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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 Dec 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
Application of “LIML_LVR” method practically according to the general formula K-CLASS on suggestion simultaneous equation
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في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR

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Publication Date
Wed Jun 10 2009
Journal Name
Iraqi Journal Of Laser
Simulation of passively Q-switched rate equation using saturable crystal Dy +2: CaF2 with ruby laser
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The simulation of passively Q-switching is four non – linear first order differential equations. The optimization of passively Q-switching simulation was carried out using the constrained Rosenbrock technique. The maximization option in this technique was utilized to the fourth equation as an objective function; the parameters, γa, γc and β as were dealt with as decision variables. A FORTRAN program was written to determine the optimum values of the decision variables through the simulation of the four coupled equations, for ruby laser Q–switched by Dy +2: CaF2.For different Dy +2:CaF2 molecules number, the values of decision variables was predicted using our written program. The relaxation time of Dy +2: CaF2, used with ruby was

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Publication Date
Fri Mar 29 2024
Journal Name
Iraqi Journal Of Science
Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment
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     This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie

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Publication Date
Tue Dec 10 2024
Journal Name
Mesopotamian Journal Of Cybersecurity
Development of Robust and Efficient Symmetric Random Keys Model based on the Latin Square Matrix
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Symmetric cryptography forms the backbone of secure data communication and storage by relying on the strength and randomness of cryptographic keys. This increases complexity, enhances cryptographic systems' overall robustness, and is immune to various attacks. The present work proposes a hybrid model based on the Latin square matrix (LSM) and subtractive random number generator (SRNG) algorithms for producing random keys. The hybrid model enhances the security of the cipher key against different attacks and increases the degree of diffusion. Different key lengths can also be generated based on the algorithm without compromising security. It comprises two phases. The first phase generates a seed value that depends on producing a rand

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Publication Date
Sat Jan 01 2022
Journal Name
Indonesian Journal Of Electrical Engineering And Computer Science
Construct an efficient distributed denial of service attack detection system based on data mining techniques
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<span>Distributed denial-of-service (DDoS) attack is bluster to network security that purpose at exhausted the networks with malicious traffic. Although several techniques have been designed for DDoS attack detection, intrusion detection system (IDS) It has a great role in protecting the network system and has the ability to collect and analyze data from various network sources to discover any unauthorized access. The goal of IDS is to detect malicious traffic and defend the system against any fraudulent activity or illegal traffic. Therefore, IDS monitors outgoing and incoming network traffic. This paper contains a based intrusion detection system for DDoS attack, and has the ability to detect the attack intelligently, dynami

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Publication Date
Sun Aug 07 2022
Journal Name
Nanomaterials
Efficient Heat Transfer Augmentation in Channels with Semicircle Ribs and Hybrid Al2O3-Cu/Water Nanofluids
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Global technological advancements drive daily energy consumption, generating additional carbon-induced climate challenges. Modifying process parameters, optimizing design, and employing high-performance working fluids are among the techniques offered by researchers for improving the thermal efficiency of heating and cooling systems. This study investigates the heat transfer enhancement of hybrid “Al2O3-Cu/water” nanofluids flowing in a two-dimensional channel with semicircle ribs. The novelty of this research is in employing semicircle ribs combined with hybrid nanofluids in turbulent flow regimes. A computer modeling approach using a finite volume approach with k-ω shear stress transport turbulence model was used in these simu

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Publication Date
Tue May 01 2018
Journal Name
International Journal Of Computer Trends And Technology
Two Phase Approach for Copyright Protection and Deduplication of Video Content in Cloud using H.264 and SHA-512
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Cloud computing offers a new way of service provision by rearranging various resources over the Internet. The most important and popular cloud service is data storage. In order to preserve the privacy of data holders, data are often stored in cloud in an encrypted form. However, encrypted data introduce new challenges for cloud data deduplication, which becomes crucial for big data storage and processing in the cloud. Traditional deduplication schemes cannot work on encrypted data. Among these data, digital videos are fairly huge in terms of storage cost and size; and techniques that can help the legal aspects of video owner such as copyright protection and reducing the cloud storage cost and size are always desired. This paper focuses on v

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Publication Date
Tue May 28 2019
Journal Name
Al-khwarizmi Engineering Journal
Heuristic D* Algorithm Based on Particle Swarm Optimization for Path Planning of Two-Link Robot Arm in Dynamic Environment
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 Finding a path solution in a dynamic environment represents a challenge for the robotics researchers, furthermore, it is the main issue for autonomous robots and manipulators since nowadays the world is looking forward to this challenge. The collision free path for robot in an environment with moving obstacles such as different objects, humans, animals or other robots is considered as an actual problem that needs to be solved.  In addition, the local minima and sharp edges are the most common problems in all path planning algorithms. The main objective of this work is to overcome these problems by demonstrating the robot path planning and obstacle avoidance using D star (D*) algorithm based on Particle Swarm Optimization (PSO)

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Publication Date
Tue Feb 15 2022
Journal Name
International Journal Of Early Childhood Special Education
Analysis of science books ( two chemistry units ) for the first and second grades of intermediate according to Environmental Ethics
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The aim of the current research is to analyze the content of the two science books (chemistry units) for the two grades ( first and second intermediate ) according to environmental ethics, as the research community and its sample of the two science books (chemistry units) for the two grades ( first and second intermediate ), approved by the Iraqi Ministry of Education for the academic year ( 2021-2022 ), and the two researchers adopted the descriptive ( analytical ) approach, and the researchers built a standard for environmental ethics, and the validity of the tool was confirmed by presenting it to a group of experts, and then the researchers analyzed the two books in light of the standard prepared based on the implicit explicit idea, and

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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of Engineering
Development and Verification of the Capacity Curve for Two Dimensional Reinforced Concrete Moment-Resisting Frames System under Earthquake Loading
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Pushover analysis is an efficient method for the seismic evaluation of buildings under severe earthquakes. This paper aims to develop and verify the pushover analysis methodology for reinforced concrete frames. This technique depends on a nonlinear representation of the structure by using SAP2000 software. The properties of plastic hinges will be defined by generating the moment-curvature analysis for all the frame sections (beams and columns). The verification of the technique above was compared with the previous study for two-dimensional frames (4-and 7-story frames). The former study leaned on automatic identification of positive and negative moments, where the concrete sections and steel reinforcement quantities the

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