This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

This work aims to find a solution to the problem under investigation and to study non-local boundary-value problems for rectangular domains and two-dimensional thirdorder partial differential equations (PDEs). A finite-difference method combined with the trapezoidal rule is used to solve problems. The numerical results were determined to be steady and accurate.

We know that the experiments which conducted by latin square in one location or in one period (season), but there are many cases that need to conduct the same experiments in many locations or in many periods (seasons) to study the interaction  between the treatments and locations or between the treatments and periods (seasons) .In this research we present  an idea for  conduct  the experiment in several locations and in many period (seasons) by using LSD , it represent  acontribution in the area of design and analysis of experiments ,we had written. we had written (theoretically)  the general plans, the mathematical models for these experiments, and finding the derivations of EMS for each component (

New series of metal ions complexes have been prepared from the new ligand [4-Amino-N-(5-methyl-isaxazol-3-yl)-benzenesulfonamide] derived from Sulfamethoxazole and 3-aminophenol. Accordingly, mono-nuclear Mn(II), Fe(III), Co (II), and Rh(III) complexes were prepared by the reaction of previous ligand with MnCl₂.4H₂O, CoCl₂.6H₂O, FeCl₃.6H₂O and RhCl₃H₂O, respectively. The compounds have been characterized by Fourier-transform infrared (FTIR), ultraviolet–visible (UV–vis), mass,  ¹H-, and ¹³C-nuclear magnetic resonance (NMR) spectra and thermo gravimetric analysis (TGA& DSC) curve, Bohr magnetic (B.M.), elemental microanal

               Microalgae have been used widely in bioremediation processes to degrade or adsorb toxic dyes. Here, we evaluated the decolorization efficiency of Chlorella vulgaris and Nostoc paludosum against two toxic dyes, crystal violet (CV) and malachite green (MG). Furthermore, the effect of CV and MG dyes on the metabolic profiling of the studied algae has been investigated. The data showed that C. vulgaris was most efficient in decolorization of CV and MG: the highest percentage of decolorization was 93.55% in case of MG, while CV decolorization percentage was 62.98%. N. paludosum decolorized MG dye by 77.6%, and the decolorization percentage of CV was 35.1%. Metabolic profiling of

This paper considers the nonlinear homogeneous fractional Burger's equation as a type of nonlinear fractional partial differential equations (FPDE). Our goal in this paper is to show that an initial value problem (IVP) can be modified with a second initial condition when (α ∈ ( 1,2 ]) as the velocity of the movement, and the obtained solution agrees with the nature of the wave with space and time for the problem. The Caputo fractional derivative is used in all the fractional derivatives. Also, the algorithm of the Laplace transform decomposition method (LTDM) for fractional PDEs is presented. The approximate solution converges to the exact solution in Theorem 1. Also, a numerical simulation is made to confirm the theoretical resu