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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
Wed Mar 30 2022
Journal Name
Journal Of Educational And Psychological Researches
Evaluating Educational Programs in Combating Indecent Behaviors Among University Students Using Structural Equation Modeling (Field study: Northern Border University)
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The study aimed to evaluate educational programs efficiency in applying the best educational practices to educate students from the dangers of indecent behaviors, in line with higher education policy and the appropriateness of educational program dimensions to spread awareness among students to not fall into the indecent behaviors clutches. The study adopted the inductive exploratory approach through structural equation modeling and the descriptive analysis of the collected data from randomly selected sample (n=385) from educational academics at Northern Border University in the Saudi Arabia using a specially designed survey tool to meet study purposes to evaluate dimensions of teaching methods, evaluation tools, training courses, course

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Publication Date
Sat Mar 01 2025
Journal Name
Iraqi Journal Of Physics
Design an Efficient Neural Network to Determine the Rate of Contamination in the Tigris River in Baghdad City
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This article proposes a new technique for determining the rate of contamination. First, a generative adversarial neural network (ANN) parallel processing technique is constructed and trained using real and secret images. Then, after the model is stabilized, the real image is passed to the generator. Finally, the generator creates an image that is visually similar to the secret image, thus achieving the same effect as the secret image transmission. Experimental results show that this technique has a good effect on the security of secret information transmission and increases the capacity of information hiding. The metric signal of noise, a structural similarity index measure, was used to determine the success of colour image-hiding t

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Publication Date
Sun Feb 25 2024
Journal Name
Baghdad Science Journal
Efficient Task Scheduling Approach in Edge-Cloud Continuum based on Flower Pollination and Improved Shuffled Frog Leaping Algorithm
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The rise of edge-cloud continuum computing is a result of the growing significance of edge computing, which has become a complementary or substitute option for traditional cloud services. The convergence of networking and computers presents a notable challenge due to their distinct historical development. Task scheduling is a major challenge in the context of edge-cloud continuum computing. The selection of the execution location of tasks, is crucial in meeting the quality-of-service (QoS) requirements of applications. An efficient scheduling strategy for distributing workloads among virtual machines in the edge-cloud continuum data center is mandatory to ensure the fulfilment of QoS requirements for both customer and service provider. E

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Publication Date
Fri Jul 01 2022
Journal Name
Journal Of Molecular Structure
Interaction behavior of curcumin encapsulated onto functionalized SBA-15 as an efficient carrier and release in drug delivery
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In this work, mesoporous silica SBA-15 was prepared and functionalized with amine groups (i.e., NH2) to form NH2/SBA-15. The curcumin (CUR) was encapsulated into the surface and pore of NH2/SBA-15 to create CUR@NH2/SBA-15 as an efficient carrier in drug delivery systems (DDSs). The three samples (i.e., SBA-15, NH2/SBA-15, and CUR@NH2/SBA-15) were characterized. The study investigated the effect of the carrier dose, initial CUR concentration, pH, and contact time on the CUR loading efficiency (DLE%) via adsorption. The best DLE% for the SBA-15 and NH2/SBA-15 were found to be 45% and 89.7%, respectively. The Langmuir isotherm had a greater correlation coefficient (R2) of 0.998 for SBA-15. A pseudo-secondorder kinetic model seemed to fit well

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Publication Date
Wed Aug 23 1989
Journal Name
J. Agric. Water Reso. Res 8 (1), 11-25‏
Response Of Two Barley Mutants CV. Arivat To Salinity‏
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Publication Date
Wed Jun 20 2012
Journal Name
Journal Of Biotechnology Research Center
Evaluation of toxic effects of two weight reduction pills
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Abstract his study involved evaluation of side effects of two weight reduction pills that had been widely distributed in the last period. Two weight reduction compounds are studied, Reductil (containing chemical substances) and Chinese’s weight reduction herbs (containing natural substances). Two doses for each compound are used in this research; 5mg/ml and 0.5mg/ml for Reductil, while 30mg/ml and 10mg/ml for Chinese weight reduction herbs. To evaluate the toxic effects of these compounds, the following parameters were determined which include mitotic index (cytogenetic analysis), serum FSH and LH hormones level (follicles stimulation hormone/FSH and lutenising hormone/LH) and histological examination of female mice ovaries. Control group

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Publication Date
Sun Dec 29 2024
Journal Name
Muthanna Journal Of Pure Science
Two-Fold Cryptography: Enhancing Image Security with Henon Map
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This paper introduces an innovative method for image encryption called "Two-Fold Cryptography," which leverages the Henon map in a dual-layer encryption framework. By applying two distinct encryption processes, this approach offers enhanced security for images. Key parameters generated by the Henon map dynamically shape both stages of encryption, creating a sophisticated and robust security system. The findings reveal that Two-Fold Cryptography provides a notable improvement in image protection, outperforming traditional single-layer encryption techniques.

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Publication Date
Mon Nov 19 2018
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
Study of Two Types Finite Graphs in KU-Semigroups
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In this ˑwork, we present theˑ notion of the ˑgraph for a KU-semigroup as theˑundirected simple graphˑ with the vertices are the elementsˑ of and weˑˑstudy the ˑgraph ofˑ equivalence classesˑofˑ which is determinedˑ by theˑ definition equivalenceˑ relation ofˑ these verticesˑ, andˑ then some related ˑproperties areˑ given. Several examples are presented and some theorems are proved. Byˑ usingˑ the definitionˑ ofˑ isomorphicˑ graph, ˑwe showˑ thatˑ the graphˑ of equivalence ˑclasses ˑand the ˑgraphˑof ˑa KU-semigroup ˑ areˑ theˑ sameˑ, in special cases.

Publication Date
Sun May 01 2022
Journal Name
Journal Of Engineering
Parametric Study of a Two-Phase Closed Thermosyphon Loop
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A theoretical and experimental investigation was carried out to study the behavior of a two-phase closed thermosyphon loop (TPCTL) during steady-state operation using different working fluids. Three working fluids were investigated, i.e., distilled water, methanol, and ethanol. The TPCTL was constructed from an evaporator, condenser, and two pipelines (riser and downcomer). The driving force is the difference in pressure between the evaporator and condenser sections and the fluid returns to the heating section by gravity. In this study, the significant parameters used in the experiments were filling ratios (FR%) of 50%, 75%, and 100% and heat-input range at the evaporator section of 215-860.2 W. When the loop reached to

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Publication Date
Sat Jul 01 2023
Journal Name
Iop Conference Series: Earth And Environmental Science
Performance Evaluation of Two Date Palm Frond Cutting Saws
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Abstract<p>Traditional tree management is laborious and costly, thus this work aimed to study the performance of two different types of frond cutting saws (reciprocating saw and vibrating saw) and examine the two saws on five date palm varieties. Four parameters were examined, including cutting time for a single frond, the power needed for cutting a single frond, frond cutting productivity expressed as tree/h, and vibration conveyed to the worker’s hand. A field experiment was designed according to the nested randomized complete block design, including five date palm varieties as the main plot and the type of saw as a sub-plot. Means were compared using the least significant differences (LSD 0</p> ... Show More
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