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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 Jun 03 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Immunohistochemical expression of MMP9, as a marker of local invasion in Hodgkin’s and Non-Hodgkin’s lymphoma of the head and neck region
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Background: Malignant lymphoma is the generic term given to tumors of the lymphoid system and specifically of lymphocytes and their precursor cells, While all lymphomas are malignant neoplasms, there is a wide spectrum of clinical behavior, with some following an indolent clinical course and others behaving in an aggressive manner (will causing death in a short time frame if left untreated). The metastatic process involves intravasation and extravasation of tumor cells, followed by reimplantation of tumor cells, formation of a new tumor stoma, Degradation of the extracellular matrix and components of the basement membrane by proteases facilitates the detachment of tumor cells, their crossing of tissue boundaries, and invasion into adjacent

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Publication Date
Tue Dec 15 2020
Journal Name
Al-academy
Simulation As One Of The Tools Of Visual Thinking And Its Effect On Developing Drawing And Design Skills To Produce Innovative Artworks: عائشة عبد الجبار العيسى
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The research emphasizes importance of preliminary drawings in design of any product. Therefore, using of simulation as tools for visual thinking in developing drawing and design skills. So that practice of drawing by hand, considering shape of ideas in first stage of visualizations, and practice of its techniques and continuous training.
Hence, the research problem arose with the role of simulation method for developing preliminary sketches in the sample of students of the Product Design Department at the College of Design and Art, PNU, as it is important tool for visual thinking that helps the designer in designing and producing innovative artistic works.
Therefore, the research axes, a number of findings and recommendations were

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Publication Date
Fri Nov 07 2014
Journal Name
Chemistry And Materials Research
Synthesis and Charactrization of New Schiff Base Derived from PVA and Erythroascorbic Acid Derivative and Study Its Effect on the Activity of ACh Enzyme (In Vitro)
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Schiff base derived from PVA and Erythroascorbic acid derivative (pentulosono-ɣ-lactone-2, 3-enedianisoate) was synthesized and characterized by Thin Layer Chromatography (TLC) and FTIR spectra, aldehyde was also characterized by (U.V-Vis), 1HNMR, 13CNMR and mass spectra. The inhibitory effect of prepared polymer on the activity of human serum Cholinesrerase has been studied in vitro. The polymer showed a remarkable activity at low concentration (4.5*10-3 – 4.5*10-8 M).

Publication Date
Fri Dec 01 2017
Journal Name
Al-nahrain Journal For Engineering Sciences (njes)
Investigation of the thermodynamic, kinetic and equilibrium parameters of batch biosorption of Pb (II), Cu (II), and Ni (II) from aqueous phase using low cost biosorbent
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In this study, low cost biosorbent ̶inactive biomass (IB) granules (dp=0.433mm) taken from drying beds of Al-Rustomia Wastewater Treatment Plant, Baghdad-Iraq were used for investigating the optimum conditions of Pb(II), Cu(II), and Ni(II) biosorption from aqueous solutions. Various physico-chemical parameters such as initial metal ion concentration (50 to 200 mg/l), equilibrium time (0-180 min), pH (2-9), agitation speed (50-200 rpm), particles size (0.433 mm), and adsorbent dosage (0.05-1 g/100 ml) were studied. Six mathematical models describing the biosorption equilibrium and isotherm constants were tested to find the maximum uptake capacities: Langmuir, Freundlich, Redlich–Peterson, Sips, Khan, and Toth models. The best fit to the P

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Publication Date
Wed Jan 02 2019
Journal Name
Journal Of The College Of Languages (jcl)
Animal-Based Metaphors as Being a Lingua-Cultural Way in the Field of Football Club Titles: Зооморфная метафора как лингвокультурологический способ в области прозвищ футбольных клубов
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       Metaphor is a linguistic phenomenon related to people's cultures. It is an integral part of cultural heritage. This paper tackles the use of animal-based metaphors in the field of football club titles so as to draw comparisons between those in Russian with their counterparts in Arabic. Names of animals are used to refer to some clubs and teams, where these names or titles reflect animal features such as strength, preying on victims; or animal figures are employed in the club symbols, or due to the similarity of the club shirt to the animal outer shapes in colours. For instance, "an-Nawaris", which means gulls in English, is used to refer to az-Zawraa club du

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Publication Date
Tue Jun 30 2020
Journal Name
Journal Of Planner And Development
Real estate acquisition barrier and its impact on urban development projects" Study Area: Infrastructure project in the capital Baghdad (North East Sewage Line project AL khansaa)
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The increase the rates of natural growth, urbanization and continuous migration, this has generated constant pressure and, as a result, the capital city of Baghdad faces a number of challenges related to its urban environment, including the challenge of acquiring real estate.

 

 and this research examines the impact of these holdings, representing the main base from which the various projects originate Urban in all areas (economic, social, and recreational).

 

this leads us to the research problem of the obstacles that arise during the process of acquiring real estate to carry out development projects, and to achieve the objectives of research, namely (work to create a regulatory methodology

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Publication Date
Sun Feb 22 2026
Journal Name
Journal Of Al-farahidi's Arts
Artificial Intelligence Tools in Literary Text Analysis: An Applied Study Using Voyant Tool: The Poem “I have now a Rifle” by Nizar Qabbani as a Model
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In recent years, literary studies have witnessed a remarkable shift towards employing digital technologies, particularly artificial intelligence tools, in analyzing literary texts and exploring their linguistic and semantic structures. This trend has provided researchers with new possibilities for understanding texts in quantitative and qualitative ways that transcend traditional methods based solely on critical reading. The current research aims to introduce professors and students of Arabic to artificial intelligence tools that contribute to the analysis of literary texts, focusing on exploring their mechanisms for studying style, meaning, structure, and emotion. It also seeks to highlight the most prominent challenges facing researchers

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Publication Date
Wed Sep 30 2015
Journal Name
College Of Islamic Sciences
Fundamentalist detective On matters of consensus   Of Khala book complete the teacher benefits of Muslim Judge Ayaz (May God have mercy on him): Comparative fundamentalist study
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Fundamentalist detective
On matters of consensus
  Of Khala book complete the teacher benefits of Muslim
Judge Ayaz
(May God have mercy on him)

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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of The College Of Languages (jcl)
Heated and silent adoration in the novel of " Desert of Love" by Francois Mauriac: Passions dévorantes et cachées dans Le Désert de lʼAmour de François Mauriac
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  François Mauriac’s novel The Desert of Love (1949) puts the reader before an experienced sociologist who is skillfully able to analyze the most mysterious human emotions and feelings.  The writer's starting point is that people are similar in feelings but different in behavior. He severely criticized the aristocratic class and uncovered its defects and faults.

         The novelist presents Courege's family as an example of the aristocratic class. It is a family torn by hatred, selfishness and disagreements due to absence of intimacy and love. This poisoned environment pushes the father and his son, Raymond, to search away for emotional ventures and banned relations

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Publication Date
Sat Jun 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Green Innovation and its Impact in Reinforcing Sustainable Competitive Advantage: An Exploratory Study of Opinions of a Sample of Employees in the Karungi group in Kirkuk
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The development of the world, and in light of the intensity of competition highlighted the need to research and create a sustainable competitive advantage is sustained from an internal source in the company earned by the scarcity and difficulty of imitation by competitors, and this source is green innovation. In order to achieve the objective of the research, which is the diagnosis and analysis of the relationship between green innovation (in products, processes) and sustainable competitive advantage in the group of companies Kronji, was developed a default model of the research reflects the nature of the relationship and influence among its variables, the research adopted the questionnaire as a key tool for collecting data and i

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