Ali Al-Fayadh

• PhD
• Professor at Nahrain University

The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concep...

This article aims to propose a new efficient hybrid method for solving different types of nonlinear differential equations. The method combines mixed Shehu and Sumudu integral transforms with the variational iteration method. The proposed method is termed the multiple transform iteration method to solve different nonlinear partial differential equa...

The aim of this article is to propose an efficient hybrid transform iteration method that combines the homotopy perturbation approach, the variational iteration method, and the Aboodh transform forsolving various partial differential equations. The Korteweg-de Vries (KdV), modified KdV, coupled KdV, and coupled pseudo-parabolic equations are given...

This research aims to present and study the convex subclasses and starlike functions of the analytic functions defined in the open unit disk Ư and to investigate the third-order Hankel determinant H3,1 for these subclasses related to the exponential function. As well as the upper bounds of H2,2 (g) and H3,1 (g) for the convex and starlike functions...

This work studies some properties of P-field, which is a generalization of s-algebra, d-field and l-algebra. The relationship between each of an a-field, as field , b-field, b-s-field, p-system and monotone class with P-field have been studied where it is shown that P-field is a stronger form of these concepts. Subject Classification: 00A05, 00A06....

Data compression is necessary for the storing, transfer, and manipulation of digital data in today's rapidly changing world due to the widespread use of medical technology and the vast data creation by various medical modalities. Many scientists and engineers have proposed new compression processes, methods, and algorithms in recent years. There is...

In this work, we establish some results for fuzzy differential for analytic functions associated with the Hadamard product for generalization Srivastava-Attiya operator is defined in the open unit disc L = {w ∈ C:|w|< 1}. In the present paper, the operator is applied to a new class of analytic functions with the Hadamard product. The goal of this a...

This work aims to introduce concepts about Γ-algebra calculate relative to Γ-algebra and outer measure in relation to Γ-algebra are examples. After that, we establish a relationship between them. The notions of null-additive and weakly null-additive as two generalizations of measure and extreme measure are introduced and studied too. Subject Classi...

In this article, a hybrid method that combines Aboodh transform, variational iteration method, and the homotopyperturbation method is presented for approximate the solution of important partial differential equations that describe wave like differential equations in one, two and three dimensions. The suggested method utilizes only the initial condi...

The inequality of finding the upper bounds for the nonlinear functional |a3 - µa²2| of the Taylor-Mclaurin series is popularly famous as the Fekete-Szegö inequality. This inequality has a rich history in the geometric function theory. Its source by Fekete-Szegö in 1933. In this paper, through the advantage of applying concepts quasi-subordinate, Sa...

The article introduces a combination form of the variation iteration method and the well-known Laplace transform for finding the solutions of the two-dimensional non-linear coupled Burger's partial differential equations. The obtained solutions were compared to the exact solutions and the existing methods. Illustrative examples show the powerful of...

The objective in this paper is to give the concept of fuzzy λ–algebra and study some of its structural properties. The relationships between fuzzy λ–algebra and other concepts like fuzzy α-σ-field, fuzzy β-σ-field, fuzzy β-field, and fuzzy α-field are presented.

In this paper, we define the concept of Γ–algebra and study some of its structural properties. We present some results and theorems about this notion. The relationships between Γ–algebra and other concepts such as α– σ–field, monotone class, β– σ–field are presented.

In this paper, the homotopy analysis method have been utilized for solving non-linear delay differential equations of multi-term fractional order, and the fractional derivative is expressed in the Caputo sense. In this approach, the solutions are found in the form of convergent power series components are easily computed. Some illustrative examples...

In this paper, we use the definition of the action on the set of semi-group of the structure of this research .We introduce the concepts of -system which is a triple , , such that is a Hausdorff compact space called phase space, is a semi-group of transformations with a continuous action of on . We study and proof some theoretical properties relate...

In this paper, we use the definition of the action on the set of semi-group of the structure of this research .We introduce the concepts of-system which is a triple (, ,) such that is a Hausdorff compact space called phase space, is a semi-group of transformations with a continuous action of on. We study and proof some theoretical properties relate...

In this paper, we introduce the notion of soft P–field. Characterization and different properties of this concept are studied as well as the restriction concept of soft P–field is introduced.

This article introduces the soft P*–field. Characterization, examples, and different properties of the proposed concept are presented. The idea of the smallest soft P*–field studies.

The main objective of this work is to generalize the concept of fuzzy algebra by introducing the notion of fuzzy algebra. Characterization and examples of the proposed generalization are presented, as well as several different properties of fuzzy algebra are proven. Furthermore, the relationship between fuzzy algebra and fuzzy algebra is studied, w...

This paper presents a new methodology for solving Schrödinger equation based on the variational iteration method and the Kashuri-Fundo transform. The Lagrange multiplier is computed using the Kashuri - Fundo transform. This approach helps in avoiding the difficulties often appearing in finding Lagrange multiplier and the complicated integration use...

In our article, we develop an efficient compined method consisting of integral transform and Homotopy Perturbation Method for solving Fractional Integro-differential equations of Fredholm type. Sawi transformation formulas of fractional types are derived and used in the proposed method. The Caputo derivative is the fractional derivative type that w...

The restriction concept is a basic feature in the field of measure theory and has many important properties. This article introduces the notion of restriction of a non-empty class of subset of the power set on a nonempty subset of a universal set. Characterization and examples of the proposed concept are given, and several properties of restriction...

The main aim of the present paper is to obtain an upper bound on the third Hankel determinant for the new class of univalent functions defined in the unit disk U using an integral operator.

This paper proposes a hybrid method that combines the Kashuri and Fundo integral transform and the Adomiande composition method to solve two types of Schrödinger equations. The exact solutions are successfully found, and the results are compared with those obtained by the existing methods. The obtained results show the accuracy and efficiency of th...

In the present paper, the authors introduce and investigate two new subclasses,namely and of the class-fold bi-univalent functions in the open unit disk. The initial coefficients for all of the functions that belong to them are determined, as well as the coefficients for functions that belong to a field determining these coefficients are also deter...

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given. As the first result, it has been proved that every σ-algebra over a fuzzy set x* is a fuzzy σ-ring-over a fuzzy set x* and construct their converse by example. Furthermore, the fuzzy ring concept h...

The aim of this research paper is to introduce the concept of bi-Γ-algebra space (bi-gamma algebra space). The concept of bi-µ-measurable set in a bi-Γ-algebra space is defined. With this concept, some properties of bi-Γ-algebra space are proved. We then define various separation axioms for bi-Γ-algebra space such as M 0 , M 1 , M 2 , M 3 , and M 4...

In this paper, we define and study some separation axioms on Γ-algebra space (gamma algebra space). The relationships between various separation axioms in Γ-algebra space are proved. In addition, the measurable function between two measurable spaces is introduced and some results are discussed.

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions. Also, we investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

In this paper, the combined form of the Elzaki transform and variation iteration method is implemented efficiently in finding the analytical and numerical solutions of the two-dimensional nonlinear coupled Burger's partial differential equations and sine-Gordon partial differential equation. The obtained solutions were compared to the exact solutio...

Its well-known that a Hankel matrix is one whose entries of the reverse diagonals are constant, i.e. Mathematician, physicists and engineers are attracted to this matrix because of their appearances and computational properties in different areas: dynamical systems, quantum mechanics, and partial differential equations. The main object in this pap...

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions. Also, we investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

The famous Toeplitz matrix is a matrix in which each descending diagonals form left to right is constant, this mean �.Mathematician, engineers, and physicists are interested into this matrix for their computational properties and appearances in various areas: ∗-dynamical systems [1], dynamical systems [6], operator algebra [2], Pseudospectrum and...

The famous Toeplitz matrix is a matrix in which each descending diagonals form left to right is constant, this mean ܶ = ൮ ܽ ܽ ଵ ⋯ ܽ ܽ ିଵ ܽ … … ⋮ ⋮ ⋱ ⋮ … ⋯ ܽ ିଵ ܽ ൲.Mathematician, engineers, and physicists are interested into this matrix for their computational properties and appearances in various areas: ‫ܥ‬ *-dynamical systems [1], dynamical syste...

In this paper the approximate solution of the non-linear equations of multi-term fractional order delay differential equations by using the homotopy perturbation method is considered. The fractional order derivative is communicated in the Caputo sense. In this methodology, the solutions are found in the form of a convergent power series with easily...

In the present paper, we have investigate the Hankel determinant H_2 (2) and H_3 (1) for functional in the class of analytic function and we have obtained the sharp bound for the third Hankel determinant|a_2 a_4-a_3^2 |fοr a subclass οf analytic functiοns. 2010 Mathematics Subject Classificatiοn: 30C45, 30C50. keywοrds: Univalent functiοn, Hankel d...

Abstract: This paper will investigate a method to achieve the exact solution of special type of nonlinear partial differential equations (NLPDEs) involving mixed partial derivatives. This proposed method named as Laplace substitution - Variation iteration method (LS-VIM). The method exploits the properties of Laplace substitution method and the Var...

The purpose of the present paper is to introduce new operator SRⁿ using the Salagean operator Sⁿ and Ruscheweyh operator Rⁿ for analytic functions. We study the differential subordinations in the general case and investigate differential subordination properties regarding the operator SRⁿ. Moreover, we determine dominants and best dominants of diff...

In the present paper, we have investigate the Hankel determinant H_2 (2) and H_3 (1) for functional in the class of analytic function and we have obtained the sharp bound for the third Hankel determinant|a_2 a_4-a_3^2 |fοr a subclass οf analytic functiοns.

The Symmetric Toeplitz determinant T q (n) = a n a n+1 · · · a n+q−1 a n+1 a n · · · a n+q a n+q−1 a n+q · · · a n of the analytic function f (z) =z + a 2 z 2 + a 3 z 3 + ... for the class of Bazilevic function A λ are studied in particular T 2 (2), T 2 (3) and T 3 (2).

Nonlinear partial differential equations represent the most important phenomena occurring in the world and are encountered in various fields of science. Generalized Burger’s-Fisher equation is very important for describing different mechanisms. Burger’s-Fisher equation arises in the field of applied mathematics and physics applications. This equati...

In the present paper, new method called (A.H. SH..Rostom Group masks) for Mycosis Fungoides Skin image Edge detection is proposed. The Group consists of 10 masks were geometry of the mask operator determines a characteristic direction in which it is most sensitive to edges. applied to the four stages of the Mycosis Fungoides disease Skin image have...

We present a novel image compression technique using a classified vector Quantizer and singular value decomposition for the efficient representation of still images. The proposed method is called hybrid classified vector quantization. It involves a simple but efficient classifier-based gradient method in the spatial domain, which employs only one t...

An efficient adaptive lossy image compression technique using classified vector quantiser and singular value decomposition for compression of medical magnetic resonance-brain images is presented. The proposed method is called adaptive hybrid classified vector quantisation. A simple but efficient classifier based gradient method without employing an...

A novel image compression technique using classified vector quantiser and singular value decomposition is proposed for the efficient representation of still images. The proposed method is called improved hybrid classified vector quantisation. The proposed technique was benchmarked with the standard vector quantiser generated using the k-means algor...

A novel adaptive image compression technique using Classified Vector Quantiser and Discrete Cosine Transform is presented for the efficient representation of still images. The proposed method is called Adaptive Hybrid Classified Vector Quantisation. It involves a simple, but efficient, classifier based gradient method in the spatial domain without...

A hybrid lossy image compression technique using classified vector quantiser and singular value decomposition is presented for the efficient representation of medical magnetic resonance-brain images. The proposed method is called hybrid classified vector quantisation. It involves a simple yet efficient classifier based gradient method in the spatia...

A novel image compression technique using classified vector quantiser and singular value decomposition is presented for the efficient representation of still images. The proposed method is called hybrid classified vector quantisation. A simple but efficient classifier based gradient method which employs only one threshold to determine the class of...

A novel image compression technique using Classified Vector Quantiser and Singular Value Decomposition is presented for the efficient representation of still images. The proposed method is called Hybrid Classified Vector Quantisation. It involves a simple, but efficient, classifier based gradient method in the spatial domain which employs only one...

The bandwidth of the communication networks has been increased continuously as results of technological advances. However, the introduction of new services and the expansion of the existing ones have resulted in even higher demand for the bandwidth. This explains the many efforts currently being invested in the area of data compression. The primary...

Nonlinear phenomena play a major role in applied mathematics and engineering. The Burger-Fisher equation which is a mixed hyperbolic-parabolic non-linear partial differential equation occurs in various areas of applied sciences and physical applications, such as modeling of gas dynamics and fluid mechanics. In this paper, Haar wavelet method was im...

In this paper, Cauchy problem for the nonlinear partial differential equations is considered. Approximate analytical solutions for mixed parabolic-hyperbolic equations are obtained using the hybrid scheme combined the well-known Laplace transform and variational iteration method. Moreover, the scheme is also used to approximate the generalized Burg...

In this paper, Variational iteration transform method is employed to determine the exact solution of the Burger equation which is one-dimensional and coupled Burger’s equations nonlinear partial differential equation. This method is combined form of the Laplace transform and Variational iteration method. The explicit solutions obtained were compare...

Nonlinear phenomena play a major role in applied mathematics and engineering. The Burger-Fisher equation which is a mixed hyperbolic-parabolic non-linear partial differential equation occurs in various areas of applied sciences and physical applications, such as modeling of gas dynamics and fluid mechanics. In this paper, Haar wavelet method was im...

Abstract A Modified Discrete Wavelet Transform (DWT) and Hybrid image compression methods which use integral transformations are introduced in this paper. Discrete Cosine Transform (DCT) as implemented in the standard JPEG compression and DWT for its useful multiresolution properties are used first. A Modified DWT method with variable thresholds us...

The main purpose of this book is to study and investigate the most important properties of integral transforms ( the discrete fourier transform, the discrete sine transform, and the discrete wavelet transform) and their mathematical aspects both from the theoretical point of view and for the application to image compression. As well as, we study th...

In this paper we present an efficient image compression technique using singular value decomposition (SVD) based classified vector quantization (CVQ) and Discrete Wavelet Transform (DWT) in both the spatial and frequency domains for the efficient representation of still images. The proposed method combines the properties of SVD, CVQ, and DWT; while...

An efficient image compression technique using singular value decomposition (SVD) based classified vector quantization (CVQ) and Discrete Sine Transform (DST) for the efficient representation of still images was presented. The proposed method combines the properties of SVD, CVQ, and DST; while avoiding some of their limitations. A simple but effici...

In the present paper, an important mathematical transform which is called Gabor transform be used to develop a method for image compression. Gabor transform is a type of wavelet-based transform. It is embedded in the standard compression algorithm (JPEG2000) as a mother wavelet. Based on the obtained results we believe that Gabor wavelet transform...

In the present paper, Mean Shift Algorithm and active contour to detect objects for CT Angiography Image Segmentation is proposed.Based on the results we believe that this method of boundary detection together with the mean-shift can achieve fast and robust tracking of the CT Angiography Image Segmentation in noisy environment. The proposed scheme...

A hybrid lossy image compression technique using classified vector quantiser and singular value decomposition is presented for the efficient representation of medical magnetic resonance-brain images. The proposed method is called hybrid classified vector quantisation. It involves a simple yet efficient classifier based gradient method in the spatia...

A hybrid lossy image compression technique using classified vector quantiser and singular value decomposition is presented for the efficient representation of medical magnetic resonance-brain images. The proposed method is called hybrid classified vector quantisation. It involves a simple yet efficient classifier based gradient method in the spatia...

We present a novel image compression technique using a classified vector Quantizer and singular value decomposition for the efficient representation of still images. The proposed method is called hybrid classified vector quantization. It involves a simple but efficient classifier-based gradient method in the spatial domain, which employs only one t...

We present a novel image compression technique using a classified vector Quantizer and singular value decomposition for the efficient representation of still images. The proposed method is called hybrid classified vector quantization. It involves a simple but efficient classifier-based gradient method in the spatial domain, which employs only one t...

A novel adaptive image compression technique using Classified Vector Quantiser and Discrete Cosine Transform is presented for the efficient representation of still images. The proposed method is called Adaptive Hybrid Classified Vector Quantisation. It involves a simple, but efficient, classifier based gradient method in the spatial domain without...

An efficient adaptive lossy image compression technique using classified vector quantiser and singular value decomposition for compression of medical magnetic resonance-brain images is presented. The proposed method is called adaptive hybrid classified vector quantisation. A simple but efficient classifier based gradient method without employing an...

An efficient adaptive lossy image compression technique using classified vector quantiser and singular value decomposition for compression of medical magnetic resonance – brain images is presented. The proposed method is called adaptive hybrid classified vector quantisation. A simple but efficient classifier based gradient method without employing...

An efficient adaptive lossy image compression technique using classified vector quantiser and singular value decomposition for compression of medical magnetic resonance - brain images is presented. The proposed method is called adaptive hybrid classified vector quantisation. A simple but efficient classifier based gradient method without employing...

A novel image compression technique using Classified Vector Quantiser and Singular Value Decomposition is presented for the efficient representation of still images. The proposed method is called Hybrid Classified Vector Quantisation. It involves a simple, but efficient, classifier based gradient method in the spatial domain which employs only one...

A novel image compression technique using Classified Vector Quantiser and Singular Value Decomposition is presented for the efficient representation of still images. The proposed method is called Hybrid Classified Vector Quantisation. A simple but efficient classifier based gradient method which employs only one threshold to determine the class of...

A novel image compression technique using classified vector quantiser and singular value decomposition is proposed for the efficient representation of still images. The proposed method is called improved hybrid classified vector quantisation. The proposed technique was benchmarked with the standard vector quantiser generated using the k-means algor...