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.
Linear regression is one of the most important statistical tools through which it is possible to know the relationship between the response variable and one variable (or more) of the independent variable(s), which is often used in various fields of science. Heteroscedastic is one of the linear regression problems, the effect of which leads to inaccurate conclusions. The problem of heteroscedastic may be accompanied by the presence of extreme outliers in the independent variables (High leverage points) (HLPs), the presence of (HLPs) in the data set result unrealistic estimates and misleading inferences. In this paper, we review some of the robust
... Show MoreObjectives: To evaluate the effect of vitamin D3 local injections on apical root resorption, alveolar bone integrity, and chair-side time following three and six months of canine retraction. Subjects and Methods: Seventeen adult patients (18-35 years old) of class I and II malocclusions were recruited, who required bilateral maxillary 1st premolars extraction before starting maxillary canines retraction. The experimental side received 25 pg dose of vitamin D3 injected locally into the distal periodontal sulcus of the canine (before force application) every three weeks, while the control side received retraction force only. Periapical radiographic evaluation was conducted after 3 and 6 months of the start of canines' retraction. Results: At
... Show MoreAcrylic polymer/cement nanocomposites in dark and light colors have been developed for coating floors and swimming pools. This work aims to emphasize the effect of cement filling on the mechanical parameters, thermal stability, and wettability of acrylic polymer. The preparation was carried out using the casting method from acrylic polymer coating solution, which was added to cement nanoparticles (65 nm) with weight concentrations of (0, 1, 2, 4, and 8 wt%) to achieve high-quality specifications and good adhesion. Maximum impact strength and Hardness shore A were observed at cement ratios of 2 wt% and 4 wt%, respectively. Changing the filling ratio has a significant effect on the strain of the nanocomposites. The contact angle was i
... Show MoreExperiments have been conducted to study the local and average heat transfer by mixed
convection for hydrodynamically fully developed, thermally developing and fully developed
laminar upward air flow in an inclined annulus with adiabatic inner cast iron tube and uniform
heated outer aluminum tube with an aspect ratio ( Ω = 0.72) and (L/Dh≈40) for both calming and
test sections). A wide range of Reynolds number from 859 to 2024 has been covered, and heat
flux has been varied from 159 W/m2 to 812 W/m2 (these values of heat flux and Reynolds
number gave Richardson number range from 0.03 to 0.٣٨), with angles of annulus inclination
φ =0o (horizontal position), φ =60o (inclined position), and φ =90o (vertical posi
The present work deals with an experimental investigation of charging and discharging processes in thermal storage system using a phase change material PCM. Paraffin wax was used as the PCM which is formed in spherical capsules and packed in a cylindrical packed column which acted as an energy storage system. Air was used as the heat transfer fluid HTF in thermal storage unit. The effect of flow rate and inlet temperature of HTF on the time of charging and discharging process were studied. The results showed that the faster storage of thermal energy can be made by high flow rate of heat transfer fluid HTF and high inlet temperature of heat transfer fluid. It was found that at 65°C HTF inlet temperature, the melting and solidification pr
... Show MoreOver application courier company (DHL) to keep the quality of service to achieve customer satisfaction the adoption of precedence delivery time - A prospective study))
Become attention to quality is a global phenomenon, and I took organizations and governments around the world attaches special attention, but we can say that quality has become the first function for many organizations, and has become a management philosophy
Background. The motor response is a fundamental ability that is evident during any physical or motor activity. However, the need for this ability varies from one sport to another and depends on the specific skills required in each sport. Objectives. This study aims to compare the average motor reaction times of the arm and leg among handball, basketball, and volleyball players aged 14 to 16 years. Methods. The sample included 30 players aged 14-16 years from the sports talent care center, evenly distributed on handball, basketball, and volleyball. Standardized tests were used to measure the speed of motor response, including the Batak Micro test for hands, which records the number of responses to light stimuli in 30 seconds, and the Saqer t
... Show MoreThis research investigated the effect of adding two groups of reinforcement materials, including bioactive materials Hydroxyapatite (HA) and halloysite nanoclay and bioinert materials Alumina (AL2O3) and Zirconia (ZrO2), each of them with various weight ratios (1,2,3,4 &5)% to the polymer matrix PMMA. The best ratios were selected, and then a hybrid was preparing Composite red from the best ratios from each group. Thermal properties, including thermal conductivity and Thermomechanical Analysis (TMA) technology, have been studied. The results showed that adding 3% Hydroxyapatite (HA) and 5% halloysite nanoclay to the polymethacrylate (PMMA) mer leads to an increase in thermal conductivity. It was also found from the Thermomechanical Analysis
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