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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, where it is shown that the fuzzy algebra is a generalization of fuzzy algebra too. In addition, the notion of restriction, as an important property in the study of measure theory, is studied as well. Many properties of restriction of a nonempty family of fuzzy subsets of fuzzy power set are investigated and it is shown that the restriction of fuzzy algebra is fuzzy algebra too.

In the present paper, the authors introduce and investigates two new subclasses and, of the class k-fold bi-univalent functions in the open unit disk. The initial coefficients for all of the functions that belong to them were determined, as well as the coefficients for functions that belong to a field determining these coefficients requires a complicated process. The bounds for the initial coefficients and are contained among the remaining results in our analysis are obtained. In addition, some specific special improver results for the related classes are provided.

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 solutions and other existing methods. Illustrative examples show the efficiency and the power of the used method.

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...

In this study we generalize the idea of σ–field by introducing the concept of 𝒫∗– field. Characterization and examples of the proposed generalization are presented, as well as several different properties of 𝒫∗– field are proven. Furthermore, we introduce the notion of 𝒫∗– field generated by the class ℐ and we show that it is smallest 𝒫∗– field that contain ℐ. Finally, we show that the 𝒫∗– field concept is a generalizations of some types classes of sets.

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 used in Variational Iteration Method, as well as it does not need to use the convolution theorem of the transform. Furthermore, the Homotopy Perturbation Method is used to dealing with the nonlinear terms arising in the problems where the He’s polynomials are calculated. The proposed method emphasises the existence of the obtained solution in the absence of any linearization, discretization, or hypothesis. The suggested method’s compactness and reliability are demonstrated by numerical examples

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 we used. The results of numerical experiments show the efficiency of our newly developed method. Exact solution and the existing method Homotopy perturbation method is used in the comparison with our new results.

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 equation shows a prototypical model for describing the interaction between the reaction mechanisms, convection effect, and diffusion transport. In this paper, variational iteration transform method that combines Laplace transform and the variational iteration method, which used to obtain approximate analytical solutions of Burger’s - Fisher equation. Comparison of the results obtained by the present method with the exact solution and other existing methods reveals the accuracy and fast convergence of the proposed method.

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 differential subordinations integral operators are also considered.

The famous Toeplitz matrix is a matrix in which each descending diagonals form left to right is constant, this mean T = ( a 0 a 1 ⋯ a n a − 1 a 0 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ ⋯ ⋯ a − 1 a 0 ) . Mathematician, engineers, and physicists are interested into this matrix for their computational properties and appearances in various areas: C *-dynamical systems [1], dynamical systems [6], operator algebra [2], Pseudospectrum and signal processing [10]. The object of this research is to define a new class Non-Bazilevi´c functions N δ in unit disk ↁ = {z ∈ ℂ: |z| < 1} related to exponential function. As well as, we obtained coefficient estimates and an upper bound for the second and third determinant of the Toeplitz matrix such that the entries these matrix are belong to this class.

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 spatial domain which employs only one threshold to determine the class of the input image block, and uses three AC coefficients of the discrete cosine transform coefficients to determine the orientation of the block without employing any threshold that results in high fidelity medical compressed images. Singular value decomposition was used to generate the classified codebooks. The proposed technique was benchmarked with JPEG-2000 standard. Simulation results indicate that the proposed approach can reconstruct high visual quality images with higher Peak Signal-to Noise-Ratio than the benchmarked technique and also meet the legal requirement of medical images archiving.

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 any threshold to determine the class of the input image block in the spatial domain that results in a high- fidelity medical compressed image was utilised. The proposed technique was benchmarked with JPEG-2000 standard. Simulation results indicated that the proposed approach can reconstruct high visual quality images with higher Peak Signal-to Noise-Ratio than the benchmarked technique, and also meet the legal requirement of medical image archiving.

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 threshold to determine the class of the input image block, and uses three AC coefficients of the discrete cosine transform coefficients to determine the orientation of the block without employing any threshold. Singular value decomposition was used to generate the classified codebooks. The proposed technique was benchmarked with the standard vector quantiser generated using the k-means algorithm, and JPEG-2000. Simulation results indicated that the proposed approach alleviates edge degradation and can reconstruct good visual quality images with higher peak signal-to noise-ratio than the benchmarked techniques.

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 threshold to determine the class of the input image block, and uses three AC coefficients of discrete cosine transform coefficients to determine the orientation of the block without employing any threshold. The proposed technique is benchmarked with each of the standard vector quantizers generated using the k-means algorithm, standard classified vector quantizer schemes, and JPEG-2000. Simulation results indicate that the proposed approach alleviates edge degradation and can reconstruct good visual quality images with higher peak signal-to-noise ratio than the benchmarked techniques, or be competitive with them.

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 algorithm, and JPEG-2000. Simulation results indicate that the proposed approach alleviates edge degradation and can reconstruct good visual quality images with higher peak signal-to-noise ratio than the benchmarked techniques.

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 goal of these works is to develop techniques of coding information sources such as speech, image and video to reduce the number of bits required to represent a source without significantly degrading its quality. With the large increase in the generation of digital image data, there has been a correspondingly large increase in research activity in the field of image compression. The goal is to represent an image in the fewest number of bits without losing the essential information content within. Images carry three main type of information: redundant, irrelevant, and useful. Redundant information is the deterministic part of the information, which can be reproduced without loss from other information contained in the image. Irrelevant information is the part of information that has enormous details, which are beyond the limit of perceptual significance (i.e., psychovisual redundancy). Useful information, on the other hand, is the part of information, which is neither redundant nor irrelevant. Human usually observes decompressed images. Therefore, their fidelities are subject to the capabilities and limitations of the Human Visual System. This paper provides a survey on various image compression techniques, their limitations, compression rates and highlights current research in medical image compression.