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.
New polymer blend with enhanced properties was prepared from (80 %) epoxy resin (Ep), (20%) unsaturated polyester resin (UPE) as a matrix material. The as-obtained polymer blend was further reinforced by adding Sand particles of particle size (53 μm) with various weight fraction (5, 10, 15, 20 %). Thermal conductivity and sorption measurements are performed in order to determine diffusion coefficient in different chemical solutions (NaOH, HCl) with concentration (0.3N) after immersion for specific period of time (30 days). The obtained results demonstrate that the addition of sand powder to (80%EP/20%UPE) blend leads to an increase of thermal conductivity, with an optimum/minimum diffusion coefficient in (HCl)/(NaOH), respectively.
In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data sets
Background: The PMMA polymer denture base materials are low in thermal and strength properties. The aim of the study was to investigate the change in glass transition temperature, E-Moudulus and coefficient of thermal expansion of acrylic denture base material by addition of Al2O3, TiO2 and SiO2nano-fillers in 5% by weight. Materials and methods: The type of polymerization is free radical bulk polymerization. one hundred twenty (120) specimens were prepared , the specimens were divided into four groups according to the material had been added (one control and three for Al2O3, TiO2 and SiO2nanocomposite) each group was subdivided in to three groups according to the test had been done on it, the degree of transition (Tg) was measured by The d
... Show MoreThe first studies on shocks and vibrations were carried out at the beginning of the 1930s to improve the behavior of buildings during earthquakes. Vibration tests on aircraft were developed from 1940 to verify the resistance of parts and equipments prior to their first use. Flutter is a well-known example of dynamic aero elasticity, where when oscillation of structure interacted with unsteady aerodynamic forces the flutter will occur. Vibration on any structure without damping means that self-harmonic oscillation will occur, and in most cases the oscillation may start to increase until structural failure. This behavior is very similar to resonance phenomena if only the oscillation is being studied as a vibration case. In vibration suppre
... Show MoreIn this research، a comparison has been made between the robust estimators of (M) for the Cubic Smoothing Splines technique، to avoid the problem of abnormality in data or contamination of error، and the traditional estimation method of Cubic Smoothing Splines technique by using two criteria of differentiation which are (MADE، WASE) for different sample sizes and disparity levels to estimate the chronologically different coefficients functions for the balanced longitudinal data which are characterized by observations obtained through (n) from the independent subjects، each one of them is measured repeatedly by group of specific time points (m)،since the frequent measurements within the subjects are almost connected an
... Show MoreIn this research, the nonparametric technique has been presented to estimate the time-varying coefficients functions for the longitudinal balanced data that characterized by observations obtained through (n) from the independent subjects, each one of them is measured repeatedly by group of specific time points (m). Although the measurements are independent among the different subjects; they are mostly connected within each subject and the applied techniques is the Local Linear kernel LLPK technique. To avoid the problems of dimensionality, and thick computation, the two-steps method has been used to estimate the coefficients functions by using the two former technique. Since, the two-
... Show MoreThe research has been talked on specific an important notions concerning with the dimensions of effectiveness of good governance and sustainable development inside all Arab states, So that the scientific article reflected the role of investments in various sections of institutional business by draw attention toward different projects about analyzing the whole political reality according to the standard indications of political and social stability on the regional level and international aspects. Therefore, the study resembled scientific contains and the dimensions of political reform and administrative overhauling within governmental system in order to achieve all raw objectives for sustainable development. All international and
... Show MoreThe present study discusses the problem based learning in Iraqi classroom. This method aims to involve all learners in collaborative activities and it is learner-centered method. To fulfill the aims and verify the hypothesis which reads as follow” It is hypothesized that there is no statistically significant differences between the achievements of Experimental group and control group”. Thirty learners are selected to be the sample of present study.Mann-Whitney Test for two independent samples is used to analysis the results. The analysis shows that experimental group’s members who are taught according to problem based learning gets higher scores than the control group’s members who are taught according to traditional method. This
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