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.
In this paper, some estimators of the unknown shape parameter and reliability function of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively
In the framework of correlation method so-called coherent density fluctuation model (CDFM) the nucleon momentum distributions (NMD) of the ground state for some even mass nuclei of fp-shell like 50Cr, 52Cr and 54Cr isotopes are examined. Nucleon momentum distributions are expressed in terms of the fluctuation function (|f(x)|2) which is evaluated by means of the nucleon density distributions (NDD) of the nuclei and determined from theory and experiment. The main characteristic feature of the NMD obtained by CDFM is the existence of high-momentum components, for momenta k ≥ 2 fm−1. For completeness, also elastic electron scattering form factors, F(q) are evaluated within the same framework.
6-Amino-4-(4-hydroxyphenyl)-5-cyano-3-methyl-1-phenyl-1, 4-dihydropyrano [2,3-c] pyrazole (compound 2) was prepared by condensation of 2-(4-hydroxylbenzylidine) malononitrile (compound 1) [which was prepared by Knoevenagel condensation of malononitrile with 4-hydroxy benzaldehyde ] with 3-methyl-1-phenyl-2-pyrazolin-5-one. Reactions of compound 2 with different reagents formic acid, formamide, and ammonium thiocyanate under microwave irradiation leads to the synthesis of 4-(4-hydroxyphenyl)- 3-methyl-1-phenyl-4,6-dihydro- pyrazolo [3', 4':5,6] pyrano [2,3-d] pyrimidine-5-one (compound 3), 4-(4-hydroxyphenyl)- 3-methyl-1-phenyl-4, 6-dihydro- pyrazolo [3', 4':5,6]pyrano[2,3-d]pyrimidine-5-imine (compound 4) and N-[4-(4-hydroxyphenyl)- 3-me
... Show MoreA field experiment was carried out during the seasons 2016 and 2017 in the farm of the Department of Field Crops Science, College of Agricultural Engineering Sciences-University of Baghdad to evaluate the effect of(Aminopyralid + Flurasulam, Coldinafop-propargyl and Flucarbazone-sodium) herbicides and seeding rate (100, 125 and 150) Kg.ha-1 and the interaction between them in growth characteristics, grain and yield components in wheat (Var. IPA99). The results showed that herbicides used were significantly efficient in studied characteristics compared to weedy treatment. Herbicide Flucarbazone-sodium gave higher weed control after 60 and 90 days of spraying the he
Abstract Portable communication devices such as WLAN, WiMAX, LTE, ISM, and 5G utilize one or more of the triple bands at (2.32.7 GHz,3.4–3.6GHz,and5–6GHz)andsufferfromtheeffectofmultipathproblemsbecausetheyareusedinurbanregions.To date, no one has performed a review of the antennas used for these types of wireless communications. This study reviewed two types of microstrip antennas (slot and fractal) that have been reported by researchers (as a single element) using a survey that included the evaluation of several important specifications of the antennas in previous research, such as operating bandwidth, gain, efficiency, axial ratio bandwidth (ARBW), and size. The weaknesses in the design of all antennas were carefully identified to de
... Show MoreDocumentary Credit passes through many practical phases starting from Opening credit and matching documents and payment of the amount of credit……etc. It is worthy to mention that there are several aspects that are varied and differed from Bank to another one which can offer Competitive Advantage for the bank …This will be shown in this research.
For the purpose of achieving the objective of this research within the theoretical aspect, the researcher had seen and briefed several books and researches which are mainly related to the subject of the research.
As for the practical aspect, has included Questionnaire which included many questions that are fit and suitable to the hypotheses.
Research sample has
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This study aims to identify the extent to which the criteria of the American Council for Teaching Foreign Languages (ACTFL) are included in the English language books for the fifth and sixth graders. To achieve the objective of the study, a content analysis card was prepared, where the classification of language proficiencies was divided into five main levels (beginner, intermediate, advanced, superior, and distinguished) of the four language skills (listening, speaking, reading, and writing), The content analysis card consisted of (89) indicators distributed at the four levels of language skills as follows: Listening (17), speaking (33), reading (15), and writing (26). The study sample consisted of Engl
... Show MoreAA wahid, journal mustansiriyah of sports science, 2023