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.
The sport of polo, the game of kings and sultans, is one of the traditional sports that has defied time throughout its long history. It has preserved its historical roots and been able to adapt to contemporary requirements, societal transformations, and temporal and spatial variables. It has moved from an aristocratic sport practiced as a form of entertainment to a professional competitive sport. It attracts many players and millions of viewers, so it is a living model of how sports develop and transform from a local tradition into global sports with organized rules managed by international institutions and with many championships worldwide. Through this, the research objectives were formulated, including exploring sports' origins. Polo in
... Show MoreThe Paleocene benthic foraminiferal zonation of the Umm Er Rhadhuma Formation from the borehole (K.H 12/7), South Anah City (Western Iraq), has been re-studied and re-analyzed precisely based on the large benthic foraminifera (LBF). They are represented by two biozone Rotorbinella hensoni Partial Range Zone, recorded from the Lower and middle parts of the Umm Er Rhadhuma Formation and Lockhartia praehaimei Partial Range Zone determined Uppermost of this unit, and dated to be the Selandian – Thanetian stage. Almost all the biogenic (micro and macro) and non-biogenic constituents, including large benthic foraminifera, Algae, Echinoderm, Bryozoans, Oyster, Gastropod fragments, and peloids, in addition to lithofacies types, indicate t
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Objectives: To find out the association between enhancing learning needs and demographic characteristic of (gender, education level and age).
Methods: This study was conducted on purposive sample was selected to obtain representative and accurate data consisting of (90) patients who are in a peroid of recovering from myocardial infarction at Missan Center for Cardiac Diseases and Surgery, (10) patients were excluded for the pilot study, Data were analyzed using descriptive statistical data analysis approach of frequency, percentage, and analysis of variance (ANOVA).
Results: The study finding shows, there was sign
... Show MoreThe purpose of this research is to identify heritage and highlight its value by drawing on its decorative vocabulary and integrating it with the Arabic calligraphy to revive the heritage in a contemporary style, and to create decorative design units inspired by Sadou and Arabic calligraphy and to employ them in the modern fashion designs. The applied descriptive approach has been used in this research, and the research community is made of women in Riyadh area. The tools used in this research were the questionnaire and the observation. The most important results of the research are: the design of decorative units from the integration of Arabic calligraphy and the decorations of the Saduo, and the use of these units in the design of the o
... Show MoreIn this study, the effect of intersecting ribs with inclined ribs on the heat transfer and flow characteristics of a high aspect ratio duct has been numerically investigated. The Relative roughness pitch (P/e) is 10 and the Reynolds number range from 35,700 to 72,800. ANSYS (Fluent-Workbench 18.0) software has been utilized to solve the Reynolds averaged Navier-Stokes (RANS) equations with the Standard k-ε turbulence model. Three ribbed models have been used in this study. Model 1 which is a just inclined ribs, Model 2 which has a single longitudinal rib at the center with inclined ribs and Model 3 which has two longitudinal ribs at the sides. The results showed that the heat transfer rate has been enhanced when the int
... Show MoreSince there is no market for bond issuance by companies in the Iraqi market and the difficulty of borrowing, companies must resort to proprietary financing to finance their investments. However, in the framework of the literature of financial management, the type of financing used by the company sends signals to investors and therefore reflected on the market value. Therefore, the problem of the study revolves around the variables of the study (Equity financing within the framework the signal theory, price of common stock in the Iraqi market).
The study aims to verify the impact of the capital increase through the issuance of new stock on the price of
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Prais be to Allah the Lord of the Worlds and prayers and peace be upon our faithfull Prophet …. I wrote this Research entitled (The Imam Shams AL-din Abdulrahman Bin Qudamah AL-Maqdsi (died: 682 A.H) Slections in Slections in proving contract annulment choice (AL-tassriah)and its duration which Iclarrified the reason of choosing this title and my method in writing Morever, a brief Overriew of the life of Imam Shams AL-din Bin Qudamah and the meaning of (AL-tassriah)and whether it proves to the buyer to return it, beside the duration which (the tassriah) proven, and a conclusion in which I showed the results I reached and some recommendations that some researchers in the field of Jurispruden
... Show MoreIn this study, the melting-cooling method was used to prepare the chalcogenide compound S60-Se40-X-PbX. Four samples were obtained by partial replacement of Selenium with Lead in the weight ratios x = 0, 10, 20, and 30, respectively. The materials were mixed separately, ground, placed in quartz ampoules, and heated to 500 degrees Celsius. After conducting several operations on the samples, their insulating properties were studied, represented by the real dielectric constant and the imaginary dielectric constant, and the electrical conductivity was measured as a function of the frequency. It was found that partial replacement plays an impo
Background: With the increase in composite material use in posterior teeth, the concerns about the polymerization shrinkage has increased with the concerns about the formation of marginal gaps in the oral cavity environment. New generation of adhesives called universal adhesive have been introduced to the market in order to reduce the technique sensitive bonding procedures to give the advantage of using the bonding system in any etching protocol without compromising the bonding strength. The aim of the study was to study marginal adaptation of two universal adhesives (Single bondâ„¢ Universal and Prime and Bond elect) using 3 etching techniques under thermal cycling aging. Materials and Methods: Forty-eight sound maxillary first premola
... Show MoreThe paper deals with the marked vocabulary of Russian and Arabic language, and the extrapolated to the phraseological layer of the mentioned language systems. Specificity of the functioning of this process is presented against the backdrop of the peculiarities of the existence of Russian and Arabic languages. Attention is focused on the fact that linguistic markers should be considered as a kind of keys that represent the specificity of the experience of being experienced by an individual in ontological reality. It is asserted that marking can be revealed practically at all levels of the language polysystem, but it is especially productive on its lexical layer, in particular, on the basis of lexicology and ph
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