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Novel Approximate Solutions for Nonlinear Initial and Boundary Value Problems
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This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving nonlinear initial and boundary value problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the proposed methods has been presented. Furthermore, the maximum error remainder () has been computed to prove the proposed methods' accuracy. The results convincingly prove that ECM and I-ECMs are effective and accurate in obtaining novel approximate solutions to the problems.

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Publication Date
Sun Sep 06 2009
Journal Name
Baghdad Science Journal
Extension of the Chebyshev Method of Quassi-Linear Parabolic P.D.E.S With Mixed Boundary Conditions
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The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

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Publication Date
Wed Jul 31 2019
Journal Name
Journal Of Engineering
Buckling Analysis of Laminated Composite Plate with Different Boundary Conditions using modified Fourier series
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Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g

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Publication Date
Thu Oct 28 2021
Journal Name
International Journal Of Research In Social Sciences And Humanities
Analysis of the Sustainable Value Chain and its Role in Reducing Quality Costs
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Contemporary developments in various sciences and the impact of technological changes require an integrated vision of the activities and work of the organization in Iraq in light of the high costs of products and their low quality compared to imported products of high quality and low cost, and the need to use modern cost techniques based on a clear and specific philosophy that contributes to increasing the efficiency and effectiveness of management In the business environment and how it can contribute to reducing product costs and being environmentally friendly at the same time, it is no secret that the main goal of most organizations is to maximize profitability and reduce costs to the minimum, but this matter is not achieved autom

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Publication Date
Fri Aug 01 2025
Journal Name
Journal Of Structural Design And Construction Practice
Exploring and Modeling Critical Success Factors of Value Management in Small Construction Projects
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Publication Date
Thu Sep 15 2022
Journal Name
Al-academy
Color diversity and its aesthetic value in the designs of children's fashion fabrics
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Fabric design is one of the arts in which humans participate functionally and aesthetically. Researching its design aspects is an important goal, especially after taking technical developments to cover many of its fields. Modern designs emphasize the importance of preparing designs and implementing them according to the child’s ability, inclinations and desires (mental, psychological and emotional). ), as the child is the real focus of the design idea, and the designer has paid most of his attention to the requirements and needs of this stage (childhood stage) because of its importance in the life of society, as he focused his attention on implementing designs that could achieve stability and stability in the child’s psyche through s

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Publication Date
Fri Mar 19 2021
Journal Name
Annals Of The Romanian Society For Cell Biology
Immunological Value of Periostin, Amphiregulin, IL-33 and sST2 Markers in Rhinosinusitis Patients
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Background: Rhinosinusitis is an inflammatory disorder that refers to inflammation of the nose and paranasal sinuses. Recent studies show that serum IL-33, periostin, ARGE and sST2 had the role in the pathogenesis of chronic rhinosinusitis as an easy, non-invasive and readily available (biomarker) for diagnosis of chronic rhinosinusitis. We tested for correlations of IL-33, periostin, ARGE and sST2 between acute and chronic rhinosinusitis in compare to healthy people. This study aimed to Measure serum levels of periostin, IL-33, sST2, and ARGE biomarkers in patients ARS and CRS. Materials and Methods: We collected serum of 30 patients with acute rhinosinusitis, 30 with chronic rhinosinusitis, and 30 controls to examine serum levels of IL-3

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Publication Date
Fri Feb 08 2019
Journal Name
Iraqi Journal Of Laser
Nonlinear Optical Properties of PMMA Composites Using Z-Scan Technique
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The nonlinear refractive index and the nonlinear absorption coefficient of unmodified and functional poly(methyl methacrylate) PMMA films were studied before and after the addition of the filler by the z-scan technique, using a Q-switched Nd:YAG laser at two wavelengths: 532 nm and 1064 nm, and at three input energies (13, 33 and 53) mJ. Both linear and nonlinear refractive indices and absorption coefficients of polymer films were studied by using UV-VIS spectrophotometer. The results show that the creation of functional PMMA from unmodified PMMA will increase the nonlinear optical properties in the functional PMMA/copper matrix more than in the unmodified PMMA/copper matrix. Hence, the functional PMMA appears promising as a useful third

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Publication Date
Tue Feb 05 2019
Journal Name
Journal Of The College Of Education For Women
African landlocked countries problems and outlets in the study and classification of geo-political
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Landlocked countries are displayed geopolitical new geo-political and intended to
countries that do not have sea views, a phenomenon present in four continents of the world
are: Africa, Europe, and Asia, and South America and the number arrived at the present time
to the (44) state the largest number of them in the continent it arrived in Africa (16) countries
in Asia (13) countries and Europe (13) In the State of South America two. This phenomenon
emerged due to the division of federations and empires and colonial treaties and others. But
the negative effects suffered by these countries may vary from one country to another, since
these countries in the continent of Europe, for example, is different from the same cou

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Publication Date
Mon Mar 07 2022
Journal Name
Journal Of Educational And Psychological Researches
Math Word Problems in Mathematics Books for the First Three Grads of the Basic Stage in Palestine (An analytical and Evaluative Study)
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This study aimed at revealing the degree of availability of standards of word problems in mathematics books for the first three grades of the basic stage in Palestine. For this purpose, the researcher prepared an analysis tool and a list of criteria consisting of two areas: linguistic formulation and mathematical content. Every area had seven items. The results of the study showed that the third-grade mathematics book has the highest degree of availability of the standards with 85.75%, and then came the second-grade mathematics book with 83.12%. Finally, the first-grade mathematics book came with 80.13%. In the light of the previous results, the researcher recommended to develop the language of word problems, to take into account their i

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Publication Date
Tue Jun 01 2021
Journal Name
Al-nahrain Journal Of Science
Medical Image Denoising Via Matrix Norm Minimization Problems
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This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given ma

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