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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
Potential Energy Expectation Value for Lithium Excited State (1s2s3s)
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The purpose of the present work is to calculate the expectation value of potential energy for different spin states (??? ? ???,??? ? ???) and compared it with spin states (??? , ??? ) for lithium excited state (1s2s3s) and Li- like ions (Be+,B+2) using Hartree-Fock wave function by partitioning techanique .The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ??? < ??? < ??? < ???

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Publication Date
Sat Dec 31 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Performance Study of Electrodialysis for Treatment Fuel Washing Wastewater
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In this work, electrodialysis (ED) has been demonstrated to be appropriate technique for reducing the electrical conductivity of real wastewater from fuel washing unit, which has been previously treated by other electrochemical technology (electrocoagulation and electrooxidation).  A five cell electrodialysis stack, with an active membrane area of 60 cm2 per cell was employed. During a batch recirculation mode ED system, the effects of parameters such as electrical potential applied (6-18 V) and flow rate of streams (0.5-1.7 L/min.) on the performance of the total dissolved solids (TDS) separation and specific power consumption (SPC) were studied. The results indicate that the process of ED under potential (15 V) and flow

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Publication Date
Mon Sep 01 2014
Journal Name
Al-khwarizmi Engineering Journal
Heterogeneous Photocatalytic Degradation for Treatment of Oil from Wastewater
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In the present study, advanced oxidation process / heterogeneous photocatalytic process (UV/TiO2/Fenton) system was investigated to the treatment of oily wastewater. The present study was conducted to evaluate the effect of hydrogen peroxide concentration H2O2, initial amount of the iron catalyst Fe+2, pH, temperature, amount of TiO2 and the concentration of oil in the wastewater.  The removal efficiency for the system UV/TiO2/Fenton at optimal conditions and dosage (H2O2 = 400mg/L, Fe+2 = 40mg/L, pH=5, temperature =30oC, TiO2=75mg/L) for 1000mg/L load was found to be 77%.

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Publication Date
Mon Jan 02 2017
Journal Name
European Journal Of Scientific Research
Fast approach for arabic text encryption using genetic algorithm
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As s widely use of exchanging private information in various communication applications, the issue to secure it became top urgent. In this research, a new approach to encrypt text message based on genetic algorithm operators has been proposed. The proposed approach follows a new algorithm of generating 8 bit chromosome to encrypt plain text after selecting randomly crossover point. The resulted child code is flipped by one bit using mutation operation. Two simulations are conducted to evaluate the performance of the proposed approach including execution time of encryption/decryption and throughput computations. Simulations results prove the robustness of the proposed approach to produce better performance for all evaluation metrics with res

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Publication Date
Sun Jul 23 2023
Journal Name
Al-rafidain Journal Of Medical Sciences ( Issn 2789-3219 )
Future of Engineered Phage Therapy for Clostridium difficile Infections
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Bacteriophages have the potential to eliminate both antibiotic-resistant and sensitive bacteria; as a result, they have become a major focus of such research. In contrast to antibiotics, which assault the entire bacterial population without discrimination, bacteriophages have a limited set of characteristics that allow them to target infectious microbes while avoiding friendly species (commensal microbiota). Nevertheless, large groups of naturally occurring bacteriophages that are well-differentiated and selective for the most clinically recognized pathogenic bacterial strains are required. Utilizing genetic engineering techniques that modify the target phage genome to synthesize phages with known characteristics in a brief period o

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Publication Date
Sun Jan 01 2012
Journal Name
International Journal Of Cyber-security And Digital Forensics (ijcsdf)
Genetic Algorithm Approach for Risk Reduction of Information Security
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Nowadays, information systems constitute a crucial part of organizations; by losing security, these organizations will lose plenty of competitive advantages as well. The core point of information security (InfoSecu) is risk management. There are a great deal of research works and standards in security risk management (ISRM) including NIST 800-30 and ISO/IEC 27005. However, only few works of research focus on InfoSecu risk reduction, while the standards explain general principles and guidelines. They do not provide any implementation details regarding ISRM; as such reducing the InfoSecu risks in uncertain environments is painstaking. Thus, this paper applied a genetic algorithm (GA) for InfoSecu risk reduction in uncertainty. Finally, the ef

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Publication Date
Wed Aug 10 2022
Journal Name
Mathematical Statistician And Engineering Applications
Results for the Groups SL(2,34 ) and SL(2,36 )
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Publication Date
Sat Oct 08 2022
Journal Name
Mathematical Statistician And Engineering Applications
Illation for the Groups SL(2,112 ) and SL(2,132 )
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Publication Date
Mon Jan 01 2024
Journal Name
Ieee Transactions On Emerging Topics In Computational Intelligence
Reservoir Network With Structural Plasticity for Human Activity Recognition
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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Interdisciplinary Mathematics
Enforcement for the groups SL(2,125) and SL(2,3125)
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The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

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