We consider non oscillatory functions and prove an everywhere Fourier Inversion Theorem for functions of very moderate decrease. The proofs rely on some ideas in nonstandard analysis.
To solve the approximate analytic solutions of the quadratic Riccati differential equations, this study introduces a hybrid method that combines an accelerated variant of the Adomian decomposition method (AADM) proposed by I. El-Kalla with the Ramadan Group transform (RGT). This hybrid technique produces accurate and dependable results, outperforming the regular Adomian decomposition method (RADM) and the Newton- Raphson version of Adomian polynomials in terms of accuracy. Three examples are provided here to demonstrate good accuracy and fast convergence when compared to the exact solution and other recent analytical methods using Shifted Chebyshev polynomials, Variation of Parameters Method (VPM), Bezier polynomials, homotopy analysis method (HAM), and Newton – Raphson based modified Laplace Adomian decomposition method.
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.
