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 research aims to know the impact of the innovative matrix strategy and the problem tree strategy in teaching mathematics to intermediate grade female students on mathematical proficiency. To achieve the research objectives, an experimental approach and a quasi-experimental design were used for two equivalent experimental groups. The first is studied according to the innovative matrix strategy, the second group is studied according to the problem tree strategy. The research sample consisted of (32) female students of the first intermediate grade, who were intentionally chosen after ensuring their equivalence, taking into several factors, most notably (chronological age, previous achievement, and intelligence test). The research tools con
... Show MoreThe mass attenuation coefficient for beta particles through pure Polyvinyl chloride (PVC) and flax fibers- reinforced PVC composite were investigated as a function of the absorber thickness and the absorber to source distance. The beta particles mass attenuation coefficients were obtained using a NaI(Tl) energy selective scintillation counter with 90Sr/ 90Y beta source having an energy range from (0.546-2.275) MeV. Pure PVC polymer samples were prepared by compacting the PVC powder in a mould at high pressure (10bar) and temperature about 140°C for 30 minutes. A hot press system was used for this process. The experimentally obtained values of mass attenuation coefficients for 90Sr and 90Y were found to be 7.72 cm2.g-1and 0.842 cm2.g-1 r
... Show MoreThe integer simulation and development finite impulse response (FIR) filters taking into account the possibilities of their realization on digital integer platforms are considered. The problem statement and solution of multifunctional synthesis of digital FIR filters such a problem on the basis of the numerical methods of integer nonlinear mathematical programming are given. As an several examples, the problem solution of synthesis FIR-filters with short coefficient word length has been given. The analysis of their characteristics is resulted. The paper discusses issues of modeling and synthesis of digital FIR filters with provision for the possibilities of their implementation on digital platforms with integer computation arithme
... Show MoreCorruption is a phenomenon that exists in all times and places, they appear in the developing countries and in developed countries, and in all political systems. And its repercussions and economic repercussions on the society in which it is rampant, and lead to the undermining of economic development and obstruction, is also working on increasing poverty and unemployment, as well as its role in the worsening of social problems, and political instability. And corruption is deviant behavior is illegal and contrary to the teachings of the religious and moral values. The emergence of this phenomenon is due to several reasons, including political, economic, social and cultura
... Show MoreIn this research, hand lay- up technique is used to prepare samples from epoxy resin reinforced with multi- walled carbon nanotubes in different weight fractions (0, 2, 3, 4, 5) wt%. The immersion effect by sodium hydroxide solution (NaOH) at normality (0.3N) for a period of (15 days) on the thermal conductivity of nanocomposites was studied, and compared to natural condition (before immersion). The thermal conductivity of epoxy nanocomposites specimens were carried out using Lee’s disk method. The experimental results showed that thermal conductivity increased with increase weight fraction before and after immersion for all specimens, while the immersion effect leads to decrease thermal conductive values compared to thermal conductivi
... Show MoreAn experiment was carried out to study the effects of Time Factor, potassium and Molybdenum on Rhizobium growth. The objective of the experiment, which conducted under laboratory conditions, was to investigate the interaction effects of using three levels of Molybdenum (0, 0.25, 2.50 mg Mo . Kg-1 sterile soil) and four levels of potassium (0, 25, 50, 100 mg K . Kg-1 sterile soil) on the viable counts of Rhizobium growth in the sterile soil after 3, 9, 15 and 21 days of incubation at 28°C. The results indicated that Molybdenum level 2.50 mg Mo . Kg-1 sterile soil and potassium level 50 mg K . Kg-1 sterile soil recorded the biggest significant increase in the viable counts of Rhizobium growth in the sterile soil especially after 15 da
... Show MoreThe aim of this research is to study the factors affecting drag coefficient (C d ) in
non-Newtonian fluids which are the rheological properties ,concentrations of non-
Newtonian fluids, particle shape, size and the density difference between particle and
fluid .Also this study shows drag coefficient (C d ) and particle Reynolds' number (Re
P ) relationship and the effect of rheological properties on this relationship.
An experimental apparatus was designed and built, which consists of Perspex pipe
of length of 160 cm. and inside diameter of 7.8 cm. to calculate the settling velocity,
also electronic circuit was designed to calculate the falling time of particles through
fluid.
Two types of solid particles were
In this work, a convex lens concentrating solar collector is designed and manufactured locally by using 10 convex lenses (concentrator) of a diameter 10cm and one Copper absorber tube of a diameter 12.5mm and 1mm in thickness 1m length. Two axes manual Tracking system also constructed to track the sun continuously in two directions. The experiments are made on 17th of May 2015 in climatic conditions of Baghdad. The experimental data are fed to a computer program to solve the thermal performing equation, to find efficiency and actual useful energy. Then this data is used in numerical CFD software for three different absorber diameters (12.5 mm, 18.75 mm and 25 mm). From the results that obtained the maximum the
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