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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
Fri Jul 01 2016
Journal Name
Journal Of Engineering
Nonlinear Behavior of Self -Compacting Reinforced Concrete Two-Way Slabs with Central Square Opening under Uniformly Distributed Loads
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This research is carried out to investigate the behavior of self-compacting concrete (SCC) two-way slabs with central square opening under uniformly distributed loads. The experimental part of this research is based on casting and testing six SCC simply supported square slabs having the same dimentions and reinforcement. One of these slabs was cast without opening as a control slab. While, the other five slabs having opening ratios (OR) of 2.78%, 6.25%, 11.11%, 17.36% and 25.00%. From the experimental results it is found that the maximum percentage decrease in cracking and ultimate uniform loads were 31.82% and 12.17% compared to control slab for opening ratios (OR

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Publication Date
Fri Jun 01 2007
Journal Name
Journal Of The College Of Languages (jcl)
TECHNIQES OF SURREALISM: A STUDY IN TWO NOVELS BY THOMAS PYNCHON, V. AND THE CRYING OF LOT 49
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Surrealism is a twentieth-century literary and artistic movement oriented toward the liberation of the mind. Surrealism is a reaction to the philosophy of rationalism which was believed to be the cause of the disaster of World War I. It emphasizes the expression of the imagination as revealed in dreams and presented without conscious control, the unexpected juxtapositions of objects, the withdrawal of the self, and the exploitation of chance effects.
Surrealism began in Paris in the early 1920s, as Europe emerged from the devastation of World War I. A group of writers, artists, and filmmakers, led by the poet André Breton, adopted the word surréaliste (meaning, roughly, "super-real") as a label for their artistic activities. Influen

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis and Biological Evaluation of Two New Analogues of Gonadotropin Releasing Hormone (GnRH)D-alanine8 and D-alanine
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So far synthesis of Gonadotropin Releasing Hormone (GnRH) analogues reported in the literature has clarified some aspects of structural activity of the naturally released GnRH. As a part of continuing efforts for further understanding of this relationship, the present investigation was undertaken which involved synthesis and biological evaluation of two GnRH analogues, firstly, by replacement of the amino acid L-Argenine in the 8th position at the backbone structure of the natural hormone by the amino acid D-Alanine; and secondly, by replacement of the amino acid L-Glycine in the 10th position by D-Alanine also at the backbone structure of the nature hormone, to obtain the following analogues respectively:

P

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Publication Date
Tue Dec 01 2015
Journal Name
Journal Of Economics And Administrative Sciences
Cognitive Bias and Organizational Inertia are Two Functions of Strategic Change An Experimental Study in Amman Stock Market
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The research aims at considering the reality of cognitive bias and organizational inertia as determinants of strategic change in a sample of companies listed in Amman Stock Market. To achieve objectives of the research, a model consisting of two independent variables has been designed, namely:

(1) The cognitive bias resulting from (escalating commitment, analogy, previous assumptions, representative generalization, command and control, convergent thinking), and (2) Organizational inertia due to (Icarus discrepancy, power distribution, rooted organizational culture), and a dependent variable, strategic change in (leadership patterns, strategy, the organization per se). 

From the model two main hypotheses were derived;

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Publication Date
Sat Jul 01 2000
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
COMPARATIVE ECOLOY OF TWO SPECIES OF BIVALVE CORBICULA FL UMINEA AND CORBICULE FL UMINALIS IN SHATT AL-ARAB
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Some aspects of population dynamics of both corbicula species inhabiting intertidal zone of
shatt al-Arab are described. These informations are explained in accordance with the possible
occurrence of competition between the two related species.

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Publication Date
Thu Apr 01 2021
Journal Name
Iraqi Journal Of Applied Physics
Effects of Solvent Properties on Absorption and Fluorescence Characteristics of Two Organic Dyes Used as Random Gain Media
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In this work, the effects of solvent properties on the characteristics of absorption and fluorescence for two laser dyes was studied. Dyes used in this work include Coumarin 5400 and DCM, while the solvents include ethanol, methanol, acetone, propanol and chloroform. Coumarin 5400 dye shows sharp fluorescence peaks in the green band of visible region while the DCM dye shows relatively wide band within 590-630 nm. Therefore, the selection of any dye for random gain medium applications should be performed after determining the most appropriate solvent as the optimum fluorescence characteristics are obtained.

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Publication Date
Tue Jan 01 2019
Journal Name
Molecular Biology Research Communications
Association study of two single nucleotide polymorphisms rs10757278 and rs1333049 with atherosclerosis, a case-control study from Iraq
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Scopus
Publication Date
Tue Mar 20 2018
Journal Name
Mustansiria Dental Journal
A comparative Study in the Antibacterial effect of Eugenol as Hand Wash Material with two Types of Soap
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Hands have consistently been an important vehicle in the transmission of disease (1). Thus, thorough hand-washing remains the single most important factor in preventing infection specially in hospitals and labs.Twenty-nine non-clinical volunteers (do not work or come in contact with a clinical or hospital setting) that lacked visible skin injuries, eczema or apparent skin disease were used, those subjects were all tested by a material of each of the three used in the study weekly and laboratory tests were done pre- and post washing.All three material were effective , Eugenol extract as effective as the bar and lotion soap. And this was confirmed statistically.Eugenol has a great antibacterial action even in small concentration and t

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Phytochemical Study of some Flavonoids Present in the Fruits of Two Ammi L. Species Wildly Grown in Iraq
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Ammi species belong to the family Umbellifereae that provide a host of bioactive compounds (mainly coumarins and flavonoids) of important biological activities, like prevention and treatment of heart and vascular disease and some types of cancer. Literature survey revealed that there was no study concerning Ammi flavonoids in Iraq. Ammi majus and Ammi visnaga, which are wildly grown in Iraq, were chosen for this study. This study concerned with extraction, identification, isolation, and purification of some biologically important flavonols quercetin and kaempferol from the fruits of Ammi majus and Ammi visnaga. Extraction of these flavonols was carried out using 85% methanol and 90% e

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Crossref (6)
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Publication Date
Sat Jan 19 2019
Journal Name
Iraqi Journal Of Agricultural Sciences
EFFECT OF TWO HARROWING SYSTEMS ON DECOMPOSITION OF ORGANIC MATTER, SOME SOIL PROPERTIES, GROWTH AND PRODUCTIVITY OF MAIZE
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A field experiment was conducted at Abu-Ghrib during 2013- 2014 season to study the effect of harrowing systems on the decomposition and fermentation on organic matter(OM) when added and mixed with the soil under special technology, as well as its effect on the growth parameters and productivity of (Zea mays L. 5018). The experiment was laid out using factorial randomized complete block design (RCBD) in split-split design with three replications in SCL bare soil with a percent of moisture ranged from 16 – 18 %. The main plots were designated to the two systems of harrowing (Rotary Harrowand Disc Harrow ). The sub main plots were specified for two organic matters ( Sheep manure ,cow manure ) . Data were statistically analyzed, and

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