This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

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Elzaki Transform Adomian decomposition technique (ETADM), which an elegant combine, has been employed in this work to solve non-linear Riccati matrix differential equations. Solutions are presented to demonstrate the relevance of the current approach. With the use of figures, the results of the proposed strategy are displayed and evaluated. It is demonstrated that the suggested approach is effective, dependable, and simple to apply to a range of related scientific and technical problems.

Introduction The Hybrid Gamma Camera (HGC) is being developed to enhance the localisation of radiopharmaceutical uptake in targeted tissues during surgical procedures such as sentinel lymph node (SLN) biopsy. Purpose To assess the capability of the HGC, a lymph-node-contrast (LNC) phantom was constructed for an evaluative study simulating medical scenarios of varying radioactivity concentration and SLN size. Materials and methods The phantom was constructed using two methyl methacrylate PMMA plates (8 mm thick). The SLNs were simulated by drilling circular wells of diameters ranging between 10 mm and 2.5 mm (16 wells in total) in one plate. These simulated SLNs were placed underneath scattering material with thicknesses ranging between 5 mm

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for

This study reports on natural convection heat transfer in a square enclosure of length (L=20 cm) with a saturated porous medium (solid glass beads) having same fluid (air) at lower horizontal layer and free air fill in the rest of the cavity's space. The experimental work has been performed under the effects of heating from bottom by constant heat flux q=150,300,450,600 W/m2 for four porous layers thickness Hp (2.5,5,7.5,1) cm and three heaters length δ(20,14,7) cm. The top enclosure wall was good insulated and the two side walls were symmetrically cooled at constant temperature. Four layers of porous media with small porosity, Rayleigh number range (60.354 - 241.41) and (Da) 3.025x10-8 has been investigated. The obtained data of temperatu

     The bubble columns are widely used as a two or three phase reactor in industrial chemical process such as absorption, biochemical reactions, coal liquefaction, etc. To design such a column, two main parameters should be taken in consideration, the gas hold-up (), and the liquid phase mass transfer coefficient K_La. The study includes the effect of gas velocity and the addition of alcohols on gas hold-up and mass transfer coefficient in bubble column with draught tube when the length of the column is 1.5m and the ratio of the draught tube diameter to the column diameter equals 0.5 and the air dispersion into the base of the draught tube using a multi hole tuyere is equivalent to a diameter of 0.15 mm and

This paper deals  with constructing mixed probability distribution  from exponential with scale parameter (β) and also Gamma distribution with (2,β), and the mixed proportions are (  .first of all, the probability density function (p.d.f) and also cumulative distribution function (c.d.f) and also the reliability function are obtained. The parameters of mixed distribution, ( ,β)  are estimated by three different methods, which are  maximum likelihood, and  Moments method,as well proposed method (Differential Least Square Method)(DLSM).The comparison is done using simulation procedure, and all the results are explained in tables.

The hydrological process has a dynamic nature characterised by randomness and complex phenomena. The application of machine learning (ML) models in forecasting river flow has grown rapidly. This is owing to their capacity to simulate the complex phenomena associated with hydrological and environmental processes. Four different ML models were developed for river flow forecasting located in semiarid region, Iraq. The effectiveness of data division influence on the ML models process was investigated. Three data division modeling scenarios were inspected including 70%–30%, 80%–20, and 90%–10%. Several statistical indicators are computed to verify the performance of the models. The results revealed the potential of the hybridized s