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Two efficient methods for solving Schlömilch’s integral equation
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Purpose

In this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.

Design/methodology/approach

First, the authors apply a regularization method combined with the standard homotopy analysis method to find the exact solutions for all forms of the Schlömilch’s integral equation. Second, the authors implement the regularization method with the variational iteration method for the same purpose. The effectiveness of the regularization-Homotopy method and the regularization-variational method is shown by using them for several illustrative examples, which have been solved by other authors using the so-called regularization-Adomian method.

Findings

The implementation of the two methods demonstrates the usefulness in finding exact solutions.

Practical implications

The authors have applied the developed methodology to the solution of the Rayleigh equation, which is an important equation in fluid dynamics and has a variety of applications in different fields of science and engineering. These include the analysis of batch distillation in chemistry, scattering of electromagnetic waves in physics, isotopic data in contaminant hydrogeology and others.

Originality/value

In this paper, two reliable methods have been implemented to solve several examples, where those examples represent the main types of the Schlömilch’s integral models. Each method has been accompanied with the use of the regularization method. This process constructs an efficient dealing to get the exact solutions of the linear and non-linear Schlömilch’s integral equation which is easy to implement. In addition to that, the accompanied regularization method with each of the two used methods proved its efficiency in handling many problems especially ill-posed problems, such as the Fredholm integral equation of the first kind.

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Publication Date
Tue Apr 21 2020
Journal Name
University Of Thi-qar Journal Of Science (university Of Thi-qar Journal Of Science (utsci) The 4th Scientific Conference Of Science College/ University Of Thi_qari) The 4th Scientific Conference Of Science College/ University Of Thi_qar
Enhancement of Nano Catalyst for an Alkaline Fuel Cells
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Publication Date
Tue Oct 30 2018
Journal Name
Iraqi Journal Of Physics
Synthesized copper nanoparticles by sonoelectrodeposition for gas filter applications
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Copper nanoparticles (CuNPs) were prepared with different diameters by sonoelectrodeposition technique using Electrodeposition process coupled with high-power ultrasound horn (Sonoelectrodeposition). The particle diameter of the CuNPs was adjusted by varying CuSO4 solution acidity (pH) and current density. The morphology and structure of the CuNPs were examined by X-ray diffraction (XRD) and Scanning Electron Microscopy (SEM). It was found that the size of the produced copper nanoparticles ranged between 22 to 77 nm, where the diameter of CuNPs increases with reduction the solution acidity from 0.5 to 1.5 pH and increasing the current density of the deposition from 100 to 400 nm. Finally the produced CuNPs were pressed to fabricate disc

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Publication Date
Thu Dec 01 2016
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
A NEW RECORD OF ZIZIPHORA SPECIES (LAMIACEAE) FOR IRAQ
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    Ziziphora persica Bunge is recorded as a new Study in Iraq. This species has been collected from Jabal Sinjar in Nineveh province in the north western part of Iraq. The morphological characters, habitat and geographical distribution of the species with a key to Ziziphora L. species in Iraq have been provided.

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Publication Date
Wed Dec 25 2019
Journal Name
Journal Of Engineering
Non-deterministic Approach for Reliability Evaluation of Steel Beam
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This paper aims to evaluate the reliability analysis for steel beam which represented by the probability of Failure and reliability index. Monte Carlo Simulation Method (MCSM) and First Order Reliability Method (FORM) will be used to achieve this issue. These methods need two samples for each behavior that want to study; the first sample for resistance (carrying capacity R), and second for load effect (Q) which are parameters for a limit state function. Monte Carlo method has been adopted to generate these samples dependent on the randomness and uncertainties in variables. The variables that consider are beam cross-section dimensions, material property, beam length, yield stress, and applied loads. Matlab software has be

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Publication Date
Tue Dec 31 2019
Journal Name
Journal Of Engineering And Applied Sciences
Design and Implementation of Electronic Infrastructure for Academic Establishment
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Publication Date
Sun Nov 01 2020
Journal Name
Journal Of Engineering
Developing an Indoor Environment Assessment Tool for Residential Buildings
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The Indoor Environmental Quality (IEQ) describes an indoor space condition that the wellbeing and comfortability are provided for the users. Many researchers have highlighted the importance of adopting IEQ criteria, although they are not yet well defined in the Kurdistan region. However, environmental quality is not necessary for the contemporary buildings of the Kurdistan Region, and there is no measurement tool in the Region. This research aims to develop an IEQ assessment tool for the Kurdistan region using Mixed method methodology, both qualitative and quantitative. Therefore, a Delphi Technique was used as a method initially developed as systematic, interactive forecasting on a panel of experts. Thirty-five Delphi C

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Publication Date
Mon Apr 01 2013
Journal Name
Journal Of Mathematical Analysis And Applications
Strong duality for generalized monotropic programming in infinite dimensions
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Publication Date
Sun Sep 01 2019
Journal Name
Baghdad Science Journal
Symmetric and Positive Definite Broyden Update for Unconstrained Optimization
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Broyden update is one of the one-rank updates which solves the unconstrained optimization problem but this update does not guarantee the positive definite and the symmetric property of Hessian matrix.

In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.

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Publication Date
Sat Dec 31 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Performance Study of Electrodialysis for Treatment Fuel Washing Wastewater
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In this work, electrodialysis (ED) has been demonstrated to be appropriate technique for reducing the electrical conductivity of real wastewater from fuel washing unit, which has been previously treated by other electrochemical technology (electrocoagulation and electrooxidation).  A five cell electrodialysis stack, with an active membrane area of 60 cm2 per cell was employed. During a batch recirculation mode ED system, the effects of parameters such as electrical potential applied (6-18 V) and flow rate of streams (0.5-1.7 L/min.) on the performance of the total dissolved solids (TDS) separation and specific power consumption (SPC) were studied. The results indicate that the process of ED under potential (15 V) and flow

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Publication Date
Wed Feb 10 2021
Journal Name
مجلة العلوم القانونية
The Civil liability of tobacco companies for smoking damage
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Tobacco products of all kinds are harmful to public health, so legislation has paid great attention to regulating the process of tobacco production and distribution, whether at the level of national or international legislation, in a way that achieves legal protection for these products, so the establishment of civil liability for tobacco companies as a result of harm to the smoker The positive and the negative provoked a jurisprudential dispute due to the specificity of the work of these companies, and the jurisprudence differed in the legal nature of tobacco companies ’liability between contractual and tort liability in a way that enables the injured smoker to obtain his right to compensation.

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