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ON NAIVE TAYLOR MODEL INTEGRATION METHOD
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Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.

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Publication Date
Wed May 08 2024
Journal Name
Journal Of Mathematics And Computer Science
How does media coverage affect a COVID-19 pandemic model with direct and indirect transmission?
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In this paper, a compartmental differential epidemic model of COVID-19 pandemic transmission is constructed and analyzed that accounts for the effects of media coverage. The model can be categorized into eight distinct divisions: susceptible individuals, exposed individuals, quarantine class, infected individuals, isolated class, infectious material in the environment, media coverage, and recovered individuals. The qualitative analysis of the model indicates that the disease-free equilibrium point is asymptotically stable when the basic reproduction number R0 is less than one. Conversely, the endemic equilibrium is globally asymptotically stable when R0 is bigger than one. In addition, a sensitivity analysis is conducted to determine which

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Publication Date
Wed Feb 01 2012
Journal Name
Ibn Al-haytham Journal For Pure And Applied Science
Using Restricted Least Squares Method to Estimate and Analyze the Cobb-Douglas Production Function with Applicatio
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Publication Date
Mon Sep 01 2025
Journal Name
Iraqi Journal Of Physics
Kinetic Study of Crystal Violet Dye Removal by Iron Oxide Nanoparticles Prepared by the Green Method
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The green method was chosen for the preparation of nano iron oxide due to its simplicity, ease of preparation, and purity, compared to other methods. Nano iron oxide was made using a substance that causes precipitation and a coating from the alcoholic extract of orange leaves from Iraq. It was examined structurally and spectrally using several techniques, including X-ray diffraction, Fourier transform infrared spectroscopy, field-emission scanning microscopy (FESEM), energy-dispersive X-ray spectroscopy, and UV-Vis spectroscopy. The diagnosis proved that the nano iron oxide was successfully prepared in a spherical form and with an average size of 71.1 nm. The nano iron oxide particles were tested for their ability to remove crystal

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Publication Date
Tue Nov 01 2022
Journal Name
Chemical Methodologies
Study of Optical and Structural Properties of CdTe Quantum Dots Capped with 3MPA Using Hydrothermal Method
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Quantum dots (QDs) can be defined as nanoparticles (NPs) in which the movement of charge carriers is restricted in all directions. CdTe QDs are one of the most important semiconducting crystals among other various types where it has a direct energy gap of about 1.53 eV. The aim of this study is to exaine the optical and structural properties of the 3MPA capped CdTe QDs. The preparation method was based on the work of Ncapayi et al. for preparing 3MPA CdTe QDs, and hen, the same way was treated as by Ahmed et al. via hydrothermal method by using an autoclave at the same temperature but at a different reaction time. The direct optical energy gap of CdTe QDs is between 2.29 eV and 2.50 eV. The FTIR results confirmed the covalent bonding betwee

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Publication Date
Fri Dec 01 2023
Journal Name
Baghdad Science Journal
Synthesis of Carbon Nanotubes Using Modified Hummers Method for Cathode Electrodes in Dye-Sensitized Solar Cell
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      In this research, carbon nanotubes (CNTs) is prepared  through the Hummers method with a slight change in some of the work steps, thus, a new method has been created for preparing carbon nanotubes which is similar to the original Hummers method that is used to prepare graphene oxide. Then, the suspension carbon nanotubes is transferred to a simple electrode position platform consisting of two electrodes and the cell body for the coating and reduction of the carbon nanotubes on ITO glass which represents the cathode electrode while platinum represents the anode electrode. The deposited layer of carbon nanotubes is examined through the scanning electron microscope technique (SEM), and the images throughout the research show the

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Publication Date
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Spectrophotometric Method Combined with HPLC for Bisphenol F Determination in Plastic Bottled Water and Thermal Paper
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Based on the diazotization-coupling reaction, a new, simple, and sensitive spectrophotometric method for determining of a trace amount of (BPF) is presented in this paper. Diazotized metoclopramide reagent react with bisphenol F produces an orange azo-compound with a maximum absorbance at 461 nm in alkaline solution. The experimental parameters were optimized such as type of alkaline medium, concentration of NaOH, diazotized metoclopramide amount, order additions, reaction time, temperature, and effect of organic solvents to achieve the optimal performance for the proposed method. The absorbance increased linearly with increasing bisphenol F concentration in the range of 0.5-10 μg mL-1 under ideal conditions, with a correlati

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Publication Date
Sun Jun 01 2025
Journal Name
Journal Of Physics: Conference Series
Optimal Variational Iteration Method for Solving Nonlinear Ordinary Differential Equations Appeared in Engineering and Applied Sciences
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Physics and applied mathematics form the basis for understanding natural phenomena using differential equations depicting the flow in porous media, the motion of viscous liquids, and the propagation of waves. These equations provide a thorough study of physical processes, enhancing the understanding of complex applications in engineering, technology, and medicine. This paper presents novel approximate solutions for the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational iteration method and the optimal variational iteration method. The variational iteration method is effectively developed by adding a control paramete

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Publication Date
Fri Jan 01 2016
Journal Name
Aip Conference Proceedings
Analysis of performance measures with single channel fuzzy queues under two class by using ranking method
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Publication Date
Fri Oct 01 2010
Journal Name
2010 Ieee Symposium On Industrial Electronics And Applications (isiea)
Distributed t-way test suite data generation using exhaustive search method with map and reduce framework
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Publication Date
Sat Jan 02 2021
Journal Name
Journal Of The College Of Languages (jcl)
The comparative method in Maupassant’s (A woman’s Life): Le système comparatif dans Une vie de Maupassant
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The comparative method plays a major role in Maupassant’s novel (A woman’s Life).This is due to a good theme choice and smooth writing style characterized by simplicity, spontaneity and brevity.

The author uses the comparative method in the introduction of his novel where he compares the monastery’s closed world to the open world of the countryside of La Normandie, which represents the dream life of the heroine Jeanne.

The present paper is an attempt to answer the question regarding the importance of applying the comparative method in the novel (A Woman’s Life) by Maupassant. The paper stresses the fact that the novelist employs the comparative method in his book for certain features .One of these features is the

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