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.

This work used the deposition method to synthesize nickel oxide nanoparticles. The materials mainly used in this study were nickel sulfate hexahydrate (as a precursor) and NaOH (as a precipitant). The properties of the nanopowder were characterized by XRD, FE-SEM, EDX, and VSM. The obtained results confirmed the presence of nickel oxide nanoparticles with a face-centered cubic (FCC) structure with a lattice constant (a=4.17834 Å). Scherer and Williamson-Hall equations were used to calculate the crystallite size of about (30.5-35.5) nm. The FE-SEM images showed that the particle shape had a ball-like appearance with a uniform and homogeneous distribution and confirmed that the particles were within the nanoscale. The presence of oxygen a

The crystal compounds Tl2-xAg2-ySryBayCa2Cu3O10+& are successfully prepared in different concentrations (x, y=0.1, 0.2, 0.3, 0.4, 0.5) by solid state reaction process. The samples were then subjected to Nano technique under hydrolic pressure 8 ton/cm2. samples have been annealed in (850 C0) for 72 hours. The results show a best value at x, y=0.3 ratio of Ag, Ba. Electrical resistivity at x, y= 0.3 of Ag, Ba are obtained when the best value of Tc= 141 K. Samples morphology were also observed by AFM (in three dimensions), the best value of Nano is 91.74 nm at x, y= 0.3. Morphological structures of the surface were also observed by (SEM) and (EDX) show that there are dark regions and light which indicate the presence of heavy elements a

     Zinc oxide films (ZnO) are prepared by an electrolysis technique and without vacuum and then annealed atvarious temperatures (300,400,500)^OC for an hour. The structural analysis performed by X-Ray diffraction (XRD) shows,dominant orientation of this films is plane (101), has a hexagonal structure and  polycrystalline pattern and it was is found that the crystal size increases(24,29) nm at annealing temperatures (300, 400)° C, but the crystal size decreases to (20 nm) at annealing temperature (500 ° C). As the results of a surface nature study of these films showed by examining the atomic force microscope (AFM), the grain  size increases from (60.79 to 88.11) nm, and the surface roughnes

Abstract:Porous Silicon (PSi) has been produced in this work by using Photochemical (PC) etching process by using a hydrofluoric acid (HF) solution. The irradiation has been achieved using quartz- tungsten halogen lamp. The influence of various irradiation times on the properties of PSi اmaterial such as layer thickness, etching rate and porosity was investigated in this work too. The XRD has been studied to determine the crystal structure and the crystalline size of PSi material

Porous Silicon (PSi) has been produced in this work by using Photochemical (PC) etching process by using a hydrofluoric acid (HF) solution. The irradiation has been achieved using quartz- tungsten halogen lamp. The influence of various irradiation times on the properties of PSi اmaterial such as layer thickness, etching rate and porosity was investigated in this work too.
The XRD has been studied to determine the crystal structure and the crystalline size of PSi material

SnO2 thin films of different two thicknesses were prepared an glass substrate by DC magnetron sputtering. The crystal structure and orientation of the films were investigated by XRD patterns. All the deposited films are polycrystalline. The grain size was calculated as 25.35, 28.8 nm. Morphological and compositions of the films were performed by SEM and EDX analyses respectively. The films appeared compact and rougher surface in nature. The allowed direct band gap was evaluated as 3.85 eV, and other optical constants such as refractive index, extinction coefficient, real and imaginary parts of dielectric constants were determined from transmittance spectrum in the wavelength range (300-900) nm and also analyzed.