The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the converge

In this study, a new Azo ligand 5-((2-(1H-indol-2-yl)ethyl)diazinyl)-2-aminophenol is synthesized from a reaction of Tryptamine with 2-aminophenol. The ligand and their metal ion complexes Ni(II), Pd(II) , Pt(IV) and Au(III) have been synthesized and characterized by various analytical techniques, including elemental microanalysis, metal content, chloride-containing, measurement of electrical conductivity, magnetic susceptibility, ¹H and ¹³C-NMR, FT-IR, UV-Vis, mass spectra (MS), and thermal analysis (TGA and DSC) curves. The DCS curve was used to calculate the thermodynamic parameters ΔH, ΔS, and ΔG. The characterization results promote the metal complexes of azo ligand structures. The results indicate that the

Storage tanks condition and integrity is maintained by joint application of coating and cathodic protection. Iraq southern region rich in oil and petroleum product refineries need and use plenty of aboveground storage tanks. Iraq went through conflicts over the past thirty five years resulting in holding the oil industry infrastructure behind regarding maintenance and modernization. The primary concern in this work is the design and implementation of cathodic protection systems for the aboveground storage tanks farm in the oil industry.

Storage tank external base area and tank internal surface area are to be protected against corrosion using impressed current and sacrificial anode cathodic protection systems. Int

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.

The presented work includes the Homotopy Transforms of Analysis Method (HTAM). By this method, the approximate solution of nonlinear Navier- Stokes equations of fractional order derivative was obtained.  The Caputo's derivative was used in the proposed method. The desired solution was calculated by using the convergent power series to the components. The obtained results are demonstrated by comparison with the results of Adomain decomposition method, Homotopy Analysis method and exact solution, as explained in examples (4.1) and (4.2). The comparison shows that the used method is powerful and efficient.

Binuclear copper, nickel, cobalt, manganese and mercury complexes of the Schiff base H2L (C40H28N2O4) obtained by condensation of 2-benzoyl benzoic acid with benzidine.  The Schiff base and their complexes have been subjected to[ FT-IR, elemental analysis ,UV-Vis, 1H and 13C NMR ] spectral studies, molar conductivity, magnetic moment and HPLC measurements. All the complexes showed tetrahedral geometries with the general structure [M2(L)2].  Generality of the synthesized components offer antibacterial efficiency to (Staphylococcu saureus), (Escherichia coli),(Bacillus subtilis) and(Pseudomonas aeruginosa).
 

Multi-document summarization is an optimization problem demanding optimization of more than one objective function simultaneously. The proposed work regards balancing of the two significant objectives: content coverage and diversity when generating summaries from a collection of text documents.

     Any automatic text summarization system has the challenge of producing high quality summary. Despite the existing efforts on designing and evaluating the performance of many text summarization techniques, their formulations lack the introduction of any model that can give an explicit representation of – coverage and diversity – the two contradictory semantics of any summary. In this work, the design of

Automatic document summarization technology is evolving and may offer a solution to the problem of information overload. Multi-document summarization is an optimization problem demanding optimizing more than one objective function concurrently. The proposed work considers a balance of two significant objectives: content coverage and diversity while generating a summary from a collection of text documents. Despite the large efforts introduced from several researchers for designing and evaluating performance of many text summarization techniques, their formulations lack the introduction of any model that can give an explicit representation of – coverage and diversity – the two contradictory semantics of any summary. The design of gener

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve