The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The undetected error probability is an important measure to assess the communication reliability provided by any error coding scheme. Two error coding schemes namely, Joint crosstalk avoidance and Triple Error Correction (JTEC) and JTEC with Simultaneous Quadruple Error Detection (JTEC-SQED), provide both crosstalk reduction and multi-bit error correction/detection features. The available undetected error probability model yields an upper bound value which does not give accurate estimation on the reliability provided. This paper presents an improved mathematical model to estimate the undetected error probability of these two joint coding schemes. According to the decoding algorithm the errors are classified into patterns and their decoding

In this paper, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

It is no secret to anyone that the Koran is a speech to people, and how it is not a speech to humans is a home to them and suitable for their understandings, and the people of rhetoric mean great care has never been before in the division of the Koranic discourse, followed by linguists and science of the Koran. After reading the letter, I followed it in the Holy Quran, taking advantage of what was written by former writers in language and interpretation. Thanks to God, I have done what I wanted. Perhaps one of the most important reasons that led me to write my research and optional for this topic; is related to the Koran. So I started to develop the research plan, and divided it as I saw it, I started to pave the way, and then divided it

The progress of network and multimedia technologies has been phenomenal during the previous two decades. Unauthorized users will be able to copy, retransmit, modify reproduction, and upload the contents more easily as a result of this innovation. Malicious attackers are quite concerned about the development and widespread use of digital video. Digital watermarking technology gives solutions to the aforementioned problems. Watermarking methods can alleviate these issues by embedding a secret watermark in the original host data, allowing the genuine user or file owner to identify any manipulation. In this study, lots of papers have been analyzed and studied carefully, in the period 2011–2022. The historical basis of the subject shou

All-optical canonical logic units at 40 Gb/s using bidirectional four-wave mixing (FWM) in highly nonlinear fiber are proposed and experimentally demonstrated. Clear temporal waveforms and correct pattern streams are successfully observed in the experiment. This scheme can reduce the amount of nonlinear devices and enlarge the computing capacity compared with general ones. The numerical simulations are made to analyze the relationship between the FWM efficiency and the position of two interactional signals. © 2015 Chinese Laser Press

       In this work, the fractional damped Burger's equation (FDBE) formula    = 0,

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

The subgrade soil is the foundation plate form of the roadway; it should sustain its structural characteristics throughout the design life of the roadway with minimal requirements for maintenance. When Gypseous soil is implemented in the construction of subgrade, problems regarding collapsibility and poor structural capacity usually occur when the subgrade came in touch with excess water. Asphalt stabilization could furnish a proper solution to such problems. In this investigation, an attempt has been made to monitor the variations in compressibility characteristics of asphalt stabilized subgrade soil subjected to 30 cycles of (freezing-thawing) and (heating-cooling). Data have been observed after each 10 cycles, and compared with that of r