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 (LTADM) is a trustworthy technique for solving differential equations. Using the Mathematica 13.3 programme, the graphs of the approximate solutions and consecutive error are presented. Two applications are presented as examples of how the proposed technique can be utilised to obtain analytical or numerical solutions for certain kinds of Random Integro Differential Equations (RIDEs) in order to demonstrate its efficacy and potential.
Abstract
The aim of the current research is to prepare an integrated learning program based on mathematics standards for the next generation of the NYS and to investigate its impact on the development of the teaching performance of middle school mathematics teachers and the future thinking skills of their students. To achieve the objectives of the research, the researcher prepared a list of mathematics standards for the next generation, which were derived from a list of standards. He also prepared a list of the teaching competencies required for middle school mathematics teachers in light of the list of standards, as well as clarified the foundations of the training program and its objectives and the mathematical
... Show MoreThe research aims to identify small and medium enterprises in accounting thought in terms of definition and concept, and this international financial reporting standard for small and medium-sized enterprises (SMEs) in the theoretical aspect. As for the practical aspect, the small and medium-sized enterprises standard has been applied to the financial statements of the company in question, the preparation of the opening entry on the date of the transition, the requirements of measurement and the accounting disclosure on the date following the application of the standard, and the preparation of the company's financial statements and the accompanying explanations according to the standard of small and medium-sized enterprises. The r
... Show MoreIn this work, polynomials and the finite q-exponential operator are constructed. The operator is used to combine an operator proof of the generating function with its extension, Mehler's formula with its extension and Roger's formula for the polynomials . The generating function with its extension, Mehler's formula with its extension and Rogers formula for Al-Salam-Carlitz polynomials are deduced by giving special values to polynomials .
The phenomenon of informal building Spread recently in Iraqi residential areas, in general, and in Baghdad, in particular, due to the urgent housing need, on the one hand, and lack of commitment to building controls, on the other hand, to highlight the phenomenon of uncommitted building to controls and housing governing legislation in Iraq, leading to heterogeneity in both building densities and plot areas, and disorder in the urban fabric and urban escape of those areas. Research problem identified as the absence of a clear vision about the General aspects of the phenomenon of informal building in residential street scene, and the role of designed housing projects as a substitute for informal building in built residential areas. The des
... Show MoreNew 1,3-oxazol-5(4H)-one(3) was synthesized by cyclization of[(4-Methyl phenyl-carbonyl)amino]acetic acid (2). The starting materials were readily obtained by acylation of 2-amino acetic acid (Glycine) with 4-methyl phenyl chloride .Imidazole(4) was synthesized by reaction of compound (3) with hydrazine hydrate (99%). Compound (4) was isolated and characterized by 1HNMR , FTIR , uv-vis spectroscopy and elemental analysis (C.H.N). Compound (4) has been used as a ligand (L) to prepare a number of metal complexes with Cr(III), Mn(II), Co(II), Ni(II) , Cu(II) and Zn(II).
The prepared complexes were isolated and characterized by FTIR and Uv-vis spectroscopy elemental analysis (C.H.N), flame atomic absorption technique, as well as magnetic
Synthesis of new heterocyclic compounds containing four five-membered rings together was the main goal of this work. The new derivatives of [tetrakis (1,2,4-triazole /1,3,4-thiadiazole /1,3,4-oxadiazole][bis-(benzene-1,3,5-triyl)] dioxymethylene A7-A18 were synthesized by the reaction of [bis-(dimethyl 5-yl-isophthalate)] dioxymethylene compound A1 which was previously prepared from the reaction of 1,2-dibromomethan and dimethyl 5-hydroxyisophthalate, then treated with hydrazine hydrate to yield the corresponding acid hydrazide A2. In the next step, compound A2 was refluxed with 4-substituted isothiocyanate to give substituted thiosemicarbazides A3-A6. The treatment of the latter compounds in basic medium of 2M o
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This research is an attempt to explain the Qur’anic verses of the vision in the practical divine vision on the Day of Resurrection, and the legal texts narrated from the Companions regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace, regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace He was greeted with regard to vision, and he explained the two sayings of Ibn Abbas and Aisha on the same subject, including an area of conflict between them.
The research dealt with the design of the cost accounting system for the transport service and its Role in improving the efficiency of pricing decisions through the application of the cost system based on ABC activities. The main activities were defined and cost guides were to measure the cost of each service and to determine the cost of each service for the purpose of providing management with appropriate information and pricing decisions The problem of research in the lack of adoption by some public companies in the service sector on the cost accounting system to calculate the cost of service as well as the lack of identification of productive activities and service activities and therefore cannot make the appropriate decision t
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