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This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

Monitoring lotic ecosystems is vital for addressing sustainability issues. The Al-Shamiyah River is the primary source of water for various daily activities in the Al-Shamiyah district. This study assessed the pollution levels of the river by measuring the concentration and distribution of heavy metals—specifically chromium, cadmium, manganese, copper, zinc, and lead—in both the river's water and sediments. The concentrations of heavy metals in the water ranged from 0.05 to 1.44µg/ L for copper (Cu), 1.57 to 7.25µg/ L for manganese (Mn), 0 to 1.7µg/ L for cadmium (Cd), 0.02 to 1.33µg/ L for lead (Pb), 0.08 to 2.74µg/ L for zinc (Zn), and 0.44 to 1.84µg/ L for chromium (Cr). In the particulate phase, the concentrations ranged from

يشهد المسرح الدولي قضايا مستجدة ومستحدثة مثل تعدد الفاعلين من الدول ومن غير الدول وتزايد مساحات نفوذهم وتأثيرهم ،ومن جانب اخر أثرت جائحة كورونا على البيئة والمناخ بشكل ملموس على جوانب عدة. فضلا عن ذلك تأثرت جميع المجتمعات البشرية بالإرهاب والهجمات الالكترونية وغيرها ومن بينها دول والمجتمع الدولي بإفراده مؤسسات وكيان اقتصادي وسياسي وقانوني وأمني وامتداد اثاره واسبابه الكثيرة والمتداخلة وما يثيره من خلق حا

This study we have made a subject of fanny podcast in electronic media, as a new way to express different issues by the public, This study focuses started on how to address social issues in Alegria by ANAS TINA vidéo on the youtube network , you are to know the trends of young amateur about the various issues dealt with as well as the most important methods used to convince browsers.
The researcher used the survey method based on studying 10 episodes videos of blogger ANAS TINA.
The result of the study found that the most important issues are the abduction of children, teaching in Algeria; women in Algeria, The negative aspects of the issues addressed have been established in order to direct public opinion and awareness of ph

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is a basic pri