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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
Mon May 01 2023
Journal Name
Journal Of Engineering
Measuring the Attribute Accuracy and Completeness for the OpenStreetMap Roads Networks for Two Regions in Iraq
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The OpenStreetMap (OSM) project aims to establish a free geospatial database for the entire world which is editable by international volunteers. The OSM database contains a wide range of different types of geographical data and characteristics, including highways, buildings, and land use regions. The varying scientific backgrounds of the volunteers can affect the quality of the spatial data that is produced and shared on the internet as an OSM dataset. This study aims to compare the completeness and attribute accuracy of the OSM road networks with the data supplied by a digitizing process for areas in the Baghdad and Thi-Qar governorates. The analyses are primarily based on calculating the portion of the commission (extra road) and

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Publication Date
Mon May 01 2023
Journal Name
Journal Of Engineering
Measuring the Attribute Accuracy and Completeness for the OpenStreetMap Roads Networks for Two Regions in Iraq
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The OpenStreetMap (OSM) project aims to establish a free geospatial database for the entire world which is editable by international volunteers. The OSM database contains a wide range of different types of geographical data and characteristics, including highways, buildings, and land use regions. The varying scientific backgrounds of the volunteers can affect the quality of the spatial data that is produced and shared on the internet as an OSM dataset. This study aims to compare the completeness and attribute accuracy of the OSM road networks with the data supplied by a digitizing process for areas in the Baghdad and Thi-Qar governorates. The analyses are primarily based on calculating the portion of the commission (extr

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Publication Date
Thu Sep 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
Determination Of The Efficient Production Plans For Al-Shaheed Public Company By Using Tatget Motad Model Under Risk And Uncertainty
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The research aims to derive the efficient industrial plans for Al – shaheed public company under risk by using Target MOTAD as a linear alternative  model for the quadratic programming models.

The results showed that there had been a sort of (trade- off) between risk and the expected gross margins. And if the studied company strives to get high gross margin, it should tolerate risk and vice versa. So the management  of Al- Shaheed Company to be invited to apply the suitable procedures in the production process, in order to get efficient plans that improves it's  performance .

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Publication Date
Sat Sep 15 2018
Journal Name
Journal Of The College Of Education For Women
Estimation of the Risk of Water Erosion in Jawarta District in Sulaymaniyah Governorate Using the Global Equation for Soil Loss (USLE)
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The present research deals with the spatial variance analysis in Jwartadistrict and conducting a comparison on the spatial and seasonal changes of the vegetation cover between (2007-2013) in order to deduce the relationship between the vegetation density and the areas which are exposed to the risk of water erosion by using Plant Variation Index  NDVI) C (coefficient and by using Satellite images of Landsat satellite which are taken in 2/7/2007 and Satellite images of Landsat satellite taken in 11/1/ 2013, the programs of remote sensitivity and the Geographic Information Systems.

    The study reveals that there is a variance in the density of vegetation cover of the area under study betwee 2007 and 2013. Howev

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Publication Date
Fri Dec 01 2017
Journal Name
2017 11th Asian Control Conference (ascc)
Super-twisting based integral sliding mode control applied to a rotary flexible joint robot manipulator
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In this paper, a single link flexible joint robot is used to evaluate a tracking trajectory control and vibration reduction by a super-twisting integral sliding mode (ST-ISMC). Normally, the system with joint flexibility has inevitably some uncertainties and external disturbances. In conventional sliding mode control, the robustness property is not guaranteed during the reaching phase. This disadvantage is addressed by applying ISMC that eliminates a reaching phase to ensure the robustness from the beginning of a process. To design this controller, the linear quadratic regulator (LQR) controller is first designed as the nominal control to decide a desired performance for both tracking and vibration responses. Subsequently, discontinuous con

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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function
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In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

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Publication Date
Thu Jul 25 2019
Journal Name
Advances In Intelligent Systems And Computing
Solving Game Theory Problems Using Linear Programming and Genetic Algorithms
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Publication Date
Sun Mar 02 2014
Journal Name
Baghdad Science Journal
On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms
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In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

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Publication Date
Mon Jan 01 2024
Journal Name
Aims Mathematics
Solving quaternion nonsymmetric algebraic Riccati equations through zeroing neural networks
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<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel

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Publication Date
Tue Sep 29 2020
Journal Name
Reaction Kinetics, Mechanisms And Catalysis
Development of two-step noncatalytic esterification of waste cooking oil for biodiesel preparation
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An innovative two-step noncatalytic esterifcation technique was proposed to synthesize alkyl esters from free fatty acids simulated in waste cooking oil, as a pretreatment process for biodiesel production, without adding any catalyst under normal conditions of pressure and temperature. The efect of methanol:oil molar ratio, reaction time, mixing rate, and reaction temperature were investigated. The results confrmed that the conversion of the reaction was increased when increasing the methanol molar ratio and decreased in prolonged reaction temperature. High conversion (94.545%) was successfully achieved at optimized conditions of 115:1, 65:1 methanol:oil molar ratio in the frst step and second step, respectively, other conditions i

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