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1

Wavelet-based numerical solution for MHD boundary-layer flow due to stretching sheet

Karkera Harinakshi, Katagi Nagaraj N.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

84--103

EN

In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters Mand βare calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter ()M1< which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods.

2

The special atom space and Haar wavelets in higher dimensions

Kwessi Eddy, Souza de Geraldo, Djitte Ngalla, Ndiaye Mariama

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

131--151

EN

In this note, we will revisit the special atom space introduced in the early 1980s by Geraldo De Souza and Richard O’Neil. In their introductory work and in later additions, the space was mostly studied on the real line. Interesting properties and connections to spacessuch as Orlicz, Lipschitz, Lebesgue, and Lorentz spaces made these spaces ripe for exploration in higherdimensions. In this article, we extend this definition to the plane and space and show that almost all the interesting properties such as their Banach structure, Hölder’s-type inequalities, and duality are preserved. In particular, dual spaces of special atom spaces are natural extension of Lipschitz and generalized Lipschitz spaces of functions in higher dimensions. We make the point that this extension could allow for the study of a wide range of problems including a connection that leads to what seems to be a new definition of Haar functions, Haar wavelets, and wavelets on the plane and on the space.

3

A new approach to numerical integration based on Coifman wavelets

Dehda Bachir

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 3

31--44

EN

In this paper, we present a new approach based on Coifman wavelets to find approximate values of definite integrals. This approach overcomes both CAS and Haar wavelets and hybrid functions in terms of absolute errors. The algorithm based on Coifman wavelets can be easily extended to find numerical approximations for double and triple integrals. Illustrative examples implemented using Matlab show the efficiency and effectiveness of this new method.

4

Characterizations of some function spaces in terms of Haar wavelets

Triebel H.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

35--53

EN

Some spaces Asp,q(Rn) with A = {B, F}, s ϵ R, 0 < p, q ≤ ∞, covering Besov spaces, Hölder-Zygmund spaces and Sobolev spaces, admit characterizations in terms of Haar bases. It is the main aim of this paper to extend this observation to corresponding Morreyfied spaces Lr Asp,q(Rn). As a by-product we obtain Littlewood-Paley theorems for (homogeneous and inhomogeneous) Morrey spaces Lrp(Rn), Lrp(Rn) and, in particular, L°rp(Rn).

5

Delamination identification using machine learning methods and Haar wavelets

Feklistova L., Hein H.

Computer Assisted Methods in Engineering and Science

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2012

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Vol. 19, no. 4

351-360

EN

The present paper focuses on the identification of delamination size and location in homogeneous and composite laminates. The modal analysis methods are employ ed to calculate the data patterns. An aggregated approach combining Haar wavelets, support vector mac hines (SVMs) and artificial neural networks (ANNs) is used to solve identification problems. The usabili ty and effectiveness of the proposed technique are tested by several numerical experiments. The advantages of the proposed method lie in the ability to make fast and accurate calculations.

6

Edge detection : wavelets versus conventional methods on DSP processors

Abdel-Qader I. M., Maddix M. E.

Machine Graphics and Vision

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2005

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Vol. 14, No. 1

83-101

EN

Edge detection is a cornerstone in any computer, robotic or machine vision system. Real time edge detection is a pre-process to many critical applications, such as assembly line inspection and surveillance. Wavelets-based algorithms are replacing traditional algorithms, especially the Haar wavelet because of its simplicity. The Haar algorithm uses a multilevel decomposition to produce images edges corresponding to high frequency wavelet coefficients. In this paper, a real time edges detection algorithm based on Haar is analyzed and compared to conventional edge detectors. Other implemented and compared algorithms are the traditional Prewitt algorithm, and, from a newer generation, the Canny algorithm. The real implementation of all algorithms is accomplished using TI TMS320C6711 card. In case of Haar, the multilevel decomposition improves the results obtained with noise images. The results show that the Haar-based edge detector has a low execution time with accurate edges results, and thus represent a suitable algorithm for on-line vision system applications. Canny has produced the thinnest edges, but is not suitable for time processing using the 6711, and falls short in edge results compared to the Haar results. The Wavelet-based algorithm has outperformed other edges detectors.