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Three Weighted Residuals Methods for Solving the Nonlinear Thin Film Flow Problem
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Abstract<p>In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4<sup>th</sup>-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.</p>
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Publication Date
Fri Feb 06 2026
Journal Name
Optik
Mitigation optical losses via plasmonic core/shell (Co/Gr) nanoparticles introduced in ultra-thin film silicon solar cell
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Optical losses represent one of the primary obstacles to increasing the efficiency of silicon solar cells. The recommended solution to minimize optical losses is the use of plasmonic metal nanoparticles; however, they act as recombination centers within the solar cell construction, leading to a decrease in performance. The goal of this article is to introduce cobalt/graphene nanoparticles into the solar cell to minimize the optical losses. An ultra-thin film silicon PIN solar cell of dimensions (400 ×400 ×900) nm3 with ring metal contact shape was designed and numerically investigated using COMSOL Multiphysics software version 6.2 by the finite element method (FEM). Core/shell cobalt-graphene (Co/Gr) nanoparticles are periodically int

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Publication Date
Wed Apr 01 2015
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
Security For Three -Tired Web Application
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Web application protection lies on two levels: the first is the responsibility of the server management, and the second is the responsibility of the programmer of the site (this is the scope of the research). This research suggests developing a secure web application site based on three-tier architecture (client, server, and database). The security of this system described as follows: using multilevel access by authorization, which means allowing access to pages depending on authorized level; password encrypted using Message Digest Five (MD5) and salt. Secure Socket Layer (SSL) protocol authentication used. Writing PHP code according to set of rules to hide source code to ensure that it cannot be stolen, verification of input before it is s

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Publication Date
Sun May 26 2019
Journal Name
Iraqi Journal Of Science
Bayesian Estimation for Two Parameters of Gamma Distribution under Generalized Weighted Loss Function
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This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

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Publication Date
Thu Apr 18 2019
Journal Name
Al-kindy College Medical Journal
Demonstration of the value of diffusion weighted MR imaging for differentiation of benign from malignant breast lesions
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Background: Radiologic evaluation of breast lesions is being achieved through several imaging modalities. Mammography has an established role in breast cancer screening and diagnosis. Still however, it shows some limitations particulary in dense breast.

Methods : Magnetic resonance imaging is an attractive tool for the diagnosis of breast tumors1 and the use of magnetic resonance imaging of the breast is rapidly increasing as this technique becomes more widely available.1 As an adjunct to mammography and ultrasound, MRI can be a valuable addition to the work-up of a breast abnormality. MRI has the advantages of providing a three-dimensional view of the breast, performing wit

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Publication Date
Fri Jan 01 2016
Journal Name
Mathematical Problems In Engineering
Enhanced Simulated Annealing for Solving Aggregate Production Planning
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Simulated annealing (SA) has been an effective means that can address difficulties related to optimization problems. is now a common discipline for research with several productive applications such as production planning. Due to the fact that aggregate production planning (APP) is one of the most considerable problems in production planning, in this paper, we present multi-objective linear programming model for APP and optimized by . During the course of optimizing for the APP problem, it uncovered that the capability of was inadequate and its performance was substandard, particularly for a sizable controlled problem with many decision variables and plenty of constraints. Since this algorithm works sequentially then the current state wi

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Publication Date
Sun Oct 01 2017
Journal Name
Journal Of The Association Of Arab Universities For Basic And Applied Sciences
Semi-analytical method for solving Fokker-Planck’s equations
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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
New Approach for Solving Two Dimensional Spaces PDE
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Abstract<p>In this paper, new approach based on coupled Laplace transformation with decomposition method is proposed to solve type of partial differential equation. Then it’s used to find the accurate solution for heat equation with initial conditions. Four examples introduced to illustrate the accuracy, efficiency of suggested method. The practical results show the importance of suggested method for solve differential equations with high accuracy and easy implemented.</p>
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Publication Date
Tue Aug 01 2023
Journal Name
Baghdad Science Journal
The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems
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In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

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Publication Date
Tue Jan 08 2019
Journal Name
Iraqi Journal Of Physics
The effects of laser intensities on nonlinear properties for Ag nanoparticles colloid
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A huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat

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Publication Date
Tue Feb 17 2026
Journal Name
Al-rafidain University College For Sciences
“Simple Regression Analysis by using Linear Programming Technique and illustration of Absolute Residuals method with another Estimation Techniques”
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This research deals with unusual approach for analyzing the Simple Linear Regression via Linear Programming by Two - phase method, which is known in Operations Research: “O.R.”. The estimation here is found by solving optimization problem when adding artificial variables: Ri. Another method to analyze the Simple Linear Regression is introduced in this research, where the conditional Median of (y) was taken under consideration by minimizing the Sum of Absolute Residuals instead of finding the conditional Mean of (y) which depends on minimizing the Sum of Squared Residuals, that is called: “Median Regression”. Also, an Iterative Reweighted Least Squared based on the Absolute Residuals as weights is performed here as another method to

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