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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
Thu Feb 07 2019
Journal Name
Iraqi Journal Of Laser
Design High Efficient Reflectivity of Distributed Bragg Reflectors
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Bragg Reflectors consist of periodic dielectric layers having an optical path length of quarter wavelength for each layer giving them important properties and makes them suitable for optoelectronics applications. The reflectivity can be increased by increasing the number of layers of the mirror to get the required value. For example for an 8 layers Bragg mirror (two layers for each dielectric pair), the contrast of the refractive index has to be equal to 0.275 for reaching reflectivity > 99%. Doubling the number of layers results in a reflectivity of 99.99%. The high reflectivity is purely caused by multiple-interference effects. It can be analyzed by using different matrix methods such as the transfer matrix method (TMM) which is the

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Publication Date
Mon Apr 26 2021
Journal Name
Journal Of Real-time Image Processing
Fast and efficient recursive algorithm of Meixner polynomials
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Publication Date
Sun Sep 11 2022
Journal Name
Electronics
IoT-Based Motorbike Ambulance: Secure and Efficient Transportation
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The predilection for 5G telemedicine networks has piqued the interest of industry researchers and academics. The most significant barrier to global telemedicine adoption is to achieve a secure and efficient transport of patients, which has two critical responsibilities. The first is to get the patient to the nearest hospital as quickly as possible, and the second is to keep the connection secure while traveling to the hospital. As a result, a new network scheme has been suggested to expand the medical delivery system, which is an agile network scheme to securely redirect ambulance motorbikes to the nearest hospital in emergency cases. This research provides a secured and efficient telemedicine transport strategy compatible with the

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Publication Date
Wed Feb 16 2022
Journal Name
Journal Of Economics And Administrative Sciences
Solving Resource Allocation Model by Using Dynamic Optimization Technique for Al-Raji Group Companies for Soft Drinks and Juices
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In this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti

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Publication Date
Tue Sep 01 2020
Journal Name
Al-khwarizmi Engineering Journal
Two-Stage Classification of Breast Tumor Biomarkers for Iraqi Women
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Objective: Breast cancer is regarded as a deadly disease in women causing lots of mortalities. Early diagnosis of breast cancer with appropriate tumor biomarkers may facilitate early treatment of the disease, thus reducing the mortality rate. The purpose of the current study is to improve early diagnosis of breast by proposing a two-stage classification of breast tumor biomarkers fora sample of Iraqi women.

Methods: In this study, a two-stage classification system is proposed and tested with four machine learning classifiers. In the first stage, breast features (demographic, blood and salivary-based attributes) are classified into normal or abnormal cases, while in the second stage the abnormal breast cases are

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Publication Date
Thu Jun 01 2023
Journal Name
Journal Of Engineering
Evaluating Roads Network Connectivity for Two Municipalities in Baghdad-Iraq
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The road network serves as a hub for opportunities in production and consumption, resource extraction, and social cohabitation. In turn, this promotes a higher standard of living and the expansion of cities. This research explores the road network's spatial connectedness and its effects on travel and urban form in the Al-Kadhimiya and Al-Adhamiya municipalities. Satellite images and paper maps have been employed to extract information on the existing road network, including their kinds, conditions, density, and lengths. The spatial structure of the road network was then generated using the ArcGIS software environment. The road pattern connectivity was evaluated using graph theory indices. The study demands the abstractio

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Publication Date
Sat Nov 12 2016
Journal Name
International Journal Of Mechanical Engineering And Technology (ijmet)
PERFORMANCE OF TWO-WAY NESTING TECHNIQUES FOR SHALLOW WATER MODELS
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A new two-way nesting technique is presented for a multiple nested-grid ocean modelling system. The new technique uses explicit center finite difference and leapfrog schemes to exchange information between the different subcomponents of the nested-grid system. The performance of the different nesting techniques is compared, using two independent nested-grid modelling systems. In this paper, a new nesting algorithm is described and some preliminary results are demonstrated. The validity of the nesting method is shown in some problems for the depth averaged of 2D linear shallow water equation.

Publication Date
Fri Aug 31 2012
Journal Name
Al-khwarizmi Engineering Journal
Empirical Equations for Analysis of Two-Way Reinforced Concrete Slabs
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There are many different methods for analysis of two-way reinforced concrete slabs. The most efficient methods depend on using certain factors given in different codes of reinforced concrete design. The other ways of analysis of two-way slabs are the direct design method and the equivalent frame method. But these methods usually need a long time for analysis of the slabs.

In this paper, a new simple method has been developed to analyze the two-way slabs by using simple empirical formulae, and the results of final analysis of some examples have been compared with other different methods given in different codes of practice.

The comparison proof that this simple proposed method gives good results and it can be used in analy

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
Effect of growth regulators on responsible rooting for two varieties
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Conducted two trials separate plants Defla first two seasons, 1998 and 1999 to test the susceptibility Altgveria three varieties including Azharha colored white and pink Qati and pink Qtmr and second seasons 1999 and 2000, two types color Azhaarhama white and pink Qati treated mind half-timbered two types of Alaoxinat IBA and NAA and three concentrations as well as repeatersAdhrt results low Almaah rooting

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Publication Date
Thu Jun 01 2023
Journal Name
Journal Of Engineering
Evaluating Roads Network Connectivity for Two Municipalities in Baghdad-Iraq
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The road network serves as a hub for opportunities in production and consumption, resource extraction, and social cohabitation. In turn, this promotes a higher standard of living and the expansion of cities. This research explores the road network's spatial connectedness and its effects on travel and urban form in the Al-Kadhimiya and Al-Adhamiya municipalities. Satellite images and paper maps have been employed to extract information on the existing road network, including their kinds, conditions, density, and lengths. The spatial structure of the road network was then generated using the ArcGIS software environment. The road pattern connectivity was evaluated using graph theory indices. The study demands the abstraction and examin

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