The performance of an antireflection coating entirely depends on the proportion of light energy transmitted or reflected by the coating material. To enhance the transmittance of an antireflection coating, evaluation of the amount of the light energy transmitted to generate charge carriers is very critical. Thus, in this paper, we demonstrate the effect of sputtering power and gas flow rate on the optical transmittance of aluminium oxide (Al\(_{2}\)O\(_{3}\)) and copper-doped zinc sulphide (ZnS:Cu) antireflection nanostructures. To this end, radiofrequency sputtering was used for the deposition of ZnS:Cu, using the ZnS:Cu target (94/6.0%) using argon (99.9% pure), and direct current sputtering was used for the deposition of Al\(_{2}\)O\(_{3}\) using the aluminium target (99.99% purity) and oxygen (99.9% pure). The gas flow rates of 40 to 100 sccm were used. The sputtering power values of 70 W to 140 W were used at a low process pressure of \(6.5 \times 10^{-3}\). The transmittance was observed to decrease with an increase in sputter power and deposition time. However, the transmittance of single-layer nanofilms was lower than that of the double-layer nanostructures. For photovoltaic applications, the Al\(_{2}\)O\(_{3}\)/ZnS:Cu(112.1 nm) nanostructure exhibited the highest transmittance of 96.9% at \(\lambda=780\) nm. The reflectance of the nanostructures increased with an increase in coating time and sputtering power, with the lowest value of 3.03% recorded at 360 nm. The nanostructures are crystalline, smooth, and dense but the crystallite sizes decreased from 0.02508 to 0.02071 \(\text{\AA}\) with an increase in gas flow rate. This decrease in crystallinity was due to the reduced adatom migration on the substrate. The optimal gas flow rate was 100 sccm, in which the Al\(_{2}\)O\(_{3}\)/ZnS:Cu(117 nm) had the highest transmittance of 97.7% at \(\lambda=741\) nm. The results demonstrate the potential use of Al\(_{2}\)O\(_{3}\)/ZnS:Cu nanostructures as antireflection materials for photovoltaic solar cells.

In this paper, we introduce a new resolvability parameter named as the local edge partition dimension \((LEPD)\) of graphs. The local edge partition dimension \((LEPD)\) makes a specialty of partitioning the vertex set of a graph into awesome instructions based totally on localized resolving properties. Our findings offer a fresh angle on graph resolvability, offering capability insights for optimizing network overall performance and structural analysis. Let \(G=(V, E)\) be a connected graph with vertex set \(V\) and edge set \(E\). A partition set \({R}_{p}=\{{R}_{p1},{R}_{p2},{R}_{p3}\dots,{R}_{pn}\}\) contain subsets of vertices of \(G\). If for every pair of adjacent edges \(p\) and \(q\) in \(G\), then \(d(p,{R}_{p})\neq d(q,{R}_{p})\) and if \(p\) and \(q\) are non-adjacent then not necessary \(d(p,{R}_{p})\neq d(q,{R}_{p})\) then \({R}_{p}\) is called a local edge resolving partition set and minimum cardinality of such set is called local edge partition dimension. We discussed local metric, local edge metric, metric, edge metric dimension, local partition, local edge partition, partition dimension, and edge partition dimension of the Petersen graph.

In this paper we construct families of bit sequences using combinatorial methods. Each sequence is derived by converting a collection of numbers encoding certain combinatorial numerics from objects exhibiting symmetry in various dimensions. Using the algorithms first described in [1] we show that the NIST testing suite described in publication 800-22 does not detect these symmetries hidden within these sequences.

This note addresses impracticalities or possible absurdities with regards to the definition corresponding of some graph parameters. To remedy the impracticalities the principle of transmitting the definition is put forward. The latter principle justifies a comprehensive review of many known graph parameters, the results related thereto, as well as the methodology of applications which draw a distinction between connected versus disconnected simple graphs. To illustrate the notion of transmitting the definition, various parameters are re-examined such as, connected domination number, graph diameter, girth, vertex-cut, edge-cut, chromatic number, irregularity index and quite extensively, the hub number of a graph. Ideas around undefined viz-a-viz permissibility viz-a-viz non-permissibility are also discussed.

A bijective mapping \(\varsigma\) assigns each vertex of a graph \(G\) a unique positive integer from 1 to \(|V(G)|\), with edge weights defined as the sum of the values at its endpoints. The mapping ensures that no two adjacent edges at a common vertex have the same weight, and each \(k\)-color class is connected to every other \(k-1\) color class. A graph \(G\) possesses \(b\)-color local edge antimagic coloring if it satisfies the aforementioned criteria and it corresponds to a maximum graph coloring. This paper extensively studies the bounds, non-existence, and results of b-color local edge antimagic coloring in fundamental graph structures.

In this article, we establish fixed point outcomes for mappings that are asymptotically regular within the context of \(b\)-metric spaces. These findings broaden and enhance the familiar outcomes found in existing literature. Additionally, we present corollaries to demonstrate that our results are more encompassing compared to the established findings in the literature.