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.

Research summary

Today, the Islamic nation is going through a phase that is one of the most dangerous that it has never experienced before. This phase was characterized by the following:

The nation is divided into states and its weakness in most of its doctrinal, political, social, economic and moral aspects.
Enemies targeting the nation's faith and capabilities, and the emergence of loyalty to the enemies of the nation from some groups of society, spreading misconceptions in the Muslim community.
Spreading the spirit of rebellion in all segments of society and striving to stir up the people against the rulers and put pressure on the rulers.

All these manifestations and others require the nation's wise men

Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.

Currently, with the huge increase in modern communication and network applications, the speed of transformation and storing data in compact forms are pressing issues. Daily an enormous amount of images are stored and shared among people every moment, especially in the social media realm, but unfortunately, even with these marvelous applications, the limited size of sent data is still the main restriction's, where essentially all these applications utilized the well-known Joint Photographic Experts Group (JPEG) standard techniques, in the same way, the need for construction of universally accepted standard compression systems urgently required to play a key role in the immense revolution. This review is concerned with Different

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.

In this study an experimental work was done to study the possibility of using aluminum rubbish material as a coagulant to remove the colloidal particles from oily wastewater by dissolving this rubbish in sodium hydroxide solution. The experiments were carried out on simulated oily wastewater that was prepared at different oil concentrations and hardness levels (50, 250, 500, and 1000) ppm oil for (2000, 2500, 3000, and 3500) ppm CaCo₃ respectively. The initial turbidity values were (203, 290, 770, and 1306) NTU, while the minimum values of turbidity that have been gained from the experiments in NTU units were (1.67, 1.95, 2.10, and 4.01) at best sodium aluminate dosages in milliliters (12, 20, 24, and 28) for

Insufficient and poor sleep quality significantly impacts the health and quality of life of persons with end-stage renal failure (ESRF) on hemodialysis. This study explored the effectiveness of teaching patients on hemodialysis, Benson’s relaxation technique. Seventy-one persons on hemodialysis in Iraq were randomly assigned to either the experimental or the control group. The experimental group received training and encouragement to use the Benson relaxation technique. The Pittsburgh Sleep Quality Index (PSQI) score was collected for all the patients before and after the intervention. After 8 weeks a repeated measurement of the post-test on sleep quality was done for both groups. The experimental group showed a statistically sign

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.