The optimal selection of a site for cement plant development is a multifaceted decision-making process that demands careful consideration of environmental, economic, and social dimensions. This research delves into the utilization of Circular Intuitionistic Fuzzy Soft Sets (CIFSS) as an advanced mathematical framework to enhance the precision and reliability of sustainable decision-making in cement plant site selection. The CIFSS approach adeptly manages the inherent uncertainties and ambiguities associated with evaluating potential locations, offering a comprehensive methodology for assessing various criteria. By embedding CIFSS within the context of sustainable development, this technique provides decision-makers with a robust and adaptable tool for identifying the most appropriate site, thereby ensuring long-term viability and minimizing environmental impacts. The results underscore the effectiveness of CIFSS in facilitating complex, multi-criteria decision-making in industrial site selection, underscoring its broader applicability in sustainable infrastructure planning.

This paper introduces the concept of the extended \(H\)-cover of a graph \(G\), denoted as \(G^*_H\) , as a generalization inspired by the extended double cover graphs discussed in Chen [1]. We explore the spectral properties and energy characteristics of \(G^*_H\), deriving formulae for the number of spanning trees in cases where both \(G\) and \(H\) are regular. Our investigation identifies several infinite families of equienergetic graphs and highlights instances of cospectral graphs within \(G^*_H\) . Additionally, we analyze various graph parameters related to the Indu-Bala product of graphs and the partial complement of the subdivision graph (PCSD) of \(G\).

A dominator coloring of a graph \(\mathscr{G}\) is a proper coloring where each vertex of \(\mathscr{G}\) is within the closed neighborhood of at least one vertex from each color class. The minimum number of color classes required for a dominator coloring of \(\mathscr{G}\) is termed the dominator chromatic number. Additionally, a total dominator coloring of a graph \(\mathscr{G}\) is a proper coloring in which every vertex dominates at least one color class other than its own. The minimum number of color classes needed for a total dominator coloring of \(\mathscr{G}\) is known as the total dominator chromatic number. In this paper, our objective is to derive findings concerning dominator and total dominator coloring of the duplication corresponding corona of specific graphs.

The topological index is a molecular property that is determined from a chemical compound’s molecular graph. Topological indices are numerical graph parameters that inform us about the topology of the graph and are generally graph invariants. In this paper, we consider some topological indices based on the second distance of each vertex of the graph \(\alpha\) and the number of unordered pairs of vertices \(\{s,q\} \subseteq V(\alpha)\) which are at distance \(3\) in \(\alpha\). These indices are called the leap Zagreb index and the Wiener polarity index, respectively. we compute these indices of \(R\)-vertex join and \(R\)-edge join of graphs.

We present an introduction to the mathematics of quantum physics and quantum computation which put emphasis on the basic mathematical aspects of definition and operations on qubits. We start by a comprehensive introduction of a qubit as a unit element of \( \mathbb{C}^2 \), and its representations on spheres in \( \mathbb{R}^3 \). This introduction leads to the interpretation of Pauli operators as basic rotations in \( \mathbb{R}^3 \). Then we study unitary operators. Their link to rotations in \( \mathbb{R}^3 \) is established using the density operator associated to a qubit. We complete this paper by some decomposition, or splitting, problems of unitary operators on \( \mathbb{C}^2 \) based on decomposition results of rotations in \( \mathbb{R}^3 \). These decomposition results are useful for the construction of quantum gates.

In this research article, the authors introduce the refinements of some special inequalities, like Lah-Ribarič type, Giaccardi, and Petrović’s inequalities. Also, the authors define Fejér, Giaccardi, and Petrović’s types of inequalities for different classes of convex functions.

In this study, an approximate solution of the Sitnikov problem was investigated using fourth-order Runge – Kutta method. We confirmed the periodicity and the symmetric nature of the orbits. The various values of eccentricities were obtained which showed that at eccentricity e = 0, the orbit moves in a circular shape and otherwise when e < 0. Also at every values of e, we found the numerical results which we demonstrated by simulations using MATCAD which showed that the range for the search of eccentricities can be narrowed down at different values of e, different sinusoidal frequencies were obtained.