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 role of teacher of kindergarten plays an important role in the educational institution for kindergarten role in the educational institution for kindergarten and the failure of its role in the development of the mental processes of children kindergarten means failing in this institution .and hence the importance and effectiveness of the role of the student applied section kindergarten application period it is there fore necessary to be aware of the importance of learning. in preschool and good professional setting and enjoy a significant level of psychological and social systems and mental qualities and study is the urgent need to find generations hare systematic thinker's mind so stay away from memorization and trad
... Show MoreThe economical and highly performed anode material is the critical factor affecting the efficiency of electro-oxidation toward organics. The present study aimed to detect the best conditions to prepare Mn-Co oxide composite anode for the electro-oxidation of phenol. Deposition of Mn-Co oxide onto graphite substrate was investigated at 25, 30, and 35 mA/cm2 to detect the best conditions for deposition. The structure and the crystal size of the Mn-Co oxide composite electrode were examined by using an X-Ray diffractometer (XRD), the morphological properties of the prepared electrode were studied by scanning electron microscopy (SEM) and Atomic force microscopy (AFM) techniques, and the chemical composition of the various
... Show MoreIn the present work, the focusing was on the study of the x-ray diffraction, dielectric constant, loses dielectric coefficient, tangent angle, alter- natively conductivity and morphology of PET/BaTio3. The PET/BaTio3 composite was prepared for polyethylene terephthalate PET polymer composite containing 0, 10, 20, 30, 40, 50, and 60 wt. % from Barium titanate BaTi03 powder. The composite of two materials leads to form mixing solution and hot-pressing method. The effect of BaTio3 on the structure and dielectric properties with morphology was studied on PET matrix polymer using XRD, LCR meter and SEM.
Fine aggregates used for concrete works in Sulaymaniyah city frequently fail to meet the standard requirements for gradation and fineness modulus in cement concrete. This paper aims to critically evaluate gradation, fineness modulus, and clay contents of various natural sands produced and used for concrete work in the region. Sixteen field sand samples were collected from various sites in Darbandikhan (5 samples), Qalat Dizah (5 samples), Koysinjaq (5 samples), and Piramagroon (1 sample) confirming to ASTM D75. The field samples were parted into test specimens based on ASTM C702. Then, sieve analysis was carried out on the oven-dry test specimens in compliance with ASTM C136. The test results of fine aggregates wer
... Show MoreBackground: Many structural or functional abnormalities can impair the production of thyroid hormones and cause hypothyroidism.Objectives: to identify the main etiological causes of hypothyroidism among patients visiting Specialized Center for Diabetes and Endocrinology.Methods: This study was conducted in the Specialized Center for Diabetes and Endocrinology on 217 patients with proved hypothyroidism, from 2006 to 2008. Every patient was tested with thyroid function tests, Ultrasound examination, thyroid autoantibodies, fine needle aspiration, radiology of skull, isotopes scan, also checking adrenal and gonadal function. Results: Out of these 217 patients 120 patients have thyroiditis 33 patients had been undergone thyroidectomy. 39 pat
... Show MoreThe construction industry plays a crucial role in the countries' economy, especially in the developed country. This point encourages the concerned institution to use new techniques and integrate many techniques and methods to maximize the benefits. The main objective of this research is to evaluate the use of risk management, value management, and building information modeling in the Iraqi construction industry. The evaluation process aims at two objectives. The direct objective was to evaluate the knowledge in risk management (RM), value management (VM), and building information modeling (BIM). The indirect objective was to support the participants with information related to the main items mentioned. The questionnaire
... Show MoreThis article presents an improvement in the properties of environmentally friendly, inexpensive, and readily available surfaces for use in addressing a significant environmental problem: pollution from dyes generated by various industrial processes. The surface of Iraqi flint clay was acidically activated and used to adsorb methyl orange dye from its aqueous solutions. The clay surface was characterized before and after acid activation using several techniques, including Fourier transform infrared spectroscopy, X-ray diffraction spectroscopy, X-ray disperse energy spectroscopy, and field-emission scanning electron microscopy. The adsorption of methyl orange dye using flint clay before and after activation was performed in batch system under
... Show MoreExploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Letters in Biomathematics · Jul 7, 2025Letters in Biomathematics · Jul 7, 2025 Show publication This paper, presents the application of the B-spline transform as an effective and precise technique for estimating key parameters i.e., drift, volatility, and jump intensity for Lévy processes. Lévy processes are powerful tools for representing phenomena with continuous trends with abrupt changes. The proposed approach is validated through a simulated biological case study on animal migration in which movements are mo
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