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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
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
A comparative study between conventional methods and Vidas UP Salmonella (SPT) to investigate salmonella species from local and imported meat
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The study was preformed for investigating of Salmonella from meat, and compared Vidas UP Salmonella (SPT) with the traditional methods of isolation for Salmonella , were examined 42 meat samples (Beef and Chicken) from the Local and Imported From local markets in the city of Baghdad from period December 2013 -February 2014 the samples were cultured on enrichment and differential media and examined samples Vidas, and confirmed of isolates by cultivation chromgenic agar, biochemical tests ,Api20 E systeme , In addition serological tests , and the serotypes determinate in the Central Public Health Laboratory / National Institute of Salmonella The results showed the contamination in imported meat was more than in the local meat 11.9% and 2

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Publication Date
Fri Mar 01 2019
Journal Name
Archives Of Plastic Surgery
Surgical outcomes of 14 consecutive bilateral cleft lip patients treated with a modified version of the Millard and Manchester methods
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Background Bilateral cleft lip deformity is much more difficult to correct than unilateral cleft lip deformity. The complexity of the deformity and the sensitive relationships between the arrangement of the muscles and the characteristics of the external lip necessitate a comprehensive preoperative plan for management. The purpose of this study was to evaluate the repair of bilateral cleft lip using the Byrd modification of the traditional Millard and Manchester methods. A key component of this repair technique is focused on reconstruction of the central tubercle.

Methods Fourteen patients with mean age of 5.7 months presented with bilateral cleft lip deformity and were operated on using a mod

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Crossref (5)
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Publication Date
Sat Jan 02 2021
Journal Name
Journal Of The College Of Languages (jcl)
Methods of computer word formation in the modern Russian language: Способы словообразования в сфере компьютерных неологизмов в современном русском языке
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This paper discusses the study of computer Russian language neologisms. Problems of studying computer terminology are constantly aggravated by the processes of computer technology that is introduced to all walks of life. The study identifies ways of word formation: the origin of the computer terms and the possibility of their usage in Russian language. The Internet is considered a worldwide tool of communication used extensively by students, housewives and professionals as well The Internet is a heterogeneous environment consisting of various hardware and software configurations that need to be configured to support the languages used. The development of Internet content and services is essential for expanding Internet usage. Some of the

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Publication Date
Mon Jan 01 2024
Journal Name
Journal Of The College Of Languages (jcl)
PERSPECTIVE METHODS AND DIRECTIONS IN STUDYING THE LANGUAGE OF RUSSIAN FOLKLORE: ПЕРСПЕКТИВНЫЕ МЕТОДИКИ И НАПРАВЛЕНИЯ В ИЗУЧЕНИИ ЯЗЫКА РУССКОГО ФОЛЬКЛОРА
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The paper deals with the language of Russian folklore. Folklore is a unique sphere of existence of the language, the most vivid expression of the national mentality. The folklore word embodied the perception and evaluation of the surrounding world. “What did the word in general mean for the life of the people? The word was equated ... with life itself. The word generated and explained life, it was ... the keeper of memory and the guarantee of the infinity of the future. The folklore text is studied by literary critics, ethnographers, historians, culturologists, and art historians. In the twentieth century, a new science emerged - linguo-folkloristics, the goals and objectives of which were formulated by A.T. Khrolenko only in the seven

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Publication Date
Wed Jun 03 2026
Journal Name
Applied Physics A
Hydrogen sulfide (H2S) gas sensor based on cobalt-manganese spinel oxide (MnCo2O4) prepared by chemical precipitation and green synthesis methods
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Hydrogen sulfide (H₂S) gas sensor based on cobalt–manganese spinel oxide MnCo₂O₄ thin films that were prepared by chemical precipitation and green synthesis methods. Structural, morphological, and compositional characterizations of MnCo₂O₄ thin films were performed using XRD, FE-SEM, EDS, and AFM. It was found through XRD patterns that MnCo₂O₄ was formed in a cubic spinel structure for both methods; however, the chemically precipitated thin films possessed better crystallinity and larger crystallite sizes, whereas the green-synthesized films exhibited slightly lower crystallinities and smaller sizes, as evidenced by the broader peaks observed. In addition, FE-SEM and AFM images revealed that the MnCo₂O₄ films prepared by

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Scopus Crossref
Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
Genotypic Study of Two Virulence Factors fimH and kpsMTII in Uropathogenic Escherichia coli Isolates from Children Patients with Urinary Tract Infections
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Adhesion (type 1 fimbriae) and host defense avoidance mechanisms (capsule or lipopolysaccharide) have been shown to be prevalent in Escherichia coli isolates associated with urinary tract infections. In this work, 50 uropathogenic Escherichia coli (UPEC) isolated from children with urinary tract infections were genotypically characterized by polymerase chain reaction (PCR) assay. We used two genes; fimH and kpsMTII, both of them previously identified in uropathogenic E.coli (UPEC) isolates. The PCR assay results identified fimH (90.0)% and kpsMTII (72.0)% isolates. In the present study, was also demonstrated that these genes may be included in both or one of them within a single isolate.

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Publication Date
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
The concept of suspense and mystery with some references to dickens s Novels ; A tale of two cities and Great expectations
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Publication Date
Tue Jan 01 2019
Journal Name
Plant Archives
Effect of two harrowing systems on decomposition of organic matter, some soil properties, growth and productivity of sunflower (helianthus annuus l.)
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Scopus
Publication Date
Thu Dec 24 2020
Journal Name
Psychology And Education
The Use of Ergative Verbs to Background the Role of the Agent in two Selected Short Stories: A Syntactico-Semantic Study
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The study explores the use of ergative verbs in constructing clauses and their impact on the backgrounding of the agent's role in two selected short stories. Contrary to hypothesis No. 1, the research indicates that changes in sentence patterns don't affect the meaning of the process. Additionally, hypothesis No. 2 is refuted as the middle structure is found to highlight the agent's role in the science fiction short story, Terra Infirmum, rather than concealing it as hypothesized for "The Invisible Man." The analysis uncovers that writers utilize ergative processes to narrate stories in various ways, including transitive/active voice, intransitive/active voice, and transitive/passive voice. Furthermore, the findings suggest that writers emp

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Preparation and diagnosis of new types of Schiff bases one-and two- claw and complexes to study the effectiveness of chemical
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In this research we prepared shiff bases unilateral claw( benzyl imine aniline ) and Bilateral claw ( benzayal-2-imine phenol ) in high purity reach to 98% , which it's prepared from aromatic amine with aldehydes, it's solid,thermosetting, not dissolved in water in general. Diagnosed prepared article by using infra red spectroscopy (IR) which shows azomethen grop at 1640cm-1 At this diagnosis we suggest tetra headral mechanism in this Circumstances For a reaction.

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