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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 Sep 12 2020
Journal Name
Al-kindy College Medical Journal
Spectrum of central nervous system infections in neurosciences hospital in two years : a retrospective study
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Background :Infectious disorders in general have high morbidity and mortality.. CNS infections include many disorders like bacterial meningitis, tuberculous and other subacute and chronic meningitis, viral meningitis, cerebral abscess, spinal cord infections, and others.
Objective: To assess our locality about prevalence of CNS infections , to have more awareness regarding CNS infections, and to try to find the proper way to reduce their prevalence and to treat them in appropriate way.
Method :We revised the records of all the cases of CNS infections excluding cases of spinal cord infections who were admitted in the wards of neuroscience hospital over the previous two years ( from July/2010 to June 2012 ),those were 132 cases.Seaso

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Publication Date
Fri Apr 01 2016
Journal Name
Journal Of Engineering
Aerobic biodegradation of phenol by Immobilized Pseudomonas sp. cells in two different bio-carrier matrices
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Biotreatment using immobilized cells (IC) technology has proved to be the most promising and most economical approach for the removal of many toxic organic pollutants found in petroleum-refinery wastewater (PRW) such as phenol. This study was undertaken to evaluate the degradation of phenol by Pseudomonas cells individually immobilized in two different bio-carrier matrices including polyvinyl alcohol-guar gum (PVA-GG) and polyvinyl alcohol-agar agar (PVA-AA). Results of batch experiments revealed that complete removal of phenol was attained in the first cycle after 150 min using immobilized cells (IC) in both PVA-GG and PVA-AA. Additional cycles were confirmed to evaluate the validity of recycling beads of immob

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Publication Date
Thu Dec 01 2011
Journal Name
Journal Of Engineering
Effect of Steering Wheel Vibration on drivers Hands in a Two-Wheel Drivers Hand tractor
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The paper presents research results of the vibration transmitted from the steering wheel of the
tractor with a 2-wheel drive to the driver’s hands. The vibration measurements were carried out on the
tractor randomly chosen from the collage of agriculture / university of Baghdad. Before testing the
tractor was examined and adjusted following the producer’s recommendations. The vibration levels
were measured during the operation tillage at idling and at full load .The field was 3١٫٧ m above level
sea. Soil was treated at soil constant moisture (1٧-20 %) with depth of plowing (١٧ cm). During
operation the weather temperature was measured (15 C) and humidity was ( 27 % ) The vibration level
on the steering whee

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Publication Date
Sun Oct 05 2025
Journal Name
Journal Of Baghdad College Of Dentistry
An Evaluation of Ion Released from Two Brands of Brackets in Three Types of Mouthwashes
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Background: Mouthwashes used widely as ancillary to mechanical oral hygiene methods. Little information provided about the effect of mouthwashes on ions released from orthodontic brackets. Therefore, the present study has been established to evaluate the effect of different mouthwashes on the corrosion resistance and the biocompatibility of two brands of brackets. Materials and Methods: Eighty premolar stainless steel brackets were used (40 brackets from each brand). They were subdivided into four subgroups (n=10) according to immersion media (deionized distilled water, Corsodyl, Listerine and Silca herb mouthwashes). Each bracket was stored in a closely packed glass tube filled with 15ml of the immersion media and incubated for 45 days at

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Publication Date
Fri Mar 31 2017
Journal Name
Al-khwarizmi Engineering Journal
Active Vibration Suppression of Smart Cantilever Beam with Sliding Mode Observer Using Two Piezoelectric Patches
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This paper presents a vibration suppression control design of cantilever beam using two piezoelectric ‎patches. One patch was used as ‎an actuator element, while the other was used as a sensor. The controller design was designed via the balance realization reduction method to elect the reduced order model that is most controllable and observable. ‎the sliding mode observer was designed to estimate six states from the reduced order model but three states are only used in the control law. Estimating a number of states larger than that used is in order to increase the estimation accuracy. Moreover, the state ‎estimation error is proved bounded. An ‎optimal LQR controller is designed then using the ‎estimated states with the slid

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Publication Date
Thu Dec 01 2016
Journal Name
Ama, Agricultural Mechanization In Asia, Africa And Latin America
Effect of three honeycomb interplant distances on growth and flowering of two cultivars of bean
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A factorial experiment (2× 3) in randomized complete block design (RCBD) with three replications was conducted to examine the effect of honeycomb selection method using three interplant distances on the vegetative growth, flowering, and fruit set of two cultivars of bean, Bronco and Strike. Interplant distances used were 75× 65 cm, 90× 78 cm, and 105× 91 cm (row× plant) represent short (high plant density), intermediate (intermediate plant density), and wide (low plant density) distance, respectively. Parameters used for selection were number of days from planting to the initiation of first flower, number of nodes formed prior to the onset of first flower, and number of main branches. Results showed significant superiority of the Strik

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Scopus
Publication Date
Sun Jan 01 2023
Journal Name
Ibero- American Journal Of Exercise And Sports Psychology
THE EFFECT OF SPECIAL EXERCISES USING TWO DESIGNED DEVICES IN DEVELOPING SOME DEFENSIVE HANDBALL SKILLS
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Scopus
Publication Date
Sun Sep 01 2019
Journal Name
Al-khwarizmi Engineering Journal
Pneumatic Control System of Automatic Production Line Using Two Method of SCADA/HMI Implement PLC
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       This work focuses on the implementation of interfaces for human machine interaction (HMI) for control and monitor of automatic production line. The automatic production line which can performance feeding, transportation, sorting functions.      

            The objectives of this work are implemented two SCADA/HMI system using two different software. TIA portal software was used to build HMI, alarm, and trends in touch panel which are helped the operator to control and monitor the production line. LabVIEW software was used to build HMI and trends on the computer screen and was linked with Micros

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Crossref (1)
Crossref
Publication Date
Sat Dec 17 2011
Journal Name
Journal Of Engineering
Effect of Steering Wheel Vibration on drivers Hands in a Two-Wheel Drivers Hand tractor
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The paper presents research results of the vibration transmitted from the steering wheel of the tractor with a 2-wheel drive to the driver’s hands. The vibration measurements were carried out on the tractor randomly chosen from the collage of agriculture / university of Baghdad. Before testing the tractor was examined and adjusted following the producer’s recommendations. The vibration levels were measured during the operation tillage at idling and at full load .The field was 31.7 m above level sea. Soil was treated at soil constant moisture (17-20 %) with depth of plowing (17 cm). During operation the weather temperature was measured (15 C) and humidity was ( 27 % ) The vibration level on the steering wheel was measured and analyzed .T

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Publication Date
Fri Jan 01 2021
Journal Name
Aip Conference Proceedings
Study of rheological and mechanical properties of bitumen blended with two alpha phases of polyamide
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