In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.
The current study examined the use of Sansevieria plant leaves extract as an environmentally acceptable, inexpensive, and safe green approach for creating titanium dioxide nanoparticles (NPs). Batch studies have been used to test the particles' capacity to bind to the azo dye congo red (CR), which has been adsorbed from its aqueous solution. The effects of many factors, including the weight of TiO2 NPs, the contact duration to reach equilibrium, the concentration of CR, temperature, and pH, have been investigated. Both the Freundlich and Langmuir models were used to analyze experimental results. According to the high values of the Freundlich model's correlation coefficient R2, it is discovered that th
... Show MoreThis work investigates the structural, optical, and surface properties of ZnO thin films prepared by sol-gel method. The effect on waveguide sensor was examined at different irradiation durations of alpha particles. The X-ray diffraction (XRD) measurements revealed that the crystalline phase of ZnO thin films does not change after irradiation and showed a hexagonal structure of wurtzite type with an orientation toward (002). Moreover, ZnO thin films absorbance was increased with increasing irradiation time, whereas the transmittance was decreased. Additionally, increasing the irradiation time of alpha particles caused an increase in the extinction coefficient and the imaginary part, while the optical energy gap of the ZnO samples w
... Show MoreMaximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.
A Modified version of the Generlized standard addition method ( GSAM) was developed. This modified version was used for the quantitative determination of arginine (Arg) and glycine ( Gly) in arginine acetyl salicylate – glycine complex . According to this method two linear equations were solved to obtain the amounts of (Arg) and (Gly). The first equation was obtained by spectrophotometic measurement of the total absorbance of (Arg) and (Gly) colored complex with ninhydrin . The second equation was obtained by measuring the total acid consumed by total amino groups of (Arg) and ( Gly). The titration was carried out in non- aqueous media using perchloric acid in glacial acetic acid as a titrant. The developed metho
... Show MoreThis paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.
This paper concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.
This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.
This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.