In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

Photocatalytic materials are being investigated as effective bactericides due to their superior ability to inactivate a broad range of dangerous microbes. In this study, the following two types of bacteria were employed for bactericidal purposes: Gram-negative Escherichia coli (E. coli) and Gram-positive Staphylococcus aureus (S. aureus). The shape, crystal structure, element percentage, and optical properties of Ag9(SiO4)2NO3 were examined after it was successfully synthesized by a standard mixing and grinding processing route. Bactericidal efficiency was recorded at 100% by the following two types of light sources: solar and simulated light, with initial photocatalyst concentration of 2 µg/mL, and 97% and 95% of bactericidal acti

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

In this study new derivatives of Schiff bases 5-8, 1, 3-oxazepine 9-16 and tetrazoles 17-19 have been synthesized from the new starting material 1 which has synthesized the reaction of one mole of dichloro acetic acid and two moles of thiophenol, the esters 2-3 were synthesized from the reaction of compound 1 with methanol or ethanol respectively in the presence of H2SO4 as catalyst then 2, 2-dithiophenylaceto Hydrazide 4 were synthesized from the reaction of 2 or 3 with hydrazine hydrate 80%, Schiff bases 5-8 were synthesized from the reaction of 4 with appropriate aldehyde or ketone. Treatment of Schiff bases with maleic and phathalic anhydride in dry benzene to give 1, 3-oxazepen derivatives 9-16 and with sodium azide in tetrahydrofuran