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.
The aim of this research is to find a relation between self-protection and the social - ignorance of the univresity students. In applying the aims of the reaearch, the ressearcher has constructed two scales to measure
self - protection and the social - ignorance. After finding their validity and stability and their discriminative power, the researcher has applied them on a sample of (200) male and female. University students, who were selected randomly. The results of the research has arrived at finding a positive relation between self-protection and social - ignorance.
The researcher has recommended a concentration on the role of parents in raising their childern depending on themselves and making f
... Show MoreBackground: Trauma to the anterior teeth is a common injury in young children. Themaxillary incisors being the most affected. Although root fractures are rare, theydo occur and were previously and often considered hopeless and were extracted.The time between the injury and the initiation of treatment, level of the fractureline, and stage of root development are some criteria to be considered whenchoosing a treatment approach for a complicated tooth fracture. This case reportdescribes the management of a traumatized immature maxillary central incisorwith Elise class IV fracture with vertical oblique subgingival fracture of the root.Materials and method: Apexification was carried out using biodentine followed byremoval of the fracture
... Show MoreOscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.
This paper presents an analytical study on the serviceability of reinforced concrete gable roof beams with openings of different sizes, based on an experimental study which includes 13 concrete gable roof beams with openings under static loading. For deflection and crack widths under static loading at service stage, a developed unified calculation procedure has been submitted, which includes prismatic beams with one opening subjected to flexure concentrated force. The deflection has been calculated with two methods: the first method calculated deflections via relevant equations and the second was Direct Stiffness Method in which the beam is treated as a structural member with several segments constituting the portions with solid sec
... Show MoreIn recent years, there has been a rapid development in research on high performance ceramics for mechanical, electrical and medical industries. This development will be shown for alumina as a representative for oxide ceramics powders.
Dry–pressing forming technique was used to prepare different ceramic compacts for alumina grafted by polymethacrylate polymers. All Alumina compact were fired firstly at 1200 ◌ْ C, then
at 1600 ◌ْ C.
Mechanical strength was examined in different means, some
depends on compression and other depends on impact. Hardness was
also measured .The results obtained were compared with that of
Alumina compact prepared under the same condition from Alumina
especially made for pressing .
A potential alternative energy resource to meet energy demands is the vast amount of gas stored in hydrate reserves. However, major challenges in terms of exploration and production surround profitable and effective exploitation of these reserves. The measurement of acoustic velocity is a useful method for exploration of gas hydrate reserves and can be an efficient method to characterize the hydrate-bearing sediments. In this study, the compressional wave velocity (P-wave velocity) of consolidated sediments (Bentheimer) with and without tetrahydrofuran hydrate-bearing pore fillings were measured using the pulse transmission method. The study has found that the P-wave velocity of consolidated sediments increase with increasing hydrate format
... Show MoreBackground: The purpose of this study is to evaluate the care of multiple trauma victims with maxillofacial injuries in terms of epidemiological distributions, types of injuries, the related different modalities of surgical treatments delivered, and their complications. Materials and Methods: This prospective study was performed on 50 patients with multiple traumas including maxillofacial injuries, caused by different etiological factors, who were brought first to the surgical emergencies department of the Medical City then referred to the Maxillofacial unit in the Specialized Surgeries Hospital, Baghdad, Iraq, during the period from April 2007 to April 2008. Information was documented prospectively from the time of the emergency call to
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