This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

   Nonlinear regression models are important tools for solving optimization problems. As traditional techniques would fail to reach satisfactory solutions for the parameter estimation problem.  Hence, in this paper, the BAT algorithm  to estimate the parameters of  Nonlinear Regression models is used . The simulation study is considered to investigate the performance of the proposed algorithm with the maximum likelihood (MLE) and Least square (LS) methods. The results show that the Bat algorithm provides accurate estimation and it is satisfactory for the parameter estimation of the nonlinear regression models than MLE and LS methods depend on Mean Square error.

It is generally accepted that there are two spectrophotometric techniques for quantifying ceftazidime (CFT) in bulk medications and pharmaceutical formulations.  The methods  are described as simple, sensitive, selective, accurate and efficient techniques. The first method used an alkaline medium to convert ceftazidime to its diazonium salt, which is then combined with the 1-Naphthol (1-NPT) and 2-Naphthol (2-NPT) reagents. The azo dye that was produced brown  and red in color with absorption intensities of ƛmax 585 and 545nm respectively. Beer's law was followed in terms of concentration ranging from  (3-40) µg .ml^-1 For (CFT-1-NPT) and (CFT-2-NPT), the detection limits were 1.0096 and 0.8017 µg.ml^-1, respec

In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica^®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

Four different spectrophotometric methods are used in this study for the determination of Sulfamethoxazole and sulfanilamide drugs in pharmaceutical compounds, synthetic samples, and in their pure forms. The work comprises four chapters which are shown in the following: Chapter One: Includes a brief for Ultraviolet-Visible (UV-VIS) Absorption spectroscopy, antibacterial drugs and sulfonamides with some methods for their determination. The chapter lists two methods for optimization; univariate method and multivariate method. The later includes different types, two of these were mentioned; simplex method and design of experiment method. Chapter Two: Includes reaction of the two studied drugs with sodium nitrite and hydrochloric acid for diazo

In this research, non-thermal plasma system of argon gas is designed to work at normal atmospheric pressure and suitable for work in medical and biotechnological applications. This technique is applied in the treatment of the Staphylococcus epidermidis bacteria and show the role of the flow rate of Argon gas on the killing rate of bacteria, and it obtained a 100 % killing rate during the time of 5 minutes at the flow Argon gas of 5 liters/ min.

Oilwell cementing operations are crucial for drilling and completion, preserving the well's productive life. However, weak and permeable formations pose a high risk of cement slurry loss, leading to failure. Lightweight cement, like foamed cement, is used to avoid these difficulties. This study is focused on creating a range of foamed slurry densities and examining the effect of gas concentration on their rheological properties. The foaming agent and foam stabilizer are tested, and the optimal concentration is determined to be 2% and 0.12%, respectively, by the weight of the cement.

Furthermore, the construction of samples of foam cement with different densities (0.8, 1.0, 1.2, 1.4, and 1.6) g/cc is performed to f