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.
Abstract
For sparse system identification,recent suggested algorithms are -norm Least Mean Square ( -LMS), Zero-Attracting LMS (ZA-LMS), Reweighted Zero-Attracting LMS (RZA-LMS), and p-norm LMS (p-LMS) algorithms, that have modified the cost function of the conventional LMS algorithm by adding a constraint of coefficients sparsity. And so, the proposed algorithms are named -ZA-LMS,
... Show MoreDrought is a natural phenomenon in many arid, semi-arid, or wet regions. This showed that no region worldwide is excluded from the occurrence of drought. Extreme droughts were caused by global weather warming and climate change. Therefore, it is essential to review the studies conducted on drought to use the recommendations made by the researchers on drought. The drought was classified into meteorological, agricultural, hydrological, and economic-social. In addition, researchers described the severity of the drought by using various indices which required different input data. The indices used by various researchers were the Joint Deficit Index (JDI), Effective Drought Index (EDI), Streamflow Drought Index (SDI), Sta
... Show MoreIn this research a new system identification algorithm is presented for obtaining an optimal set of mathematical models for system with perturbed coefficients, then this algorithm is applied practically by an “On Line System Identification Circuit”, based on real time speed response data of a permanent magnet DC motor. Such set of mathematical models represents the physical plant against all variation which may exist in its parameters, and forms a strong mathematical foundation for stability and performance analysis in control theory problems.
The research seeks to examine the ability of fifth preparatory students in solving a mathematical problem in relation to system thinking. To this end, the researcher chose (140) fifth preparatory students from four-different secondary schools in Kirkuk city for the academic year (2016-2017). Two tests were adopted to collect study data: a test of (5) items about skills in solving math problem designed by (Al-raihan, 2006); and a test of system thinking skills designed by the researcher himself consisted of (14) items. It was divided into four skills (analyzing the main system to subsystems, eliminating all inner gaps of system, identifying the inner connection of system, and reorganizing the system). The findings indicated a good ability
... Show MoreReduce the required time for measuring the permeability of clayey soils by using new manufactured cell
In this research, we dealt with the study of the Non-Homogeneous Poisson process, which is one of the most important statistical issues that have a role in scientific development as it is related to accidents that occur in reality, which are modeled according to Poisson’s operations, because the occurrence of this accident is related to time, whether with the change of time or its stability. In our research, this clarifies the Non-Homogeneous hemispheric process and the use of one of these models of processes, which is an exponentiated - Weibull model that contains three parameters (α, β, σ) as a function to estimate the time rate of occurrence of earthquakes in Erbil Governorate, as the governorate is adjacent to two countr
... Show MoreBackground: The Epstein-Barr virus (EBV) relates to the torch virus family and is believed to have a substantial impact on mortality and perinatal events, as shown by epidemiological and viral studies. Moreover, there have been documented cases of EBV transmission occurring via the placenta. Nevertheless, the specific location of the EBV infection inside the placenta remains uncertain. Methods: The genomic sequences connected to the latent EBV gene and the levels of lytic EBV gene expression in placental chorionic villous cells are examined in this work. A total of 86 placentas from patients who had miscarriage and 54 placentas from individuals who had successful births were obtained for analysis. Results: The research employed QPCR to dete
... Show MoreThis study aimed to detect Anaplasma phagocytophilum in horses through hematological and molecular tests. The 16S rRNA gene of the Anaplasma phagocytophilum parasite was amplified by polymerase chain reaction (PCR), then sequenced, and subjected to phylogenetic analysis to explore "Equine Granulocytic Anaplasmosis" (EGA) infection in three important gathering race horses areas in Baghdad governorate, Iraq. Blood samples were obtained from 160 horses of varying ages, three breeds, and both sexes, between January and December 2021. Prevalence and risk variables for anaplasmosis were analyzed using statistical odds ratio and chi-square tests. Results demonstrated that clinical anaplasmosis symptoms comprised jaundice, wei
... Show MoreThe study included the investigation of fungi which associated with heavy animal's leather (Cows and Buffalos) and light (Sheep’s and Goats )through different processing stages (raw hides ,dehairing ,pickling,chrome tanned and stainning or finished stages)there were 10 genera and 25 species in addition to sterile fungi associated with animal leathers which included Alternaria ,Aspergillus,Cladosporium,Fusarium, Mucor , Penicillium , Rhizopus , and Trichoderma .Aspergillus and Penicillium have observed in all leather samples and different processing stages, and that the first time isolate two genera Helminthosporium , Stemphylium form leather for staining stage.