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 the accuracy and efficiency of all methods, highlighting their superiority over the classical ADM.
One of the most common procedures in oral surgery is the removal of impacted mandibular third molars, often followed by pain, swelling, alveolitis, and trismus. Purpose. To compare the outcomes of the intrasocket application of 1% hyaluronic acid oral gel (HA) and advanced platelet-rich fibrin (A-PRF) on the expected postoperative complications, pain, swelling, and trismus follow the surgical extraction of the impacted mandibular third molar. Material and Methods. A randomized controlled trial was conducted at the Oral and Maxillofacial Surgery Unit, Dental Teaching Hospital. Healthy patients who required surgical removal of the impacted mandibular third molar were divided randomly into three groups. The extraction site of the group
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This research deals with the two item namely, the monetary policy central Bank of Iraqi and money supply . that contribute in up the problem of the paper that is concerned with the fact that to what extent the effectiveness of monetary policy conducted by the central Bank of Iraqi is valid in controlling money supply as well as the possibility of applying it in practical environment restricted to the scope of financial in stitiutions particularly in research population represented by central Bank of Iraqi .
For the purpose of a practical contribution for monetary and financial institutions . To achieve this , A hypothesis has been carried out and it suggested that the mon
... Show MoreBack ground: This in vitro study was carried out to investigate the effect of post space regions (coronal, middle and apical), Time and the mode of polymerization (dual, self-cured) of the cements used on the bond strength between translucent fiber post and root dentin by using push-out test. Materials and Methods: Forty eight extracted mandibular first premolars (single root) were instrumented with ProTaper Universal system files (for hand use) and obturated with gutta percha for ProTaper and AH26® root canal sealer following the manufacturer instructions, after 24 hours post space was prepared using FRC postec® plus drills no.3 creating 8 mm depth post space. The prepared samples were randomly divided into two main groups (24 samples ea
... Show MoreThis work concentrates on the effect of a flex-skin trailing edge flap on the aerodynamic characteristics of SD7037 airfoil at low Reynolds numbers, in the range of 2^10 to 5^10 using computational methods. The study used a range of angle of attack (AOA) associated with the take-off phase and different flap angles. The numerical model was set up in Siemens STAR-CCM+ package using the κ-ω shear stress transport turbulence model and the (γ-Reθ) transition model which ensured the approximate solution of Navier-Stokes equations. The verification of the computational solution was done by the comparison with the available experimental data of the plain flap, and it was discovered that the results matched pretty well at lower AoAs. Results in
... Show MoreA series of new compounds including p-bromo methyl pheno acetate [2]. N-( aminocarbonyl)–p-bromo pheno acetamide [3] , N-( aminothioyl) -p-bromo phenoacetyl amide [4], N-[4-(p-di phenyl)-1,3-oxazol-2-yl]-p-bromopheno acetamide [5],N-[4-p-di phenyl]-1,3-thiazol-2-yl-p-bromo phenoacet amide [6], p-bromopheno acetic acid hydrazide [7] , 1-N-(p-bromo pheno acetyl)-1,2-dihydro-pyridazin-3,6- dione [8], 1-N-(p-bromo pheno acetyl)-1,2-dihydro-phthalazin-3,8- dione[ 9], 1-(p-bromo pheno acetyl)-3-methylpyrazol-5-one [10] and 1-(p-bromo phenol acetyl)- 3,5-dimethyl pyrazole [11] have been synthesized. The prepared compounds were characterized by m.p.,FT-IR and 1H-NMR spectroscopy. Also ,the biological activity was evaluated .
In this research prepare membranes pure silicon carbide (SiC) as well as gas Alloy (ammonia) and using a laser was leaked membrane of glass flooring. To Drasesh optical properties of membranes prepared depending on the technique (Swanepoel) and Adhrt results obtained in general increased permeability pure silicon membranes
A new mixed ligand complexes have been prepared between 8- hydroxy quinoline and o-hydroxybenzylidene-1-phenyl-2,3-dimethyl-4-amino-3-pyrazolin-5-on with Mn(II),Fe(II),Co(II),Ni(II) and Cu(II) ions . the prepared complexes were isolated and characterized by (FT-IR)and (UV-Vis) spectroscopy. Elemental analysis (C.H.N) Flame atomic absorption technique . in addition to magnetic susceptibility and conductivity measurement.
The usual methods of distance determination in Astronomy parallax and Spectroscopic with Expansion Methods are seldom applicable to Nebulae. In this work determination of the distances to individual Nebulae are calculated and discussed. The distances of Nebulae to the Earth are calculated. The accuracy of the distance is tested by using Aladin sky Atlas, and comparing Nebulae properties were derived from these distance made with statistical distance determination. The results showed that angular Expansions may occur in a part of the nebulae that is moving at a velocity different than the observed velocity. Also the results of the comparison of our spectroscopic distances with the trig
Some metal ions (Mn+2, Co+2, Ni+2, Cu+2, Zn+2, Cd+2 and Hg+2) complexes of quinaldic acid (QuinH) and α-picoline (α-Pic) have been synthesized and characterized on the basis of their , FTIR, (U.V-Vis) spectroscopy, conductivity measurements, magnetic susceptibility and atomic absorption. From the results obtained the following general formula has suggested for the prepared complexes [M(Quin)2( α-Pic)2].XH2O where M+2 = (Mn, Co, Ni, Cu, Zn, Cd and Hg), X = 2, X = zero for (Co+2 and Hg+2) complexes, (Quin-) = quinaldate ion, (α-Pic) = α-picoline. The results showed that the deprotonated ligand (QuinH) by using (KOH) coordinated to metal ions as bidentate ligand through the oxygen atom of the carboxylate group (-COO-) and the nitrogen ato
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