Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector.  Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art a

Background: The prediction of changes in the mandibular third molar position and eruption is an important clinical concern because third molar retention may be beneficial for orthodontic anchorage. The aims of this study were to assess the mandibular third molar position by using medical CT scan and lateral reconstructed radiograph and evaluate gender differences. Materials and Methods: The sample of present study consisted of 39 patients (18 males and 21 females) with age range 11-15 years who were attending at Al-Suwayra General Hospital/ the Computerized Tomography department. The distance from anterior edge of ramus to distal surface of permanent mandibular second molar and mesio-distal width of developing mandibular third molar were

The -multiple mixing ratios of γ-transitions from levels of populated in the are calculated in the present work by using the a2-ratio methods. We used the experimental coefficient (a2) for two γ-transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions. This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa. The weight average of the -values calcu

This study introduced the effect of using magnetic abrasive finishing method (MAF) for finishing flat surfaces. The results of experiment allow considering the MAF method as a perspective for finishing flat surfaces, forming optimum physical mechanical properties of surfaces layer, removing the defective layers and decreasing the height of micro irregularities. Study the characteristics which permit judgment parameters of surface quality after MAF method then comparative with grinding

Background/Objectives: The purpose of this study was to classify Alzheimer’s disease (AD) patients from Normal Control (NC) patients using Magnetic Resonance Imaging (MRI). Methods/Statistical analysis: The performance evolution is carried out for 346 MR images from Alzheimer's Neuroimaging Initiative (ADNI) dataset. The classifier Deep Belief Network (DBN) is used for the function of classification. The network is trained using a sample training set, and the weights produced are then used to check the system's recognition capability. Findings: As a result, this paper presented a novel method of automated classification system for AD determination. The suggested method offers good performance of the experiments carried out show that the

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

The main objective of this study is to experimentally investigate the effect of the CMC polymeric drag reducer on the pressure drop occurred along the annulus of the wellbore in drilling operation and investigate the optimum polymer concentration that give the minimum pressure drop. A flow loop was designed for this purpose consist from 14 m long with transparent test section and differential pressure transmitter that allows to sense and measure the pressure losses along the test section. The results from the experimental work show that increasing in polymer concentration help to reduce the pressure drop in annulus and the optimum polymer concentration with the maximum drag reducing is 0.8 kg/m³. Also increasing in flow rate a