This paper deals with finding the approximation solution of a nonlinear parabolic boundary value problem (NLPBVP) by using the Galekin finite element method (GFEM) in space and Crank Nicolson (CN) scheme in time, the problem then reduce to solve a Galerkin nonlinear algebraic system(GNLAS). The predictor and the corrector technique (PCT) is applied here to solve the GNLAS, by transforms it to a Galerkin linear algebraic system (GLAS). This GLAS is solved once using the Cholesky method (CHM) as it appear in the matlab package and once again using the Cholesky reduction order technique (CHROT) which we employ it here to save a massive time. The results, for CHROT are given by tables and figures and show

    In this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth

In the present work, the ternary compound MgxZn7-x O7Wurtzoid with variable Zn and Mg contents was analyzed using density functional theory with B3LYP 6-311G**basis set. The electronic and vibrational properties of MgxZn7-xO7 wurtzoids, were investigated, including energy gaps, bond lengths, spectral properties, such like infrared spectra and Raman. IR and Raman spectra were compared with experimental longitudinal optical modes frequency results. The theoretical results agree well with experiments and previous data. It has been found that the energy gap is increasing with the increased Mg concentration, and that the longitudinal optical position exposes a UV shift movement with an increase in the concentration.

This paper includes the synthesis of some new nucleoside analogues starting with 2-substituted benzimidazole derivative (7-9), that synthesized by condensation of O-phenylenediamine with p-chloro benzaldehyde and two substituted benzoic acid , which on nucleophilic substitution with propargyl bromide gave a new N-substituted compounds (10-12). D-Fructose and D-galactose were chosen as a sugar moiety which were protected, brominated and azotated to give azido sugars (5) and (6), then they were subjected to 1,3-dipolar cycloaddition reaction with N-substuted compounds afforded bloked nucleoside analoges (13-16), which after hydrolysis gave our target the free nucleoside analogues (17-20). All prepared compounds were identified by FT-IR

     With and without the use of magnetic fields, titanium dioxide (TiO₂) nanoparticles were synthesized using the hydrothermal method at extremely high temperatures and pressures. Titanium tetra isopropoxide [Ti(C₁₂H₂₈O₄)] was used for the preparation, which was performed at pH 7 and under temperatures of 160 and 190 ˚C. UV spectroscopy, XRD crystallography, FE-SEM microscopy were used for characterizations. From UV spectroscopy, the energy gap values were clearly affected by the increase in temperature and the presence of the magnetic field. At the temperatures of 160 and 190 ^oC for TiO₂ without magnetic field, FE-SEM microscopy images have shown an average c