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 way used to estimate the fuzzy reliability differs according to the nature of the information of failure time which has been dealt in this research.The information of failure times has no probable distribution to explain it , in addition it has fuzzy quality.The research includes fuzzy reliability estimation of three periods ,the first one from 1986 to 2013,the second one from 2013 to 2033 while the third one from 2033 to 2066 .Four failure time have been chosen to identify the membership function of fuzzy trapezoid represented in the pervious years after taking in consideration the estimation of most researchers, proffional geologists and the technician who is incharge of maintaining of Mosul Dam project. B
... Show MoreIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
... Show MoreThe purpose of this research is to demonstrate the effectiveness of a program to address the problem of mixing similar letters in the Arabic language for students in the second grade of primary and to achieve the goal of the research. The researcher followed the experimental method to suit the nature of this research and found that there are statistically significant differences between the tribal and remote tests, The effectiveness of the proposed educational program. At the end of the research, the researcher recommends several recommendations, the most important of which are: 1 - Training students to correct pronunciation of the outlets, especially in the first three stages of primary education (primary) and the use of direct training
... Show MoreIn 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 MoreThis study is qualitative, it illustrates H.G. Wells\\'s The Time Machine through the scientific and social framework of the Victorian Era. Wells\\'s portrayal of future societies examines the rapid technological progress and social changes of the 19th century. The analysis scrutinizes the division between the Eloi and the Morlocks, tracing the consequences of social division. To meet the objective of the study, Victorian frame of mind is utilized to examine the class struggle that is symbolized by the Eloi and the Morlocks. The analysis highlights the economic and social effects of industrialization and how Wells examines the capitalist system and its impact on human relationships and class division. The study also utilizes concepts from D
... Show MoreReduce the required time for measuring the permeability of clayey soils by using new manufactured cell
Indium oxide In2O3 thin films fabricated using thermal evaporation of indium metal in vacuum on a glass substrate at 25oC using array mask, after deposition the indium films have been subjected to thermal oxidation at temperature 400 °C for 1h. The results of prepared Indium oxide reveal the oxidation method as a strong effect on the morphology and optical properties of the samples as fabricated. The band gap (Eg) of In2O3 films at 400 °C is 2.7 eV. Then, SEM and XRD measurements are also used to investigate the morphology and structure of the indium oxide In2O3 thin films. The antimicrobial activity of indium oxide In2O3 thin films was assessed against gram-negative bacterium using inhibition zone of bacteria which improved higher ina
... Show MoreThe Experiment was carried out to determine the level vibration transfer in three axes Horizontal X, Lateral Y and Vertical Z direction to seat driver tractor, Vector sum of vibration and Daily Vibration Exposure (8 hours) in seat driver tractor, and vibration in steering wheel tractor, Heart Rate, Systolic and Diastolic blood pressure and temperature were measure to all Drivers before and after used Chisel plow in operation tillage. Statistical analysis system was used, Split-Split Plot Design under Randomized Complete Block Design, Three factors were used in this experiment included Two types of Soil Moist and Dry soil which represented main plot, Three Velocity Tractor was second factor included 1.6,3.5 and 5.4 km/hr and Three Drivers Tr
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