IT environments. So, it is essential to identify teaching–learning processes and methods that allow students to understand and act adequately with a constantly evolving reality. Transdisciplinary themes can be introduced to enrich the students' curriculum by anchoring them strongly to the wealth of emerging technologies, using their potential and designing educational activities focused on technology and attractive to the various spheres of knowledge. In this paper is presented an experimental activity of designing Smart objects in the Internet of Things conducted with students of the "Mathematical High School" project. [ABSTRACT FROM AUTHOR]