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.

Praise be to God, prayer and peace be upon the Messenger of Allah and after :
For the Holy Qur’an is the constitution of this nation, and it has included everything that the nation needs, and it has appropriate solutions for all the problems it faces, and for a long time the nation has its vision for the future, waiting for a leader who carries the concerns of this nation and proceeds towards progress and progress, so that it rises to the glory and glory. He brings it out from what it is today, from its deterioration in all levels.
The world has witnessed in recent decades the development of programs and curricula, and books have been prepared showing how to prepare leaders and their industry, and what programs they should adopt

Three stations were chosen on the water treatment plan of al- madaan .The Samples collected from the (Raw water) and the Sedimentation, filtration and storage water and the drinking water of outlet. Coliform densities T.S and F.C and TS and F.S and total bacterial count as bacteriological pollution indicators, as moste probable number (MPN) method was studied in test. Also some of the chemical characteristics of the water like pH , total suspended solid T.S.S, T.D.D.and S04 , T.Hardness , Ca++ , Mg++ . From the results it were indicated . The study showed the drinking water of outlet (distriputed in system) was agree with WHO criteria and Iraqi limits standards .

Background: Restoration of root canal treated teeth with a permanent restoration affect in the success of endodontically treated teeth. This in vitro study was performed to evaluate and compare the fracture strength of endodontically treated teeth restored by using custom made zirconium posts and cores, prefabricated carbon fiber, glass fiber and zirconium ceramic posts. Materials and method: Forty intact human mandibular second premolars were collected for this study and were divided into five groups. Each group contains 8 specimens: Group1: Teeth restored with Carbon Fiber Posts; Group2: Teeth restored with Glass Fiber Posts; Group3: Teeth restored with Zirconium Ceramic prefabricated Posts; Group4: Teeth restored with Zirconium Posts

      Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir

One of the diseases on a global scale that causes the main reasons of death is lung cancer. It is considered one of the most lethal diseases in life. Early detection and diagnosis are essential for lung cancer and will provide effective therapy and achieve better outcomes for patients; in recent years, algorithms of Deep Learning have demonstrated crucial promise for their use in medical imaging analysis, especially in lung cancer identification. This paper includes a comparison between a number of different Deep Learning techniques-based models using Computed Tomograph image datasets with traditional Convolution Neural Networks and SequeezeNet models using X-ray data for the automated diagnosis of lung cancer. Although the simple details p

The love of the world and its lusts are the head of sins and the corruptors of religion, and the one who loves and loves them who prefers them over the hereafter is one of the most pitiful of creation, and the least intelligent of them, as he prefers imagination over reality, sleep over wakefulness, fleeting shadow over eternal bliss and the mortal abode over the eternal abode, and he sold the life of eternity for the most luxurious life. In life, it is dreams and sleep or as a fleeting shadow, and as it was said: The intelligent person is not deceived.
The reason for choosing this topic is due to two things:
The first: When I contemplated the reasons for the differences and conflicts that afflicted our wounded and occupied country