Abstract. We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local TAF-domains are the atomic pseudo-valuation domains.

For mammals, l-valine, which is a glycogen, is an essential amino acid. A protein made of 20 amino acids, salicylidene and l-valine make the carboxylate ligand which is the base of chiral Schiff. On a large scale, complexes with the ligand are utilized to help in the research work. To locate the exact location of a specific node from all the nodes, the entire node set is developed in a specific manner by choosing a particular subset and this subset is known as the resolving/locating set. This study contributed to the metric dimension of chemical complexes of supramolecular chain in dialkyltin from N-salicylidene-l-valine. We considered the complexes of 2,3,4 and ( C λ ⁎ ) ({C}_{\lambda }^{\ast }) chains and proved that the members of resolving sets are highly dependent on the number of vertices.

We study a system of rational dierence equations in this article. For equilibrium points, we present the stability conditions. In addition, we show that the system encounters period-doubling bifurcation at the trivial equilibrium point O and Neimark-Sacker bifurcation at the non-trivial equilibrium point E. To control the chaotic behavior of the system, we use the hybrid control approach. We also verify our theoretical outcomes at the end with some numerical applications.

In this study, we apply fractional calculus on certain convex functions and derive many novel mean-type inequalities by employing fractional calculus and convexity theory. In order to investigate fractional mean inequalities, we first build an identity in this study. Then, with its help, we derive many mean-type inequalities and estimate the error of HH inequality using a generalized version of RL-fractional integrals and certain classes of convex functions. The results obtained are validated by taking specific functions. Many mean-type inequalities that exist in the literature are generalized by the main results of this study.

The use of information–theoretical methodologies to assess graph-based systems has received a significant amount of attention. Evaluating a graph’s structural information content is a classic issue in fields such as cybernetics, pattern recognition, mathematical chemistry, and computational physics. Therefore, conventional methods for determining a graph’s structural information content rely heavily on determining a specific partitioning of the vertex set to obtain a probability distribution. A network’s entropy based on such a probability distribution is obtained from vertex partitioning. These entropies produce the numeric information about complexity and information processing which, as a consequence, increases the understanding of the network. In this paper, we study the Benes network and its novel-derived classes via different entropy measures, which are based on information functionals. We construct different partitions of vertices of the Benes network and its novel-derived classes to compute information functional dependent entropies. Further, we present the numerical applications of our findings in understanding network complexity. We also classify information functionals which describe the networks more appropriately and may be applied to other networks.