The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

     This paper introduced a hybrid technique for lossless image compression of natural and medical images; it is based on integrating the bit plane slicing and Wavelet transform along with a mixed polynomial of linear and non linear base. The experiments showed high compression performance with fully grunted reconstruction.

The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

In this paper, a fast lossless image compression method is introduced for compressing medical images, it is based on splitting the image blocks according to its nature along with using the polynomial approximation to decompose image signal followed by applying run length coding on the residue part of the image, which represents the error caused by applying polynomial approximation. Then, Huffman coding is applied as a last stage to encode the polynomial coefficients and run length coding. The test results indicate that the suggested method can lead to promising performance.

          Sentiment analysis refers to the task of identifying polarity of positive and negative for particular text that yield an opinion. Arabic language has been expanded dramatically in the last decade especially with the emergence of social websites (e.g. Twitter, Facebook, etc.). Several studies addressed sentiment analysis for Arabic language using various techniques. The most efficient techniques according to the literature were the machine learning due to their capabilities to build a training model. Yet, there is still issues facing the Arabic sentiment analysis using machine learning techniques. Such issues are related to employing robust features that have the ability to discrimina

In this paper, a compression system with high synthetic architect is introduced, it is based on wavelet transform, polynomial representation and quadtree coding. The bio-orthogonal (tap 9/7) wavelet transform is used to decompose the image signal, and 2D polynomial representation is utilized to prune the existing high scale variation of image signal. Quantization with quadtree coding are followed by shift coding are applied to compress the detail band and the residue part of approximation subband. The test results indicate that the introduced system is simple and fast and it leads to better compression gain in comparison with the case of using first order polynomial approximation.

This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

In some cases, researchers need to know the causal effect of the treatment in order to know the extent of the effect of the treatment on the sample in order to continue to give the treatment or stop the treatment because it is of no use. The local weighted least squares method was used to estimate the parameters of the fuzzy regression discontinuous model, and the local polynomial method was used to estimate the bandwidth. Data were generated with sample sizes (75,100,125,150 ) in repetition 1000. An experiment was conducted at the Innovation Institute for remedial lessons in 2021 for 72 students participating in the institute and data collection. Those who used the treatment had an increase in their score after

The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic