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.
The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production
... Show MoreAl-Chibayish Marsh (CM) is considered as the major part of Central Marshes area of this marsh is 1050 Km². The water quality of these marshes is suffering from salt accumulation due to intensive dam construction, limited supply of water from sources, climate change impacts, and the absence of outlet flow from these marshes, specifically at low flow periods. So, the current research aims to assess and improve these marshes' hydraulic behavior and water quality and define the best location for outlet drains. Field measurements and laboratory tests were conducted for two periods (November 2020 and February 2021) to define the (TDS) concentrations at nine different locations. Samples were also examined for water's phy
... Show MoreIn this study; a three-dimensional model was created to simulate groundwater in Al-Haydariyah area of the governorate of Al-Najaf. A solid model was created to utilize the cross sections of 25 boreholes in the research region, and it was made out of two layers: sand and clay. The steady-state calibration was employed in six observation wells to calibrate the model and establish the hydraulic conductivity, which was 17.49 m/d for sand and 1.042 m/d for clay, with a recharge rate of 0.00007 m/day. The wells in the research region were reallocated with a distance of 1500 m between each well, resulting in 140 wells evenly distributed throughout the study area and with a discharge of 5 l/s, and the scenarios were run for 1000
... Show MoreAsthma is a chronic inflammatory disease of respiratory airways characterized by distinctive history of respiratory symptoms due to variable airflow obstruction which reverses either spontaneously or in response to certain medications. Acetylcholine is a parasympathetic neurotransmitter which plays fundamental roles in the development of persistent asthma. Treatment guidelines recommend using medium doses of inhaled corticosteroids in addition to another controller bronchodilator instead of using high doses inhaled steroid alone for treatment of moderate to severe persistent asthma. The inhaled long acting muscarinic antagonist, tiotropium, was approved recently to control unresponsive asthma to inhaled corticosteroid with or without a long
... Show MoreMultiple sclerosis (MS) is a neurodegenerative disorder with various clinical types. Glial fibrillary acidic protein (GFAP) is significantly elevated in the cerebrospinal fluid (CSF) of MS patients compared with that of healthy controls. The aim of this study is to evaluate serum levels of GFAP in relation to disease activity in relapsing-remitting MS patients and to compare them with those of healthy controls. Method: This study involved 58 MS patients of relapsing-remitting MS (RRMS) type, 22 in an active stage of the disease and 36 in remission, and 50 healthy individuals as age- and sex-matched controls. Blood samples were taken from the patients at the MS Clinic of the Baghdad Teaching Hospital, and the serum levels of GFAP were determ
... Show MoreThe purpose of this paper is to investigate Religious Human Rights Violations. Religious liberty is essential for everyone, everywhere. Because religion is significant to everyone, everywhere. Humans are religious by nature. Our nature drives us to seek answers to deep questions about ultimate things. We cannot live a fully human life unless we are free to seek those answers and live according to the truths we discover. In this study, the researcher used Marsh and White model for analysis A sample of an offensive image of an Islamic concept from the book "Mohammad believes it or else." this book is a comic book written by pseudonym Abdullah Aziz and published by Crescent Moon Publishing company. The book is marked with anti- Mohammad, preju
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The multiple linear regression model of the important regression models used in the analysis for different fields of science Such as business, economics, medicine and social sciences high in data has undesirable effects on analysis results . The multicollinearity is a major problem in multiple linear regression. In its simplest state, it leads to the departure of the model parameter that is capable of its scientific properties, Also there is an important problem in regression analysis is the presence of high leverage points in the data have undesirable effects on the results of the analysis , In this research , we present some of
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