This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
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
... Show Moreيشهد 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
... Show MoreThis 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
... Show MoreHygienic 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
... Show MorePing message focused on highlighting the fact commodity trading in Iraq, and increased exposure to world merchandise trade imbalance, which dominate Iraq's foreign trade major commodity is oil, and therefore the inability of Iraq to control financial revenue as a result of the fluctuations in the international market, the shortage of commodity products will lead inevitably to the weakness in the ability of the local market to meet the internal demand and due to the lack of flexible production machine For agricultural, industrial and economic sectors are responding to changes in the domestic or external demand which will open the door to merchandise imports to invade these markets, since the adoption of the Iraq oil exports,
... Show MoreThe reciprocal relationship between the text and the mask in the printed product is one of the most important relationships that frame the level of communication between the appearance and the interior, although it is not cared for by some designers and publishing institutions. Therefore, the problem of research is determined by the following question (What is the dialectical relationship between the text and the mask in the literary books covers design?). The research aims to shed light on this problematic relationship at the level of reception and aesthetics at the same moment. The theoretical framework included two sections: the first (mask and text ... the concept and the mutual relationship), while the second section (trends in the
... Show MoreThe marshes are one of the important environmental features affecting human and animal systems, so the studying of changes they undergo is one of the important topics. This study is concerned with the changes occurring in the Al Saadya marsh for the period from 1987 to 2017 exclusively in the winter season (the marshes’ revival season in Iraq revive). In order to inspect the changes in this marsh, we choose 7 years to cover the study period as a criterion years, namely 1987, 1990, 1995, 2000, 2007, 2014 and 2017. The “Maximum Likelihood” classifier was used to separate the stacked land cover features, where the minimum overall accuracy ratio that recorded for all years of study was 96%. The results revealed that Al-Saadya marsh went t
... Show MoreThe world is currently facing a medical crisis. The epidemic has affected millions of people around the world since its appearance. This situation needs an urgent solution. Most countries have used different solutions to stop the spread of the epidemic. The World Health Organization has imposed some rules that people should adhere. The rules are such, wearing masks, quarantining infected people and social distancing. Social distancing is one of the most important solutions that have given good results to confront the emerging virus. Several systems have been developed that use artificial intelligence and deep learning to track social distancing. In this study, a system based on deep learning has been proposed. The system includes monitor
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