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A PARTICULAR SOLUTION OF THE TWO AND THREE DIMENSIONAL TRANSIENT DIFFUSION EQUATIONS
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A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)

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Publication Date
Thu Dec 30 2004
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
History of a Two-Phase Bubble Condensing in an immiscible Liquid
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Publication Date
Fri Sep 15 2023
Journal Name
Sumer 2
Response of Three Citrus Rootstocks to Organic and Biological Fertilizers
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This study was conducted in a lath house, Dept of Hort. and Landscape, College of Agricultural Engineering Sciences, Univ. During the 2021 growing season, Baghdad will investigate the influence of organic and Biological fertilizers on three Citrus rootstocks' growth and leaf mineral content. The first factor is the addition of liquid organic fertilizers Vit-Org (O) at three levels without addition (O0), soil addition at 10 ml.L-1 (O10) and soil addition at 20 ml.L-1 (O20). The second factor is the addition of nitrogen-fixing bacteria without addition (N1), add 30 ml.Transplant-1 of Azotobacter chroococcum (N2) and add 30 ml.Transplant-1 of Azospirillum brasilemse (N3). The third factor is three citrus rootstocks: sour orange (R1), R

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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Volterra Runge- Kutta Methods for Solving Nonlinear Volterra Integral Equations
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In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

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Publication Date
Thu Nov 01 2012
Journal Name
Journal Of Cutaneous And Aesthetic Surgery
Topical zinc sulphate (25%) solution: a new therapy for actinic keratosis
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KE Sharquie, SA Al-Mashhadani, AA Noaimi, AA Hasan, Journal of Cutaneous and Aesthetic Surgery, 2012 - Cited by 19

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Publication Date
Wed Mar 30 2022
Journal Name
Journal Of Educational And Psychological Researches
Analyzing the content of the two science books (the two chemistry units) for the intermediate stage according to environmental problems
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    The main goal of the current research is to know -Environmental problems included in the content of the two science books (chemistry units) for intermediate stage

A list of environmental problems had been prepared  and  consisting of (8) main areas which are (air and atmosphere pollution, water pollution, soil pollution, energy, disturbance of biodiversity and environmental balance, waste management, food and medicinal pollution, investment of mineral wealth). Of which (60) sub-problems,  at that time the researcher analyzed the two science books (two chemistry units) for the intermediate stage of the academic year (2020-2021) in light of the list that was prepared, and the validity and consisten

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Publication Date
Tue Oct 27 2020
Journal Name
Proceedings Of The 2020 2nd International Conference On Sustainable Manufacturing, Materials And Technologies
The complex dynamic in three species food webmodel involving stage structure and cannibalism
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A three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the p

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Publication Date
Sun Jun 02 2013
Journal Name
Baghdad Science Journal
Some Probability Characteristics Functions of the Solution of Stochastic Fredholm Integral Equation Contains a Known Sine Wave Function
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Abstract:In this paper, some probability characteristics functions (moments, variances,convariance, and spectral density functions) are found depending upon the smallestvariance of the solution of some stochastic Fredholm integral equation contains as aknown function, the sine wave function

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Publication Date
Tue Oct 01 2024
Journal Name
Journal Of Physics: Conference Series
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 </p> ... Show More
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Publication Date
Sun Jul 04 2021
Journal Name
(al-qadisiyah-journal Of Pure Science(qjps
Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations
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The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

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Publication Date
Sun Jul 28 2019
Journal Name
Open Access Macedonian Journal Of Medical Sciences
Value of Combination of Standard Axial and Thin-Section Coronal Diffusion-weighted Imaging in Diagnosis of Acute Brainstem Infarction
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AIM: To determine the value of the combination of thin-section 3 mm ‎coronal and standard ‎axial DWI and their impact in facilitating the diagnosis of ‎‎acute brainstem infarction. METHODS: A cross-sectional study conducted from the 1st of April 2017 to the end of February 2018 on 100 consecutive patients (66% were male, and 34% were female) with isolated acute ischemic infarction in the ‎brainstem. The abnormal MRI findings concerning the ischemic lesions were interpreted on standard axial 5 mm and thin-section coronal 3mm DWI. RESULTS: The mean age of the studied group was 69.2 ± 4.3 for male and 72.3 ± 2.5 years. The standard axial DWI can diagnose 20%, 6.7% and 6.7% of the infarctions in midbrain, pons an

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