doi:10.1515/jiip-2019-0046

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Publication Date

Tue Mar 10 2020

Journal Name

Journal Of Inverse And Ill-posed Problems

Volume

28

DOI

10.1515/jiip-2019-0046

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Direct and inverse source problems for degenerate parabolic equations

M. S.

Daniel

Vitaly L.

Andrey B.

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AbstractDegenerate 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.

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Publication Date

Sat Oct 01 2022

Journal Name

Lark Journal

The problem of synonyms and similar words in the translation of the Holy Quran into Russian (based on the translation by Elmir Kuliev) اشكالية الترادف والكلمات المتقاربة في المعنى في ترجمة القران الكريم الى اللغة الروسية (بناءا على ترجمة إلمير كولييف) Проблема синонимов и близких по значению слов в переводе Священного Корана на русский язык (на материале перевода Эльмира Кулиева)

Tandem

Holy Quran

verse

surah

Translation.

Ashwaq Mohammed

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In our research, we dealt with one of the most important issues of linguistic studies of the Holy Qur’an, which is the words that are close in meaning, which some believe are synonyms, but in the Arabic language they are not considered synonyms because there are subtle differences between them. Synonyms in the Arabic language are very few, rather rare, and in the Holy Qur’an they are completely non-existent. And how were these words, close in meaning, translated in the translation of the Holy Qur’an by Almir Kuliev into the Russian language.

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Publication Date

Thu Apr 06 2023

Journal Name

Materials Science Forum

Study of the Effect of Ce 3+ on the Gas Sensitivity and Magnetic Properties of CuxCe0.3-XNi0.7Fe2O4 Ferrite Nanoparticles

Tagreed M.

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This study includes the preparation of the ferrite nanoparticles Cu_xCe_0.3-XNi_0.7Fe₂O₄ (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) using the sol-gel (auto combustion) method, and citric acid was used as a fuel for combustion. The results of the tests conducted by X-ray diffraction (XRD), emitting-field scanning electron microscopy (FE-SEM), energy-dispersive X-ray analyzer (EDX), and Vibration Sample Magnetic Device (VSM) showed that the compound has a face-centered cubic structure, and the lattice constant is increased with increasing Cu ion. On the other hand, the compound has apparent porosity and spherical particles, and t

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