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.
This study was conducted to prepare protein concentrates from AL-Zahdidate’s pits by using alkaline methods where the chemical composition of the pits were (7.30, 1.04, 5.80, 8.68 and 77.19) % for each of the moisture, ash, protein, fat and carbohydrates respectively and the chemical composition of the concentrate protein was (6.62, 4.10, 26.70, 0.93, and 58.65) % respectively. The content of protein concentrate from the metallic elements (144.07, 25.11, 15.02, 0.49, 0.59, 0.27, 0.22 and 234.6) mg/ 100 g each of potassium, magnesium, calcium, iron, manganese, copper, zinc and phosphorus respectively. The results of SDS-PAGE showed five bands with weights molecular ranged between 11000-70000 Dalton. Give the biscuit which contain protei
... Show MoreObjective: To evaluate two kinds of extraction (aqueous and ethanolic) for coriander using seeds, leaves and stems and
studying their antibacterial activity against nine different microorganisms.
Methodology: Coriander was selected to carry out this study. Seeds, leaves and stems were collected from local markets in
Baghdad then dried in shade for at least 10 days and grinded to fine powder. Aqueous hot extracts for 1hr. at (50
c) and
cold extracts for 24 hrs at (4
c) were performed by using seeds, leaves and stems then studied antibacterial effect against
nine different microorganisms by using well diffusion technique. Cold aqueous extracts of coriander seeds for 48 hrs. and
72 hrs and ethanolic extraction
A new ligand (H4L) and its complexes with ( ZnII, CdII and HgII) were prepared. This ligand was prepared in two steps. In the first step a solution of terephthaldehyde in methanol was reacted under reflux with 1,2-phenylenediamine to give an precursor compound which reacted in the second step with 2,4-dihydroxybenzaldehyde to give the ligand. The complexes were then synthesized by direct reaction of the corresponding metal chloride with the ligand. The ligand and complexes were characterized by spectroscopic methods FT-IR, UV-Vis, 1 HNMR, and atomic absorption, chloride content, HPLC, mole-ratio determination. in addition to conductivity measurement. The data of these measurements suggest a distorted tetrahedral geometry for ZnII, C
... Show MoreA new ligand (H4L) and its complexes with ( ZnII, CdII and HgII) were prepared. This ligand was prepared in two steps. In the first step a solution of terephthaldehyde in methanol was reacted under reflux with 1,2-phenylenediamine to give an precursor compound which reacted in the second step with 2,4-dihydroxybenzaldehyde to give the ligand. The complexes were then synthesized by direct reaction of the corresponding metal chloride with the ligand. The ligand and complexes were characterized by spectroscopic methods FT-IR, UV-Vis, 1HNMR, and atomic absorption, chloride content, HPLC, mole-ratio determination. in addition to conductivity measurement. The data of these measurements suggest a distorted tetrahedral g
... Show MoreThis topic is considered to be of a high degree of importance to every Muslim, and its importance is due to the fact that monotheism is:
Prove that God Almighty is the God who created everything and everything opposite to monotheism is polytheism, and it is taking other than God Almighty as a deity.
Therefore, we have to know the concept of God. If he is known, then he knows the concept of monotheism and the concept of polytheism
Objective: Evaluation the national standards for exposure to chemical materials and dusts in The State
Company for Drugs Industry in Samarra.
Methodology: A descriptive evaluation design is employed through the present study from 25th May 2011
to 30th November 2011 in order to evaluate the national standards for exposure chemical materials and dusts
in The State Company for Drugs Industry in Samarra. A purposive (non-probability) sample is selected for the
study which includes (110) workers from the State Company for Drugs Industry in Samarra. Data were
gathered through the workers` interviewed according to the nature of work that they perform. The evaluation
questionnaire comprised of three parts which include the w
A taxonomic keys was established of book and bark lice Order Psocoptera to isolated insects in Iraq from different localities of Baghdad and Babylon provinces. Thirteen species belong to eight genera and five families have been studied and described in details, these species were recorded for the first time in Iraq. These species are: Belaphopsocus badonneli New, 1971; Belaphotroctes oculeris Bodonnel, 1973; Embodopsocosis newi Bodonnel, 1973; Epipsocus stigamaticus Mockeord, 1991; Lepinotus huoni Schmidt and New, 2008; Liposcelies decolor Peramane 1925 Liposcelies paeta Pearman 1942 Liposclies bostrychphila Badonnel 1931; Liposclies brunnea Mostchulsky 1852; Liposclies entoophila Enderlein 1907; Neopsocopsis minuscule Li 2002 ;
... Show MoreLinguistic research according to modern curricula:
It is one of the important matters that occupy the ideas of those concerned with linguistic studies, whether Arabic or otherwise. Recent years have witnessed the advancement of this methodological approach, and books and studies in Arabic have been written on important, multifaceted issues, of grammatical and linguistic origins, and their balance with new developments and ideas attracted mostly from Western studies.
The comparative approach - as they call it - is one of the modern approaches that is based on balancing a language with other sisters belonging to its family, to reach similarities and differences between them, and to know the c