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The operational matrices for Elliptic Partial Differential Equations with mixed boundary conditions
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Abstract<p>The purpose of this research is to implement the orthogonal polynomials associated with operational matrices to get the approximate solutions for solving two-dimensional elliptic partial differential equations (E-PDEs) with mixed boundary conditions. The orthogonal polynomials are based on the Standard polynomial (<italic>x<sup>i</sup> </italic>), Legendre, Chebyshev, Bernoulli, Boubaker, and Genocchi polynomials. This study focuses on constructing quick and precise analytic approximations using a simple, elegant, and potent technique based on an orthogonal polynomial representation of the solution as a double power series. Consequently, a linear partial differential equation is transformed into a linear algebraic system which is solved by the Mathematica®12. Approximate solutions can be found if the answers are polynomials in and of itself. Three applications involving well-known linear problems Laplace, Poisson, and Helmholtz equations have been solved by using the proposed methods, and a comparison of the approaches has been provided. Furthermore, the computation of the error norm <italic>L<sub>∞</sub> </italic> has been done to show the accuracy of the suggested approaches. The results clearly demonstrate how precise, efficient, and dependable the proposed methods are in obtaining rough solutions to the problem. Bernoulli was one of the best methods in most examples.</p>
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Publication Date
Wed Dec 22 2021
Journal Name
Iraqi Journal Of Agricultural Sciences
THE EFFECIENCY OF ENTERIC LACTOBACILLUS IN PREVENTING HEMORRHAGIC COLITIS AND BLOCKING SHIGA TOXINS PRODUCTIONS IN RATS MODELS INFECTED WITH ENTEROHEMORRHAGIC ESCHERICHIA COLI (EHEC)
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The objective of this study was to investigate the prophylactic roles of human enteric derived Lactobacillus plantarum L1 (Ll) and Lactobacillus paracasei L2 (L2), on EHEC O157:H7 infection in rodent models (In vivo). The Lactobacillus suspensions (L1 and L2) were individually and orally administered to experimental rats at a daily two consecutives of 100 μl (108 CFU/ ml/rat) for up to two weeks.  Thereafter, on the 8th day of experiment rats were orally challenged with one dose infection of EHEC (105 CFU/ml/rat). Animals mortality and illness symptoms have been monitored. There was no fatal EHEC infection in rats that had been pre‑colonized with the Lactobacillus strains, while most of EHEC infected rats were died (90%).  The

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Publication Date
Wed Jul 22 2026
Journal Name
Journal Of Baghdad College Of Dentistry
The effect of autologous bone marrow-derived stem cells with estimation of molecular events on tooth socket healing in diabetic rabbits (Immunohistochemical study)
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Background: Healing of a tooth extraction socket is a complex process involving tissue repair and regeneration. It involves chemotaxis of appropriate cells into the wound, Transformation of undifferentiated mesenchymal cells to osteoprogenitor cells, proliferation and differentiation of committed bone forming cells, extracellular matrix synthesis, mineralization of osteoid, maturation and remodeling of bone. These cellular events are precisely controlled and regulated by specific signaling molecules. Some of these like transforming growth factor beta (TGF-?), vascular endothelial growth factor (VEGF), bone morphogenetic proteins (BMP) and insulin like growth factors (IGF) are well conserved proteins involved in the initial response to injur

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Publication Date
Fri Jan 01 2010
Journal Name
مجلة الانبار للعلوم الزراعية
Effect of injected with gibberllic acid ga3 and addition of vitamin d3 to the diet on some productive parameters of aged laying hens
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This experiment was conducted to examine the effects of injected gibberellic acid GA3 in subcutaneous of hens neck and supplemental vitamin D3 to control basal diet on productive performance and egg shell thickness ,relative weight of egg shell of aged laying hens. Two hundred and seventy Lohmann Brown laying hens at 73 weeks of age were randomly assigned to three treatments groups. Each treatment consist of three replicates (30 hens / replicate). The treatments were : T1 control were injected subcutaneous with 0.2 ml / kg of body weight of ethanol: sesame oil solution, T2 and T3 were injected subcutaneous with 0.2 ml / kg of body weight of ethanol: sesame oil solution which contained 400 μg GA3/ kg of body weight /week during 8 weeks (tre

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Publication Date
Sun Dec 01 2019
Journal Name
Saudi Medical Journal
The diagnostic power of circulating micro ribonucleic acid 34a in combination with cancer antigen 15-3 as a potential biomarker of breast cancer
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Publication Date
Mon Jun 12 2023
Journal Name
Agbioforum
Assessing the Impacts of Consumer Awareness on Consumer Purchase Intention with Moderating Role of Product Label: Evidence from Consumers of Iraqi Manufacturing Firms
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Publication Date
Sat Sep 01 2007
Journal Name
Al-khwarizmi Engineering Journal
Free Convective Heat Transfer with Different Sections Lengths Placed at the Exit of a Vertical Circular Tube subjected to a Constant Heat Flux
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A free convective heat transfer from the inside surface of a uniformly heated vertical circular tube has been experimentally investigated under a constant wall heat flux boundary condition for laminar air flow in the ranges of RaL from 6.9108 to 5109. The effect of the different sections (restrictions) lengths placed at the exit of the heated tube on the surface temperature distribution, the local and average heat transfer coefficients were examined. The experimental apparatus consists of aluminum circular tube with 900 mm length and 30 mm inside diameter (L/D=30). The exit sections (restrictions) were included circular tubes having the same inside diameter as the heated tube but with different lengths of

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Publication Date
Wed Jul 22 2026
Journal Name
Journal Of Baghdad College Of Dentistry
The Salivary Inflammatory Biomarkers (Interleukin-6, C - reactive protein) in Relation with Caries-Experience among a Group of 12 Year Old Obese Boys
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Background: Obesity and dental caries are multifactorial diseases related to poor eating habits and show a close relationship with the sociodemographic characteristics of individuals presenting these diseases. This research aimed to investigate the severity of dental caries among group of obese boys aged 12 year in relation to salivary interleukin-6 (IL-6) and C-reactive protein (CRP) of unstimulated whole saliva in comparison with normal weighted boys of the same age. Materials and Methods: The study group included 40 obese boys, with an age of 12 year. The control group included 40 normal weighted boys of the same age. The total sample involved for nutritional status assessment using Body Mass Index specific for age and gender according t

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Publication Date
Fri Jan 01 2016
Journal Name
Iraqi Journal Of Agricultural Sciences
Effect of extraction of sheep manure with warm water on the growth and nutrients content of tomato plants under cultivation of plastic houses
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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Relationship between Uric Acid Concentration and Some of Plasma Lipids in Patients with C. V. Disease in General Hospital of Al-Nasseriya
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         Cardiovascular disorders  are  refer to the class of diseases that involve the heart or blood vessels (arteries and veins). While the term technically refers to any disease that affects the cardiovascular system. Cholesterol is classified as a sterol (a contraction of steroid and

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Publication Date
Mon Nov 03 2025
Journal Name
Frontiers In Dental Medicine
Effects of cavity depth (moderate vs. deep with pulp exposure) on the release of prostaglandin E2 and nitric oxide in rat mandibular incisors
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Background/objectives: Inflammatory mediators such as prostaglandin E2 (PGE2) and nitric oxide (NO) are key indicators of pulp response to mechanical trauma. However, the influence of cavity depth on their release dynamics remains unclear. This study aimed to evaluate the effects of different cavity depths—moderate (without pulp exposure) and deep (with pulp exposure)—on the release of PGE2 and NO in the pulp tissue of rat mandibular incisors at two time intervals (3 and 9 h).Methods: In total, 40 male Wistar rats were divided into two main groups (n = 20) based on cavity depth. A split-mouth design was used, with cavities of different depths prepared on the left mandibular incisors, leaving the right incisors without cavities as

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