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.

تسعى تركيا ضمن سياساتها المائية ومنذ زمن بعيد وبأصرار على تنفيذ المزيد من بناء السدود والمشاريع التخزينية المائية على حوضي دجلة والفرات، الامر الذي يؤدي بالضرورة الى تناقص معدل الواردات المائية لنهري دجلة والفرات الداخلة للاراضي العراقية .وبالتالي التأثير على مقومات التنمية الزراعية العربية بشكل عام والتنمية الزراعية بالعراق بشكل خاص ومن ثم تهديد الامن الغذائي الوطني.

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When exercising their authority in the jurisprudence, judges are subject to a set of restrictions that they must adhere to, as they do not want their jurisprudence to be accepted and welcomed by law practitioners in general, and legal scholars in particular, and in contrast to it, the arrows of criticism and defamation will extend to that jurisprudence, and then they will have to reverse them . Perhaps the most important of those restrictions imposed on judges is their observance of justice between the parties to the lawsuit through their lack of bias for one of the parties at the expense of the other, in addition to their observance of public order and public morals, as well as their observance of the legal texts that they work under its u

Abstract

   The extremes effects in parameters readings which are BOD (Biological Oxygen Demands) and DO(Dissolved Oxygen) can caused error estimating of the model’s parameters which used to determine the ratio of de oxygenation and re oxygenation of the dissolved oxygen(DO),then that will caused launch big amounts of the sewage pollution  water to the rivers and it’s turn is effect in negative form on the ecosystem life and the different types of the water wealth.

   As result of what mention before this research came to employees Streeter-Phleps model parameters estimation which are (K_d,K_r) the de oxygenation and re oxygenation ratios on respect

In this paper, we study flow of photons rate production in a quark-gluon QG plasma. General theory of this study is based on the field theory for hard interaction. The kinetic of photons production from hard interaction in charm with anti-top to production photons with gluon due to plasma phase at high temperatures (150, 200,250,300 and 350 MeV) .It has been investigated and studied using the postulate of quantum chromodynamic theory QCD .The photons production rate of hard photons with( GeV) are insensitive to strength coupling and depend mainly on the temperature of system T . Despite the different critical temperature (150 and 190MeV) comes, we find that same order of flow rate photons magnitude in both cases. In both cases, the f

The formal diversity in designs is achieved by creating shapes and lines with a distinct movement pattern, which are preceded by mental processes. The greatest source of diversity in design in general and industrial design in particular is the creation of multiple directions for the completion of designs and the diversification of intellectual proposals for the design idea. The human activity that takes place around us in various fields of life takes place due to the diversity of movement in the form of the design product and its effectiveness through the dynamic diversity in the form, which differs in the methods of designing and showing it. He invents material value as a distinct artistic product that he owns A specific form or system

This research examines aspects of Imam Al-Qurtubi's efforts in matters related to the topics of faith that he dealt with in his interpretation (the provisions of the provisions of the Qur’an); and it has been shown that Imam Al-Qurtubi in most of the doctrinal issues dealt with in his interpretation approximates the doctrine of the Sunnis of Ash'aris, Maturids and people of impact. He had responses to some of the teams, such as stereoscopic, karami, and Mu'tazilite, reinforcing the responses with transfer and mental evidence.
    It was found that Imam Al-Qurtubi says that there is an increase in faith and a decrease in it, that the increase is through actions (so obedience increases and decreases in sin) and that the

The almighty Al-Bari imposed on Muslims easy and accessible worshipers for every individual who is eligible to commission, so whoever performed it rightfully, God rewarded it with the best reward. From the Muslim, the Almighty made the Almighty to the types of acts of worship and acts of righteousness as a reason for the remission of sins that were advanced and late, so I chose a topic (from the hadiths of righteous deeds mentioned in the atonement of sins) as a research drawn from the master’s thesis called (the hadiths of the atoners of sins that were presented and delayed - An analytical study- ), And collect in this research kinds of acts of righteousness that bring the mercy of God Almighty to His servants and be a reason for the

The paired sample t-test for testing the difference between two means in paired data is not robust against the violation of the normality assumption. In this paper, some alternative robust tests have been suggested by using the bootstrap method in addition to combining the bootstrap method with the W.M test. Monte Carlo simulation experiments were employed to study the performance of the test statistics of each of these three tests depending on type one error rates and the power rates of the test statistics. The three tests have been applied on different sample sizes generated from three distributions represented by Bivariate normal distribution, Bivariate contaminated normal distribution, and the Bivariate Exponential distribution.