This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm th

Social Aspects in the Kingdom of Mali Through Ibn Battuta's book Tuhfat   Alnuddar  in  Garaeb  Al Amsar  Wa  Ajaeb  Al  Asfar 

    In this study, the dung beetles Aphodius (Bodilus) ictericus (Laicharting, 1781) and Aphodius (Planolinellus) vittatus Say, 1825 which belongs to the family of Aphodiidae (Order: Coleoptera) are redscribed here as to being found for the first time in Iraq.

    The specimens were collected from different regions in the middle of Iraq; the main diagnostic characters and some morphological features of males were drawn and pictured.

This paper deals with the preparation and investigation studies of a number of new complexes of Cu(II) , Zn(II) , Hg(II) , Ag(I) , Pt(IV) and Pb(II).The complexes were formed by the reaction of the mentioned metal ions with the ligand which is derived from oxadiazole (OXB), 2- (2-butyl) thio-5- phenyl – 1,3,4 – oxadiazole in the mole ratio (1:1) , (1:2) and (1:3) (metal to ligand ).The result complexes having general formulae :M(OXB)Cl2] [M(OXB)X2]H2O [ M= Cu(II) , Zn(II) M= Hg(II) , Pb(II) [M(OXB)2 X2] X= Cl– M = Cu (II), Zn (II), Hg (II), Pb (II) X= Cl–, NO3-, CH3COO- [Pt(OXB)3]Cl4 [Ag(OXB)]NO32-(2-??????? ) ???? -5- ???

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.

A number of ehemical ion materials were used as an absorber against solar energy. These materials were selected according to their absorption spectra in the wavelength range 300-800nm where the solar spectrum is coventrated. A solar olleetorw^esigd and The ability of each material inside the collector for absorbing the solar radiation was examined by a converter parameter “R”.According to the “R” parameter, the cohaltous and copperic ions material seems to be of higher capability for absorbing solar energy than the other materials.All the results were analyzed by means of a least-squared fitting program.

ABSTRACT Planetary Nebulae (PN) distances represent the fundamental parameter for the determination the physical properties of the central star of PN. In this paper the distances scale to Planetary Nebulae in the Galactic bulge were calculated re- lated to previous distances scales. The proposed distance scale was done by recalibrated the previous distance scale technique CKS/D82. This scale limited for nearby PN (D ≤ 3.5 kpc), so the surface fluxes less than other distance scales. With these criteria the results showed that the proposed distance scale is more accurate than other scales related to the observations for adopted sample of PN distances, also the limit of ionized radius (Rio) for all both optically thick and optically thin in

The partial level density PLD of pre-equilibrium reactions that are described by Ericson’s formula has been studied using different formulae of single particle level density . The parameter  was used from the equidistant spacing model (ESM) model and the non- equidistant spacing model (non-ESM) and another formula of  are derived from the relation between  and level density parameter . The formulae used to derive  are the Roher formula, Egidy formula, Yukawa formula, and Thomas –Fermi formula. The partial level density results that depend on  from the Thomas-Fermi formula show a good agreement with the experimental data.