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 objective of the research is to identify the effect of an instructional design according to the active learning modelsالباحثين in the achievement of the students of the fifth grade, the instructional design was constructed according to the active learning models for the design of education. The research experience was applied for a full academic year (the first & the second term of 2017-2018). The sample consisted of 58 students, 28 students for the experimental group and 30 students for the control group. The experimental design was adopted with partial and post-test, the final achievement test consisted of (50) objectives and essays items on two terms, the validity of the test was verified by the adoption of the Kudoric
... Show MoreDensity Functional Theory (DFT) with B3LYP hybrid exchange-correlation functional and 3-21G basis set and semi-empirical methods (PM3) were used to calculate the energies (total energy, binding energy (Eb), molecular orbital energy (EHOMO-ELUMO), heat of formation (?Hf)) and vibrational spectra for some Tellurium (IV) compounds containing cycloctadienyl group which can use as ligands with some transition metals or essential metals of periodic table at optimized geometrical structures.
This study aimed to identify and describe one of the bacterial feeder nematode Acrobeloides varius Kim, Kim and Park, 2017 (Rhabditida, Cephalobidae), which was isolated from soil samples that were collected from Baghdad, central of Iraq, and was classified using both morphological and molecular criteria. All specimens of A. varius were cultured, identified and described using morphometric criteria. Selected specimens (Zah. IRQ3 OR994579.1 isolate) of this species were characterized by having the body length of the male ranging from (184.94 – 221.72 μm), the body length of the female ranging (507.38 – 521.92 μm) and the body length of the juvenile ranging from (355.53 – 490.35 μm). Selected specimens of this species were m
... Show MoreA simple, rapid, sensitive and inexpensive approach is described in this work based on a combination of solid‐phase extraction of 8‐hydroxyquinoline (8HQ), for speciation and preconcentration of Cr(III) and Cr(VI) in river water, and the direct determination of these species using a flow injection system with chemiluminescence detection (FI–CL) and a 4‐diethylamino phenyl hydrazine (DEAPH)–hydrogen peroxide system. At different pH, the two forms of chromium [Cr(III) and Cr(VI)] have different exchange capacities for 8HQ, therefore two columns were constructed; the pH of column 1 was adjusted to pH 3 for retaining Cr(III) and column 2 was adjusted to pH 1 for retaining of Cr(VI). The sorbe
Poly (viny1 alcohol) (PVA) of 72000 g mol -1 molar mass was cross linked through cold cast esterification with different mol % of MA and EDTA (10 % , 20 % and 30 % ), and two different mol % mixture of MA l EDTA (20 %/5% and 20%/10% .
This study seeks to address the impact of marketing knowledge dimensions (product, price, promotion, distribution) on the organizational performance in relation to a number of variables which are (efficiency, effectiveness, market share, customer satisfaction), and seeks to reveal the role of marketing knowledge in organizational performance.
In order to achieve the objective of the study the researcher has adopted a hypothetical model that reflects the logical relationships between the variables of the study. In order to reveal the nature of these relationships, several hypotheses have been presented as tentative solutions and this study seeks to verify the validity of these hypotheses.
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