In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Aluminum oxide thin films were prepared by dc reactive sputtering technique using different mixing ratios of argon and oxygen gases (90:10, 70:30, 50:50, 30:70, and 10:90). These films were characterized to introduce their crystalline structures, surface morphology, and elemental composition. A progressive transition occurs from a predominantly amorphous to a highly crystalline Al2O3 film as the oxygen content in the Ar:O2 gas mixture is increased. Increasing the oxygen content leads to a progressive decrease in surface roughness, resulting in smoother and more uniform films with finer granular features. The oxygen-rich environments yield the smoothest surfaces, while argon-rich environments result in significantly rougher surfaces. These f

Optical properties of chromium oxide (Cr2O3) thin films which were prepared by pulse laser deposition method, onto glass substrates. Different laser energy (500-900) mJ were used to obtain Cr2O3 thin films with thickness ranging from 177.3 to 372.4 nm were measured using Tolansky method. Then films were annealed at temperature equal to 300 °C. Absorption spectra were used to determine the absorption coefficient of the films, and the effects of the annealing temperature on the absorption coefficient were investigated. The absorption edge shifted to red range of wavelength, and the optical constants of Cr2O3 films increases as the annealing temperature increased to 300 °C. X-ray diffraction (XRD) study reveals that Cr2O3 thin films are a

In this work, study the optical properties of composites consisting of poly Methyl Methacrylate and Berry Paper Mulberry. The samples of composites were prepared using casting method .The Berry Paper Mulberry (BPM) was added by different concentrations are (0, 2, 4 and 6)wt.%. The optical properties of composites have been studied in the wavelength range (200-800)nm. The absorption coefficient ,energy gap, refractive index, extinction coefficient and dielectric constants have been determined. The results show that the optical constants change with increase of BPM concentrations .

     In the present investigation two different types of fiber reinforced polymer composites were prepared by hand lay-up method using three different parameters (curing temperature, pressing load and fiber volume fraction). These composites were prepared from the polyester resin as the matrix material reinforced with glass fibers as first group of samples and mat Kevlar fibers as the second group, both with different volume fractions (4%, 8%, and 12%) of fibers. They were then tested by tensile strength and impact strength. The main objective in this study is to use Taguchi method for predicting the better parameters that give the better tensile and impact strength to the composites, and then preparing composites at