ZnO nanopowders doped with bismuth oxide, from synthesis to electrical application

In the present paper, the properties of Boubaker orthonormal polynomials are used to construct new Boubaker wavelet orthonormal functions which are continuous on the interval [0, 1). Then, a Boubaker wavelet orthonormal operational matrix of the derivative is obtained with the new general procedure. The matrix elements can be expressed in a simple form that reduces the computational complexity. The collocation method of the Boubaker orthonormal wavelet functions together with the application of the derived operational matrix of the derivative are then utilized to transform the higher-order integro-differential equation into a solution of linear algebraic equations. As a result, the solution of the original problem reduces to the solution of a linear system of algebraic equations and can be sufficiently solved by an approximate technique. The main advantage of the suggested method is that the orthonormality property greatly simplifies the original problem and leads to easy calculation of the coefficients of expansion. Special attention is needed to perform the convergence analysis. The error is analyzed when a sufficiently smooth function is expanded in terms of the Boubaker orthonormal wavelet functions, then an estimation of the upper bound of the error is calculated. The results obtained by the technique in the current work are reported by solving some numerical examples and the accuracy is checked by comparing the results with the exact solution.

Section: Introductionmentioning

confidence: 99%

Boubaker Wavelet Functions for Solving Higher Order Integro-Differential Equations

Ouda¹,

Shihab²,

Rasheed³

2020

“…They provide effective solutions to these problems, which are summarized in the quantitative, coding and decoding stages that compose the compression process [9], [10], [11], [12]. Image processing can be utilized to a larger or smaller extent with a lot of ranges of available: Nondestructive examination methods contain Tunneling Emission Microscope (TEM) images, profilometers, optical microscope, ellipsometer, Raman Spectroscopy, Atomic Force Microscope (AFM), and Scanning Electronic Microscope (SEM) [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40].…”

Section: Introductionmentioning

confidence: 99%

Image Compression Based with Multi Discrete Laguerre Wavelets Transform

Hadi¹,

Abdulrahman²

2020

The colored image has a large array of numbers that take up a lot of space, creating a problem with transportation and storage, which needs to be urgently solved. It’s essential to find a mathematical tool that shrinks this space when transferring and storing the colored image over the years. Continuous waves such as Fourier and discrete waves such as Haar Symlet 2, coiflet 2, and daubecheis 2 were founded by shrinkage and expansion and characterized with the help of s and r parameters. With the help of the MATLAB program, these basic wavelets installed supplication and image compression, analysis, and lifting procedures. In this study, new waves based on polynomials were discovered, relying on the parent function and through many calculations, clarifying many theories and important features that this wave possesses, such as the orthogonal feature and approach that qualifies these new waves in image processing such as squeeze, jam, and analyze images by searching for a filter. It is suitable and new for carrying out the analysis and reconstruction process with high-pass and low-pass filters resulting from the scaling and wavelet function. Four samples of color images are shown. The compression process was carried out with the help of MATLAB. The use of new waves is Multi Discrete Laguerre Wavelet Transfer, where the standard criteria resulting from the compression process were calculated and the most efficient results were obtained without losing the original information of the image, compared to the standard waves’ tables, which will demonstrate the efficiency of these new wavelets in Multi Discrete Laguerre Wavelet transform.

“…The second purpose is to introduce the notion of a Pseudo G-normed space and prove a series of important concepts related to it. Other applications of these spaces are illustrated in [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47].…”

Section: Introductionmentioning

confidence: 99%

Some Results on G-Normed Linear Spaces

Mohammedali¹,

Sabri²,

Rasheed³

et al. 2020

In the present work, our goal is to define the Cartesian product of two generalized normed spaces depending on the notion of generalized normed space. It is a background to state and prove that the Cartesian product of two complete generalized normed spaces is also a complete generalized normed space. Furthermore, the definition of the pseudo-generalized normed space is introduced and essential concepts related to this space are discussed and proved.