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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
Fri Dec 01 2023
Journal Name
Iraqi Journal Of Physics
Structural and Magnetic Properties of MnxZn1-xFe2O4 Prepared via Sol-Gel Method
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      Manganese-zinc ferrite MnxZn1-xFe2O4 (MnZnF) powder was prepared using the sol-gel method. The morphological, structural, and magnetic properties of MnZnF powder were studied using X-ray diffraction (XRD), atomic force microscopy (AFM), energy dispersive X-ray (EDX), field emission-scanning electron microscopes (FE-SEM), and vibrating sample magnetometers (VSM). The XRD results showed that the MnxZn1-xFe2O4 that was formed had a trigonal crystalline structure. AFM results showed that the average diameter of Manganese-Zinc Ferrite is 55.35 nm, indicating that the sample has a nanostructure dimension. The EDX spectrum revealed the presence of transition metals (Mn, Fe, Zn, and O) in Mang

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Publication Date
Thu May 25 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Optical and Structural Properties of SnO2 Thin Films Prepared by Sputtering Method
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SnO2 thin films of different two thicknesses were prepared an glass substrate by DC magnetron sputtering. The crystal structure and orientation of the films were investigated by XRD patterns. All the deposited films are polycrystalline. The grain size was calculated as 25.35, 28.8 nm. Morphological and compositions of the films were performed by SEM and EDX analyses respectively. The films appeared compact and rougher surface in nature. The allowed direct band gap was evaluated as 3.85 eV, and other optical constants such as refractive index, extinction coefficient, real and imaginary parts of dielectric constants were determined from transmittance spectrum in the wavelength range (300-900) nm and also analyzed.
 

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Publication Date
Thu Sep 01 2022
Journal Name
Iraqi Journal Of Physics
Positron Interactions with Some Human Body Organs Using Monte Carlo Probability Method
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In this study, mean free path and positron elastic-inelastic scattering are modeled for the elements hydrogen (H), carbon (C), nitrogen (N), oxygen (O), phosphorus (P), sulfur (S), chlorine (Cl), potassium (K) and iodine (I). Despite the enormous amounts of data required, the Monte Carlo (MC) method was applied, allowing for a very accurate simulation of positron interaction collisions in live cells. Here, the MC simulation of the interaction of positrons was reported with breast, liver, and thyroid at normal incidence angles, with energies ranging from 45 eV to 0.2 MeV. The model provides a straightforward analytic formula for the random sampling of positron scattering. ICRU44 was used to compile the elemental composition data. In this

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Publication Date
Mon Apr 20 2020
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Spectrophotometric Method for the Estimation of Ceftriaxone in Pure Form and Pharmaceuticals
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Ceftriaxone sodium were one of the widely antibacterial drugs used. Azo dye derivatization of diazonium salt that formed via the reaction between ceftriaxone with hydrochloric acid and sodium nitrite was developed for the on-research drug analysis then coupling with each one 2,5-dimethylphenol (2,5-DMP) and 4-tertbutylphenol (4-TBP) respectively in the alkaline media. The developed diazonium coupling methods include an optimization study. The results show a limit of detection and limit of quantification 0.482, 0.284 µg/mL, and 1.607, 0.945 µg/mL using 2,5-DMP and 4-TBP reagents respectively. Moreover, the recovery % obtained was 100.89%, and 103.37% at linear concentration range 3.0 – 50, and 10 – 30 µg/mL, with mo

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Publication Date
Fri Jul 05 2024
Journal Name
Journal Of Applied Spectroscopy
Spectrophotometric Method Using the Derivative for the Determination of the Drug Losartan
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Publication Date
Mon Mar 13 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Indirect Spectrophotometric Determination of Oxymetazoline Hydrochloride in Pharmaceutical Formulation Using Fluorophotometric Method
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This research involves an indirect Fluorophotometric method for the determination of microgram amount of oxymetazoline hydrochloride in the concentration range 0.1-5.0 g/ml. The method is based on the oxidation of the drug by cerium sulphate solution which is acidic medium where Ce IV is reduced to Ce III which can be excited at 259 nm to give an emitted light at 377 nm which  is directly proportional to the concentration of Ce III which is equivalent to Ce IV that is needed to oxidize the studied drug. The average recovery of the method is 100.19% and relative standard deviation (RSD) < 0.37% . The method have been successfully applied to the determination of the studied drug in its pure and pharmaceutical preparations and it wa

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Publication Date
Sun Jun 01 2014
Journal Name
International Journal Of Inventive Engineering And Science,
Increase the Capacity Amount of Data Hiding to Least Significant BIT Method
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Publication Date
Sat Mar 18 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Preparation of Silver Nanoparticles by Sol - Gel Method and Study their Characteristics
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 Powder of silver nanoparticles was prepared by Sol - Gel method successfully using silver nitrate , (AgNO3) gesture is added to sodium citrate (C6H5O7Na3) as a reducing agent and by using  Magnetic Stirrer to mix the solutions and heated then using centrifuge machine to separate the silver nanoparticles from solution .It is then dried in an oven at a temperature 40oC for 24 hours.     Structure characteristics was studied , the synthetic silver powder was prepared through the use of an (XRD). Results showed the composition of silver nanoparticles is a (fcc) and a constant lattice (4.086 ± 0.006 Ã…) by comparing it with standard tables (JCPDS) which is found perfectly matched to file with a number 04-0783, which

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Publication Date
Fri Jan 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Improved Runge-Kutta Method for Oscillatory Problem Solution Using Trigonometric Fitting Approach
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This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions. Compared to the traditional Runge-Kutta method, the Improved Runge-Kutta (IRK) method is a natural two-step method requiring fewer steps. The suggested method extends the fourth-order Improved Runge-Kutta (IRK4) method with trigonometric calculations. This approach is intended to integrate problems with particular initial value problems (IVPs) using the set functions  and   for trigonometrically fitted. To improve the method's accuracy, the problem primary frequency  is used. The novel method is more accurate than the conventional Runge-Ku

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Publication Date
Wed Mar 16 2022
Journal Name
2022 Muthanna International Conference On Engineering Science And Technology (micest)
Fast Synthesis and Characterization of Nano-SSZ-13 Zeolite by Hydrothermal Method
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