In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

This research focuses on improvement of the corrosion behaviour of commercial pure titanium (Ti) grade II when exposed to Hank’s solution through different surface treatments. The disc shape of titanium samples were constructed to be divided according to their surface treatment. The first experimental group the Ti sample was exposed to computer numerical control (CNC) fiber laser machine. Whereas, the other experimental group the Ti sample was only coated with Polyetherketon keton (PEKK) by using carbon dioxide (CO2) laser technique while the last experimental group the Ti sample was treated with CNC fiber laser followed by PEKK coating by using CO2 laser technique. All were compared with the untreated control group. The electrochemical a

The electrochemical behavior of Al-17%Si alloy is investigated in 3.5wt% NaCl solution. Many alloys with addition of the different wt% magnesium metal of  1wt%, 2%, 3wt% ,4.5wt% ,and 9wt% were prepared by gravity die casting . The microstructures of prepared alloys were examined by optical and SEM microscopes. Corrosion behavior was investigated by using potentiostat instrument under static potentials test and corrosion current was recorded to determine corrosion resistance of all prepared samples. It was found that the addition of Mg metal improves the corrosion resistance of Al-17%Si alloy in 3.5%NaCl solution. The alloy containing 1%Mg shows less corrosion rate than the others while the alloys containing 4.5%Mg, 9%Mg content have

The majority of real-world problems involve not only finding the optimal solution, but also this solution must satisfy one or more constraints. Differential evolution (DE) algorithm with constraints handling has been proposed to solve one of the most fundamental problems in cellular network design. This proposed method has been applied to solve the radio network planning (RNP) in the forthcoming 5G Long Term Evolution (5G LTE) wireless cellular network, that satisfies both deployment cost and energy savings by reducing the number of deployed micro base stations (BSs) in an area of interest. Practically, this has been implemented using constrained strategy that must guarantee good coverage for the users as well. Three differential evolution

The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex

The pandemic SARS-CoV-2 is highly transmittable with its proliferation among nations. This study aims to design and exploring the efficacy of novel nirmatrelvir derivatives as SARS entry inhibitors by adapting a molecular modeling approach combined with theoretical design. The study focuses on the preparation of these derivatives and understanding their effectiveness, with a special focus on their binding affinity to the S protein, which is pivotal for the virus’s access to the host cell. Considering molecular docking aspects in the scope of a study on nirmatrelvir derivatives and S protein, dynamics simulations with 25 nanoseconds of their binding are explored. The study shows that these derivatives might work as effective antivi

A theoretical analysis studied was performed to study the opacity broadening of spectral lines emitted from aluminum plasma produced by Nd-YLF laser. The plasma density was in the range 1028-1026 )) m-3 with length of plasma about ?300) m) , the opacity was studied as function of plasma density & principle quantum number. The results show that the opacity broadening increases as plasma density increases & decreases with the spacing between energy levels of emission spectral line.

Abstract: The aim of the current research is to identify (the relationship between deep understanding skills and mathematical modeling among fifth grade students) the research sample consisted of (411) male and female students of the fifth grade of biology distributed over the General Directorates of Education in Baghdad / Al-Rusafa / 2 / and Al-Karkh / 1 /, and two research tools were built: 1- A test of deep understanding skills, consisting of (20) test items and a scale for two skills. 2- The second test consists of (24) test items distributed among (18) essay items and (6) objective items. The psychometric properties of validity, stability, discriminatory strength, and effectiveness of alternatives were verified for the two tests fo