F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

The work is devoted to the study of the plastics features in modern construction use. The plastics classification in modern construction is generalized. This classification includes: the field of building products application, the features of the materials properties and products, a backup group that includes those products that are not included in the previous groups. The classification considered is the basis for choosing the basic materials properties that affect the quality and durability of products. To improve the plastics types in the construction, the Venn diagram is used. The main materials types for manufacturing a product of the "window profile" type are analyzed; the result of the studies is a comparative diagram.

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

Machine learning (ML) is a key component within the broader field of artificial intelligence (AI) that employs statistical methods to empower computers with the ability to learn and make decisions autonomously, without the need for explicit programming. It is founded on the concept that computers can acquire knowledge from data, identify patterns, and draw conclusions with minimal human intervention. The main categories of ML include supervised learning, unsupervised learning, semisupervised learning, and reinforcement learning. Supervised learning involves training models using labelled datasets and comprises two primary forms: classification and regression. Regression is used for continuous output, while classification is employed

Recently, the theory of Complex Networks gives a modern insight into a variety of applications in our life. Complex Networks are used to form complex phenomena into graph-based models that include nodes and edges connecting them. This representation can be analyzed by using network metrics such as node degree, clustering coefficient, path length, closeness, betweenness, density, and diameter, to mention a few. The topology of the complex interconnections of power grids is considered one of the challenges that can be faced in terms of understanding and analyzing them. Therefore, some countries use Complex Networks concepts to model their power grid networks. In this work, the Iraqi Power Grid network (IPG) has been modeled, visua

Fast dissolving film can be defined as a dosage form, which when placed in the oral cavity. It will rapidly disintegrate and dissolves to release the medication for oral mucosal absorption or allow for the gastrointestinal absorption to be achieved when swallowed.

Flurbiprofen is non-steroidal anti-inflammatory agent with antipyretic and analgesic properties and can be used   in low doses 8.75 mg as analgesic and anti inflammatory agent in sore throat infection. This study aims to   formulate flurbiprofen as oral dissolving films,   to improve the effective relief of pain with severe sore throats with little or no adverse effect.

Nine formulas were prepared using solvent-casting method, and t