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.

In this paper, we presented new types of Mc-function by using 𝜔-open and 𝑁-open sets some of them are weaker than Mc-function and some are stronger, which are 𝜔Mc-function, M𝜔c-function, 𝜔M𝜔c-function, 𝑁Mc-function, M𝑁c-function and 𝑁M𝑁c-function, also we submitted new kinds of continuous functions and compact functions and we illustrated the relationships between these types. The purpose of this paper is to expand the study of Mcfunction and to get results that we need to find the relationship with the types that have been introduced.

   The most likely fusion reaction to be practical is Deuterium and Helium-3 (𝐷−𝐻𝑒
 3 ), which is highly desirable because both Helium -3 and Deuterium are stable and the reaction produces a 14 𝑀𝑒𝑉 proton instead of a neutron and the proton can be shielded by magnetic fields. The strongly dependency of the basically hot plasma parameters such as reactivity, reaction rate, and energy for the emitted protons, upon the total cross section, make the problems for choosing the desirable formula for the cross section, the main goal for our present work.

    A theoretical calculation of the binding and excitation energies have been used at low – lying energies based on shell model and quantum theory. In this model, we evaluated the energies under assume Ni 28 56 30 as inert core with two nucleon extra, nucleons in the  2P3/2 ,  1f 5/2  and 2P1/2  configuration. Modified Surface Delta Interaction (MSDI) and Reid's Potential (RP) theory for two body matrix elements are evaluated by using a Matlab program to calculate the energies of experimental and Reid single particle energies. Our results of the theoretical calculation have been compared with the experimental results, which show no good agreement with the experiment but have a good agreement wit

New complexes of first series of transition metals with P-amino benzene dithiocarbamate of the general formula [M(PABdtc)2] and [ M(PABdtc)2(L)n] M=Fe( ІІ ),Co( ІІ ),Ni( ІІ ) ,Cu(ІІ) and Zn (ІІ). PABdtc = Paraamino benzene dithiocarbamate ,n=2 when  L= Py,É£-Pic,iso qunoline ,3,5lutidine  n=1when L=1,10-phenanthroline, en, 2,-2bipy.and the type(R)4N[Ni(PABdtc)3] R= methyl, ethyl are prepared. Physico chemical characterization of these complexes was applied  using magnetic susceptibility measurements, molar conductance , Infrared and electronic spectra, Metal content measurements, molar conductance indicate complexes of the type [M(PABdtc)2] and [M(PABdtc)2(L)n] are non-electrolyte

The reaction of ethylenediamine with [2,4,6-trihydroxyacetophenon] and KOH (Schiff Base) to gives the new tetradentate ligand 2-(1-{2-{1-2,6-Dihydroxy-4-methyl phenyl)ethyliden amino}- ethylimino}-ethyl-benzene- 1,2,5-triol [HCl]. This ligand was reacted with some metal ions (Cu(II), Co(II), Ni(II), Zn(II), and Cd(II)) in methanol with (1:1) metal :  ligand ratio to give a series of new complexes of the general formula [M(H4L)], where: M= Cu(11), Co(II), Ni(II), Zn(II), and Cd(II).      All compounds were characterized by spectroscopic methods [I.R, U.V.-Vis, C.H.N., analysis H.P.L.C, atomic absorption, magnetic susceptibility, (EI-mass for the ligand)], and microanalysis along with conductivity measurements

     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

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

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

We introduced the nomenclature of orthogonal G -m-derivations and orthogonal generalized G -m-derivations in semi-prime G -near-rings and provide a few essentials and enough provision for generalized G -n-derivations in semi-prime G -near-rings by orthogonal.