Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Background: The size of the nasopharyngeal airway was believed to have an important role in the development of the dentofacial structure. This study was carried out to test the relation between the nasopharyngeal dimensions with some dento-cranial measurements in class I and II jaw relationship. Materials and Methods: This study was done on 60 subjects (30 males and 30 females) at age range 18-25 years. Cephalometric radiograph has been taken to each subject and the measurements were recorded. The sample was divided into two groups, class I skeletal relationship (15 males and 15 females) and class II skeletal relationship (15 males and 15 females). Comparisons between the different study groups were undertaken. Results: In class I skeletal
... Show MoreBackground: The polymethyl methacrylate is the most reliable material for the construction of complete and partial dentures, despite satisfying esthetic demand itsuffered from having unsatisfactory properties like impact strength and transverse strength. This study was designed to improve the impact strength and transverse strength of heat cure acrylic resin by adding untreated and oxygen plasma treated polypropylene fibers and investigate the effect of this additive on some properties of acrylic resin materials. Materials and methods: Untreated and oxygen plasma treated polypropylene fibers was added to PMMA powder by weight 2.5 %. Specimens were constructed and divided into 5 groups according to the using tests; each group was subdivided
... Show MoreAbstract
This study aims at investigating the effectiveness of the cooperative inquiry strategy in developing the achievement and development of mathematical communication skills of elementary school students. To achieve this aim, the experimental method was utilized. The study sample consisted of an experimental group (n = 34) and a control group (n = 31), which were randomly selected from primary schools. A Teacher's Guide for teaching a unit entitled "Statistics and Graphic Representations" for the sixth elementary graders in the first semester were devised. A (30) multiple-choice item achievement test distributed at the levels of (recall, comprehension, and application), as well as an (18) item mathematical c
... Show Moresome ecological (physical and chemical varible) of water samples were studies monthly from December 2008 to May 2009 at two stations( St.1) Al - Chibayesh marsh and (St.2) Abu – Zirik marsh which are located in the south of Iraq . These variables included : Temperature, pH, EC, Dissolved oxygen , Total alkalinity, Nitrate, Sulphate, and phosphate, Si-SiO2 and Ca ,Mg, Cl, The marsh Considered as fresh water and alkaline. Abu-Zirik less than Al-Chibayesh.
The: currency Auction is one of the monetary policy tools created after 2003, in order to keep pace with the changes that the monetary and financial policies will witness from financial openness and expectations of high levels of liquidity after international economic restrictions. It is necessary to re-evaluate the work of the currency Auction from time to time and observation its efficiency in adjustment the exchange rate And its reflection on the general level of prices as one of the objectives of its inception, and during the analytical aspect, it was confirmed that the currency Auction for selling the currency had a major role in adjustment the exchange rate and controlling inflation levels, due to the market’s dependence
... Show MoreKE Sharquie, AA Noaimi, RA Flayih, Am J Clin Res Rev, 2020 - Cited by 4
In the contemporary political history of Iraq, a unique protest broke out on October 1st, 2019. This protest reappeared on October 25th and lasted up to the following weeks making this protest as the most comprehensive and deepest one. It has the possibility of lengthening and the diversification of methods among all the social protesting movements during the century for Iraq. This desperate youth movement presents various images and methods to highlight the image of the protesting movement. The role of the Iraqi woman was clear, which was embodied through the mural paintings expressing her artistic and social role in conveying and expressing the goal of the protest. The aim of the current research is to identify the social artistic implica
... Show MoreThis study aimed to show the extent of compliance with the income taxpayer to provide tax returns and increase the speed of collection of these taxes in addition to increasing confidence in Income Tax department and reduce the number of cases transferred to the courts and promote taxpayer awareness in charge of the importance of self-assessment system, and study sought to investigate the effect of the existence of records documents, technical audit, and computational audit and documentary audit on income tax collections in Jordan, from the point of viewof Jordanian income tax auditors ,results shows there's a strong relation between these variables and Income Tax collections.
In this research, the performance of asphalt mixtures modified with polyethylene polymer (PE) by adding 2%, 4%, and 6% percentages was evaluated. Two kinds of PE are employed: Low-Density PE (LDPE) and High-Density PE (HDPE). The semi-wet mixing technique (SWM) was conducted to avoid stability issue for PE-modified binder during storage condition. Many experimental tests were conducted to evaluate the ability of these mixtures to withstand the effects of loads and moisture. The hardness index of these mixtures was also measured to determine their resistance to the effects of high temperatures without causing permanent deformations. The results showed that adding PE led to a remarkable enhancement in the performance of PE-modified mixtures.
... Show More