This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

The goal of this study was to investigate the protein peroxidation role by measuring serum levels of advanced oxidation protein products (AOPP) in type 2 diabetic patients with or without retinopathy and comparing them to controls to see if circulating AOPP levels can be used as a detection biomarker for DR. And see which of the two widely used antidiabetic treatment groups had the most impact on this oxidative stress marker. The groups were divided into two subgroups: 1) 70 type 2 diabetic patients (36 male, 34 female), 35 with diabetic retinopathy (DR) and 35 with no evidence of DR, and 2) non-diabetic controls (11 male, 9 female) were chosen from Ibn AL-Haitham Hospital for Ophthalmology and a Specialized Center for Endocrinology and Dia

The degradation and mineralization of 4-chlorophenol (4-CP) by advanced oxidation processes (AOPs) was investigated in this work, using both of UV/H2O2 and photo-Fenton UV/H2O2/Fe+3 systems.The reaction was influenced by the input concentration of H2O2, the amount of the iron catalyst, the type of iron salt, the pH and the concentration of 4-CP. A colored solution of benzoquinon can be observed through the first 5 minutes of irradiation time for UV/H2O2 system when low concentration (0.01mol/L) of H2O2 was used. The colored solution of benzoquinon could also be observed through the first 5 minutes for the UV/H2O2/Fe+3 system at high
concentration (100ppm) of 4-CP. The results have shown that adding Fe+3 to the UV/H2O2 system enhanced

In the present work advanced oxidation process, photo-Fenton (UV/H2O2/Fe+2) system, for the treatment of wastewater contaminated with oil was investigated. The reaction was influenced by the input concentration of hydrogen peroxide H2O2, the initial amount of the iron catalyst Fe+2, pH, temperature and the concentration of oil in the wastewater. The removal efficiency for the system UV/ H2O2/Fe+2 at the optimal conditions and dosage (H2O2 = 400mg/L, Fe+2 = 40mg/L, pH=3, temperature =30o C) for 1000mg/L load was found to be 72%.

This research is carried out to investigate the behavior of self-compacting concrete (SCC) two-way slabs with central square opening under uniformly distributed loads. The experimental part of this research is based on casting and testing six SCC simply supported square slabs having the same dimentions and reinforcement. One of these slabs was cast without opening as a control slab. While, the other five slabs having opening ratios (O_R) of 2.78%, 6.25%, 11.11%, 17.36% and 25.00%. From the experimental results it is found that the maximum percentage decrease in cracking and ultimate uniform loads were 31.82% and 12.17% compared to control slab for opening ratios (O_R

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat

    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