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Direct and inverse source problems for degenerate parabolic equations
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Abstract<p>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.</p>
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Publication Date
Wed Nov 27 2019
Journal Name
Environmental Science And Pollution Research
Application of emulsion and Pickering emulsion liquid membrane technique for wastewater treatment: an overview
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Publication Date
Fri Jan 01 2016
Journal Name
Diabetic Foot &amp; Ankle
Risk factors for occurrence and recurrence of diabetic foot ulcers among Iraqi diabetic patients
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Publication Date
Thu Apr 12 2012
Journal Name
Pramana
Nucleon momentum distributions and elastic electron scattering form factors for some 1p-shell nuclei
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Publication Date
Wed Mar 15 2023
Journal Name
Journal Of The Turkish-german Gynecological Association
Obstetric and neonatal complications in large for gestational age pregnancy with late gestational diabetes
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Publication Date
Thu Jan 01 2026
Journal Name
Journal Of Interdisciplinary Mathematics
An approximate solution for PDEs of third order under mixed and nonlocal boundary conditions
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This work aims to find a solution to the problem under investigation and to study non-local boundary-value problems for rectangular domains and two-dimensional thirdorder partial differential equations (PDEs). A finite-difference method combined with the trapezoidal rule is used to solve problems. The numerical results were determined to be steady and accurate.

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Publication Date
Fri Feb 28 2025
Journal Name
International Journal Of Intelligent Engineering And Systems
MCNet: Mask Cell of Multi Class Deep Network for Blood Cells Detection and Classification
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Physicians are likely to expend significant labor and time while manually calculating blood smears. Automatic computer-based methods for classifying acute lymphoblastic leukemia have trouble correctly lighting stained white blood cell microscopy images and accurately separating cells that touch or overlap. Additionally, incorporating machine learning techniques into medical services is very hard because doctors can deal with rough guesses as long as the results aren't too bad, but they can't use these calculations for actual medical care. Enabling a A deep network having knowledge of the accuracy of its own predictions is a fascinating and crucial issue. Most instances segmentation frameworks weigh the mask quality during the instance

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Publication Date
Fri Nov 03 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences( P-issn 1683 - 3597 E-issn 2521 - 3512)
Diacerein Loaded Novasome for Transdermal Delivery: Prepartion , In-Vitro Characterization and Factors Affecting Formulation
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Diacerein (DCN) is a semi-synthetic anthraquinone derivative of Rhein that is indicated for the management of osteoarthritis. Diacerein exhibits poor dissolution in the GIT fluids and suffers from low bioavailability upon oral administration in addition to the laxative effect of Rhein metabolites. The aim of the present study was to develop novasomal vesicles with optimized entrapment efficiency and size to serve as a carrier for transdermal delivery of diacerein. Novasomal vesicles were prepared by thin film hydration method thin film hydration. The prepared vesicles were optimized utilizing different surfactant to cholesterol molar ration, sonication type, different sonication times and varying fatty acid level. The prepared vesicles were

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Publication Date
Wed Nov 01 2023
Journal Name
The Saudi Dental Journal
Salivary lactate dehydrogenase and salivary total protein as potential biomarkers for screening periodontal disease
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Abstract Background: Timely diagnosis of periodontal disease is crucial for restoring healthy periodontal tissue and improving patients’ prognosis. There is a growing interest in using salivary biomarkers as a noninvasive screening tool for periodontal disease. This study aimed to investigate the diagnostic efficacy of two salivary biomarkers, lactate dehydrogenase (LDH) and total protein, for periodontal disease by assessing their sensitivity in relation to clinical periodontal parameters. Furthermore, the study aimed to explore the impact of systemic disease, age, and sex on the accuracy of these biomarkers in the diagnosis of periodontal health. Materials and methods: A total of 145 participants were categorized into three groups based

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Publication Date
Fri Jan 01 2016
Journal Name
Diabetic Foot &amp; Ankle
Risk factors for occurrence and recurrence of diabetic foot ulcers among Iraqi diabetic patients
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There are a few studies that discuss the medical causes for diabetic foot (DF) ulcerations in Iraq, one of them in Wasit province. The aim of our study was to analyze the medical, therapeutic, and patient risk factors for developing DF ulcerations among diabetic patients in Baghdad, Iraq.

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Publication Date
Wed May 01 2019
Journal Name
Reports Of Practical Oncology &amp; Radiotherapy
Estimation of tumor and local tissue dose in gold nanoparticles radiotherapy for prostate cancer
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The objective of this research was to estimate the dose distribution delivered by radioactive gold nanoparticles (198 AuNPs or 199 AuNPs) to the tumor inside the human prostate as well as to normal tissues surrounding the tumor using the Monte-Carlo N-Particle code (MCNP-6.1. 1 code). Background Radioactive gold nanoparticles are emerging as promising agents for cancer therapy and are being investigated to treat prostate cancer in animals. In order to use them as a new therapeutic modality to treat human prostate cancer, accurate radiation dosimetry simulations are required to estimate the energy deposition in the tumor and surrounding tissue and to establish the course of therapy for the patient. Materials and methods A simple geometrical

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