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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
Sat Oct 03 2026
Journal Name
Al–bahith Al–a'alami
Methods and Means of public relation in dealing with Bureaucracy
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The importance of Public Relations activity has increased during the last half of the last century as a specialized and modern administrative function in most institutions. It has, moreover, become an integral part of activities of those institutions of various types, due to its pivotal role in building its reputation and drawing a good mental image among its audiences, as well as its influential and basic role in maintaining communication and the communication between its members at its various levels and their job tasks to ensure the greatest amount of understanding and to enhance trust between them. This is why public relations activity has become indispensable in all institutions, and without it, it is difficult to achieve any coordi

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Publication Date
Wed Jan 30 2019
Journal Name
International Journal Of Applied Pharmaceutics
THE IMPACT OF NEW TARGETING METHODS IN THE CANCER THERAPY
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Rapid development has achieved in treating tumor to stop malignant cell growth and metastasis in the past decade. Numerous researches have emerged to increase potency and efficacy with novel methods for drug delivery. The main objective of this literature review was to illustrate the impact of current new targeting methods to other previous delivering systems to select the most appropriate method in cancer therapy. This review first gave a brief summary of cancer structure and highlighted the main roles of targeting systems. Different types of delivering systems have been addressed in this literature review with focusing on the latest carrier derived from malarial protein. The remarkable advantages and main limitations of the later

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Publication Date
Wed Dec 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison Between Nelson-Olson Method and Two-Stage Limited Dependent Variables (2SLDV ) Method for the Estimation of a Simultaneous Equations System (Tobit Model)
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This study relates to  the estimation of  a simultaneous equations system for the Tobit model where the dependent variables  ( )  are limited, and this will affect the method to choose the good estimator. So, we will use new estimations methods  different from the classical methods, which if used in such a case, will produce biased and inconsistent estimators which is (Nelson-Olson) method  and  Two- Stage limited dependent variables(2SLDV) method  to get of estimators that hold characteristics the good estimator .

That is , parameters will be estim

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Publication Date
Sun Nov 04 2018
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
MEASURING OBESITYLEVEL BY BIO-ELECTRICAL IMPEDANCE ANALYSIS TECHNIQUE AND COMPARED TO TRADITIONAL METHODS: MEASURING OBESITYLEVEL BY BIO-ELECTRICAL IMPEDANCE ANALYSIS TECHNIQUE AND COMPARED TO TRADITIONAL METHODS
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This study aimed to determine obesity level of some population in Baghdad by using Bio-electrical impedance analysis (BIA) and compared with anthropometric measurements such as body mass index (BMI), waist circumference (WC) and waist-to-hip ratio (WHR). Statistical analysis results of linear correlation coefficients for obesity indicators showed that BIA correlation 0.92 was most significant and reliable for obesity measurement.

Results of BIA method for age group 20-29 years showed that 44.4% of females were healthy body while 37.8% of males suffer from increased body fat. Results of age group 30-39 year showed that 32.6 of females were in healthy body and 42% of males were obese. In case age group 40-4

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Publication Date
Fri Sep 15 2023
Journal Name
Journal Of Baghdad College Of Dentistry
FEM: Mono-implant cement retained crown with two different adhesive materials
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Background: The finite element method (FEM) is expected to be one of the most effective computational tools for measuring the stress on implant-supported restorations. This study was designed using the 3D-FEM to evaluate the effect of two adhesive luting types of cement on the occlusal stress and deformation of a hybrid crown cemented to a mono-implant. Materials and Method: The mono-screw STL file was imported into the CAD/CAM system library from a database supported by De-Tech Implant Technology. This was to assist in the accurate reproduction of details and design of a simulated implant abutment. Virtually, a digital crown was designed to be cemented on an abutment screw. A minimum occlusal thickness of 1mm and marginal fitting of 1.2

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Publication Date
Mon Jun 01 2015
Journal Name
Journal Of The College Of Languages (jcl)
A Stylistic Analysis of Two Selected, English and Arabic, War Poems
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War as a human phenomenon, has its own literature. Poetry is a major genre in this literature. This paper is an attempt to investigate and analyse some stylistic features in two selected, English and Arabic, war poems. These poems share the same theme.Both promote the principle of sacrificing one’s own life for the sake of homeland.  This paper limits itself to analyse, thecontent words, tenses, semantic grouping of vocabulary and foregrounding in the two poems. The areas of analysis show great similarities in distributing the general content words (nouns, verbs, adjectives, and adverbs). In the analysis of the semantic areas of each content word, these poems reveal some similarities and some differences in their frequency rates.

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Publication Date
Thu Aug 25 2022
Journal Name
Special Education
Speech Act of Persuasion in two Political Speeches American and British.
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BN Rashid…, Special Education, 2022

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Publication Date
Thu Dec 01 2016
Journal Name
Iraqi Journal Of Physics, 2016
Energy transfer process between two laser compounds coumarin 334 & rhodamine 590
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Abstract: In the current research the absorption and fluorescence spectrum of Coumarin (334) and Rhodamine (590) in ethanol solvent at different concentration (10-3, 10-4, 10-5) M had been studied. The absorption intensity of these dyes increases as the Concentration increase in addition to that the spectrum was shifted towards the longer wavelength (red shift). The energy transfer process has been investigated after achievement this condition. The fluorescence peak intensity of donor molecule was decrease and its bandwidth will increases on the contrary of the acceptor molecule its intensity increase gradually and its bandwidth decreases as the acceptor concentration increase.

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Publication Date
Tue Dec 01 2009
Journal Name
Iraqi Journal Of Physics
Two-dimensional Crystallization of Silica nanospheres using Coplanar DC Electric field
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Abstract:Two-dimensional crystal has been achieved and controlled with the aid of DC electric field applied between two electrodes at 5 millimeters separating distance between them. Sol-gel method has been used to prepared nanosilica particle which used in this work as well as TiO2 nanopaowder. The assembly of the silica particles is due to the interaction between the electrical force, the particles dipole, and the interaction between the particles themselves. When a DC voltage is applied, the particles accumulated and crystallized on the surface between the electrodes. The Light diffraction demonstrates that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is

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Publication Date
Thu Jun 16 2022
Journal Name
Al-khwarizmi Engineering Journal
Intelligent Tuning Control of two Link Flexible Manipulator with Piezoelectric Actuator
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This paper represents an experimental study on the application of smart control represented by the use of the fuzzy logic controller. Two-link flexible manipulators that are used in airspace and military applications are made of flexible materials characterized by low frequency and damping ratio. To solve this problem, this paper proposes the use of smart materials (piezoelectric transducers), where each link is bonded with a pair of piezoelectric transducers that act as a sensor and another as an actuator. As the arm vibrates because of the movement generated by the motor, this voltage is controlled by a regulator inside the LABVIEW® 2020 software and sends the output control voltage to the piezoelectric actuator. Experimental results

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