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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
Wed Nov 01 2023
Journal Name
Iop Conference Series: Earth And Environmental Science
Two New Records of Cerceris Latreille, 1802 (Hymenoptera: Apoidea: Crabronidae) from Iraq
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Abstract<p>In a survey of the crabronid fauna of Iraq during June to October 2022; 9species belonging to the genus <italic>Cerceris</italic> Latreille, 1802 were identified. Twospecies are new record of the fauna of Iraq: <italic>C. dorsalis</italic> Eversmann, 1849 and <italic>C. priesneri</italic> Mochi, 1939. Brief description, diagnostic characters, some collecting information, and photographs of each species are provided. As well provides a key to the species depending on many morphological features especially: propodeal enclosure, semicircular plate at base of second gastral sternites and free margin of clypeus. Moreover, this study observed that most collecte</p> ... Show More
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Publication Date
Tue Jul 01 2008
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
TESTING THE EFFICACY OF SOME METHODS RECOMMENDED ABROAD FOR CONTROLLING THE ORIENTAL HORNET, VESPA ORIENTALIS L., ATTACKING HONEY BEE, APIS MELLIFERA L., COLONIES IN IRAQ
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Some methods recommended abroad to control the oriental hornet, Vespa orientalis L., attacking the honey bee, Apis mellifera L., colonies were tested, with some modifications, for the first time under the Iraqi conditions. One of these methods was carried out by covering the hive entrance with a piece of queen excluder to prevent the hornet from entering the hive. Also, the position of hive stand was reversed to deprive the hornet from using the flight board as a stage for waiting and creeping toward the defending bees. The second method was carried out by fixing a cardboard cone as a bee passage at the hive entrance to hinder the entry of the hornet into the hive. Both of these methods were found to be unsuccessful to

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Publication Date
Fri Nov 01 2019
Journal Name
Iop Conference Series: Earth And Environmental Science
The comparison of several methods for calculating the degree of heritability and calculating the number of genes in maize (Zea mays L.). I. Agronomic traits
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Abstract<p>The objective of present study was to compare of several methods for estimating the degree of heritability and calculating the number of genes using generation mean analysis of maize (<italic>Zea mays</italic>L.). The experiment was conducted at the field of Field Crop Dept. College of Agric / Univ. of Baghdad, for many seasons, spring and fall seasons 2009, 2010, spring 2011 and fall 2013.Six diverse inbred lines were crossed to produce F1,F2,BC1 and BC2 for four superior crosses.Broad-sense and narrow sense heritability estimates based on variance of different generations. The results showed that the four formulas used to estimate the heritability were different in estimating the values o</p> ... Show More
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Publication Date
Mon Sep 09 2013
Journal Name
Plant Biology
Comparing simple root phenotyping methods on a core set of rice genotypes
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Abstract<p>Interest in belowground plant growth is increasing, especially in relation to arguments that shallow‐rooted cultivars are efficient at exploiting soil phosphorus while deep‐rooted ones will access water at depth. However, methods for assessing roots in large numbers of plants are diverse and direct comparisons of methods are rare. Three methods for measuring root growth traits were evaluated for utility in discriminating rice cultivars: soil‐filled rhizotrons, hydroponics and soil‐filled pots whose bottom was sealed with a non‐woven fabric (a potential method for assessing root penetration ability). A set of 38 rice genotypes including the Oryza<styled-content style="fixed-case">SNP</styled-content></p> ... Show More
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Publication Date
Sat Feb 12 2022
Journal Name
Engineering, Technology &amp; Applied Science Research
Evaluating the Efficiency of Finance Methods in Residential Complex Projects in Iraq
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Financial funding of a construction firm plays an important role in all aspects of the process development. It has been noted that financial crises have a direct impact on the construction industry. The Iraqi government, whether locally or globally, has faced a severe shortage of financing which has resulted in incomplete projects. Due to the financial crisis that Iraq went through which led to the suspension of many residential complex projects and the difficulty of the use of public financing methods, we researched the private financing (public-private partnership) methods instead of public financing methods in residential complex projects implementation. This study verified the financial problems and the factors that relate to th

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Publication Date
Sun Jan 01 2023
Journal Name
Aip Conference Proceedings
Different estimation methods of reliability in stress-strength model under chen distribution
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Publication Date
Sun Feb 03 2019
Journal Name
Iraqi Journal Of Physics
Change detection of remotely sensed image using NDVI subtractive and classification methods.
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Change detection is a technology ascertaining the changes of
specific features within a certain time Interval. The use of remotely
sensed image to detect changes in land use and land cover is widely
preferred over other conventional survey techniques because this
method is very efficient for assessing the change or degrading trends
of a region. In this research two remotely sensed image of Baghdad
city gathered by landsat -7and landsat -8 ETM+ for two time period
2000 and 2014 have been used to detect the most important changes.
Registration and rectification the two original images are the first
preprocessing steps was applied in this paper. Change detection using
NDVI subtractive has been computed, subtrac

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Publication Date
Wed Feb 14 2024
Journal Name
Aip Conference Proceedings
Segmentation Moon Images Using Different Segmentation Methods and Isolate the Lunar Craters
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Segmentation is the process of partition digital images into different parts depending on texture, color, or intensity, and can be used in different fields in order to segment and isolate the area to be partitioned. In this work images of the Moon obtained through observations in Astronomy and space dep. College of science university of Baghdad by ( Toward space telescopes and widespread used of a CCD camera) . Different segmentation methods were used to segment lunar craters. Different celestial objects cause craters when they crash into the surface of the Moon like asteroids and meteorites. Thousands of craters appears on the Moon's surface with ranges in size from meter to many kilometers, it provide insights into the age and ge

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Publication Date
Mon Dec 18 2017
Journal Name
Al-khwarizmi Engineering Journal
Synthesis of CuO Nano structure via Sol-Gel and Precipitation Chemical Methods
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CuO nanoparticles were synthesized in two different ways, firstly by precipitation method using copper acetate monohydrate Cu(CO2CH13)2·H2O, glacial acetic acid (CH3COOH) and sodium hydroxide(NaOH), and secondly by sol-gel method using copper chloride(CuCl2), sodium  hydroxide (NaOH) and ethanol (C2H6O). Results of scanning electron microscopy (SEM) showed that different CuO nanostructures (spherical and Reef) can be formed using precipitation and sol- gel process, respectively, at which the particle size was found to be less than 2 µm. X-ray diffraction (XRD)manifested that the pure synthesized powder has no inclusions that may exist during preparations. XRD result

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Publication Date
Wed Feb 14 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Segmentation moon images using different segmentation methods and isolate the lunar craters
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Segmentation is the process of partition digital images into different parts depending on texture, color, or intensity, and can be used in different fields in order to segment and isolate the area to be partitioned. In this work images of the Moon obtained through observations in Astronomy and space dep. College of science university of Baghdad by ( Toward space telescopes and widespread used of a CCD camera) . Different segmentation methods were used to segment lunar craters. Different celestial objects cause craters when they crash into the surface of the Moon like asteroids and meteorites. Thousands of craters appears on the Moon's surface with ranges in size from meter to many kilometers, it provide insights into the age and geology

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