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 article aims to study the liquidity that is required to be provided optimally and the profitability that is required to be achieved by the bank, and the impact of both of them on the value of the bank, and their effect of both liquidity and profitability on the value of the bank. Hence, the research problem emerged, which indicates the extent of the effect of liquidity and profitability on the value of the bank. The importance of the research stems from the main role that commercial banks play in the economy of a country. This requires the need to identify liquidity in a broad way and its most important components, and how to
... Show MoreDiscriminant analysis is a technique used to distinguish and classification an individual to a group among a number of groups based on a linear combination of a set of relevant variables know discriminant function. In this research discriminant analysis used to analysis data from repeated measurements design. We will deal with the problem of discrimination and classification in the case of two groups by assuming the Compound Symmetry covariance structure under the assumption of normality for univariate repeated measures data.
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BACKGROUND: Many genetic factors are known to be related to osteoporosis, and currently the role of the glucagon-like peptide-1 receptor (GLP-1R) gene in bone health has been studied intensively. Some variation of this gene, such as rs1042044 and rs6458093, are known to be linked to metabolic diseases and lower bone mineral density, however their specific contribution to osteoporosis remains largely unexplored. Therefore, this study was conducted to investigate the combined genotypic effect of rs1042044 and rs6458093 as a genetic risk factor for osteoporosis in postmenopausal Iraqi women.METHODS: Blood samples from 75 osteoporosis patients and 75 healthy controls, aged 45-85, were collected. DNA was extracted, and a region of GLP-1R
... Show MoreThe majority of the environmental outputs from gas refineries are oily wastewater. This research reveals a novel combination of response surface methodology and artificial neural network to optimize and model oil content concentration in the oily wastewater. Response surface methodology based on central composite design shows a highly significant linear model with P value <0.0001 and determination coefficient R2 equal to 0.747, R adjusted was 0.706, and R predicted 0.643. In addition from analysis of variance flow highly effective parameters from other and optimization results verification revealed minimum oily content with 8.5 ± 0.7 ppm when initial oil content 991 ppm, tempe
This work includes preparation of Az, Qz, and Tz derivatives from the reaction of Schiff base (Sb) derivative with anthranilic acid, chloroacetyl chloride, and sodium azide, as well as, the characterization via FT-IR, 1H-NMR, and 13CNMR. The anticorrosion inhibition of these compounds was studied and the measurements of carbon steel (CS) corrosion in sodium chloride solution 3.5% (blank) and inhibitor in solutions were calculated at a temperature range of 293-323 K by the technique of electrochemical polarization. In addition, some thermodynamic and kinetic activation parameters for inhibitor and blank solutions (Ea⋇, ΔH⋇, ΔS⋇, and ΔG⋇) were determined. The results showed high inhibition efficacy for all the prepared compounds,
... Show MoreMaterial obtained from the demolition of concrete structures and milling of flexible pavements has the highest potential for recyclability. This study aimed to evaluate the performance of hot mix asphalt with the concurrent use of recycled asphalt pavement (RAP) and recycled concrete aggregate (RCA). Contents of RAP and RCA were varied from 0% to 50% by fixing the total recycling materials percentage to 50%. Penetration grade 40/50 virgin binder and waste engine oil (WEO) as rejuvenator were used in the present study. A series of tests, such as Scanning electron microscopy (SEM), Marshall stability, indirect tensile strength test, IDEAL CT, uniaxial compression test, and resilient modulus test, were carried out to assess the performance of
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