This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
God Almighty put in his great book secrets that do not end, and wonders that do not expire, for he is the one from which the scholars are not satisfied, and he does not create due to the multitude of response, and it is the comprehensive and inhibitory book that God conceals to the worlds, and he challenged the two heavyweights to come up with something like it.
At all times, issues arise in the Noble Qur’an that fit the needs of the people of that time and their culture, for it is an eternal book, characterized by the ability to give, extend and respond to addressing the problems of the age and its variables, when the Arabs had little luck at the time of the message’s descent from the scientific culture, and their proficienc
... Show MoreThe typical test for diagnosis of severe acute respiratory syndrome coronavirus 2 is a reverse transcription-polymerase chain reaction (RT-PCR) technique, but the chest CT scan might play a complementary role at the first detection of Coronavirus Disease 2019 (COVID-19) pneumonia. Objectives: To determine the sensitivity of CT scan on patients with COVID-19 in Al-Najaf, Iraq, and to compare the accuracy of CT scan with that of RT-PCR technique. Material and Method: This is a prospective study. The patients suspicious of having COVID-19 infection and respiratory symptoms were registered. All patients were diagnosed by RT-PCR and chest CT. Diagnostic performance of CT was intended using RT-PCR as the reference sta
... Show MoreThe Paleocene benthic foraminiferal zonation of the Umm Er Rhadhuma Formation from the borehole (K.H 12/7), South Anah City (Western Iraq), has been re-studied and re-analyzed precisely based on the large benthic foraminifera (LBF). They are represented by two biozone Rotorbinella hensoni Partial Range Zone, recorded from the Lower and middle parts of the Umm Er Rhadhuma Formation and Lockhartia praehaimei Partial Range Zone determined Uppermost of this unit, and dated to be the Selandian – Thanetian stage. Almost all the biogenic (micro and macro) and non-biogenic constituents, including large benthic foraminifera, Algae, Echinoderm, Bryozoans, Oyster, Gastropod fragments, and peloids, in addition to lithofacies types, indicate t
... Show MoreThe author addresses the issue of the linguoculturological component in the process of teaching Russian to Arabic students, focuses on the peculiarities of the national character of students. The author also refers to the long-standing ties of Russian and Arab cultures, thus emphasizing the relevance of this aspect for the current state and situation of the Russian language in Arab countries.
Автор статьи обращается к вопросу лингвокультурологической составляющей в процессе преподавания русского языка арабским студентам, останавливается на особенностях национального хара
... Show MoreThe added value of internal audit greatly contributes to adding value to the institution, but most departments of economic units in Iraq neglected the role of internal audit and the added value that can be achieved by those institutions, since the term added value of internal audit is a relatively vague term from the premise that what cannot be measured is difficult Determine it, and perhaps descriptive standards for it is the extent of compliance with international auditing standards (IIA).
The research aims to study the procedures and results of auditing to verify that they have given an added value to the audit with a positive impact, develop its aspects and research, identify deficiencies for the audi
... Show MoreObjective: To suggest a weighted measure to diagnose the reasons for the low student success ratios in mathematics concerning the third grade of intermediate schools in light of components educational system represented by: [Students, Teachers, Curriculum, and Environmental reasons (others reasons)] assuming differentiated and interrelated components, Also the effectiveness forming of these components according to the gender variable. Methods: Data collection tools were prepared by constructing two questionnaires for each of (Students and Teachers), which included a number of items that involved some domains for studied components of educational system, which demonstrated a high level of validity and reliability in the pilot study, in addi
... Show MoreThe purpose of this resesrh know (the effectiveness of cooperative lerarning implementation of floral material for calligraphy and ornamentation) To achieve the aim of the research scholar put the two zeros hypotheses: in light of the findings of the present research the researcher concluded a number of conclusions, including: -
1 - Sum strategy helps the learner to be positive in all the information and regulations, monitoring and evaluation during the learning process.
2 - This strategy helps the learner to use information and knowledge and their use in various educational positions, and to achieve better education to increase its ability to develop thinking skills and positive trends towards the article.
In light of this, the