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 analysis of time series considers one of the mathematical and statistical methods in explanation of the nature phenomena and its manner in a specific time period.
Because the studying of time series can get by building, analysis the models and then forecasting gives the priority for the practicing in different fields, therefore the identification and selection of the model is of great importance in spite of its difficulties.
The selection of a standard methods has the ability for estimation the errors in the estimated the parameters for the model, and there will be a balance between the suitability and the simplicity of the model.
In the analysis of d
... Show MoreThe effect of time (or corrosion products formation) on corrosion rates of carbon steel pipe in aerated 0.1N NaCl
solution under turbulent flow conditions is investigated. Tests are conducted using electrochemical polarization
technique by determining the limiting current density of oxygen reduction in Reynolds number range of 15000 to 110000
and temperature range of 30 to 60oC. The effect of corrosion products formation on the friction factor is studied and
discussed. Corrosion process is analyzed as a mass transfer operation and the mass transfer theory is employed to
express the corrosion rate. The results are compared with many proposed models particularly those based on the
concept of analogy among momentum, heat,
Phase change materials (PCMs) such as paraffin wax can be used to store or release large amount of energy at certain temperature at which their solid-liquid phase changes occurs. Paraffin wax that used in latent heat thermal energy storage (LHTES) has low thermal conductivity. In this study, the thermal conductivity of paraffin wax has been enhanced by adding different mass concentration (1wt.%, 3wt.%, 5wt.%) of (TiO2) nano-particles with about (10nm) diameter. It is found that the phase change temperature varies with adding (TiO2) nanoparticles in to the paraffin wax. The thermal conductivity of the composites is found to decrease with increasing temperature. The increase in thermal conductivity ha
... Show MoreABSTRACT Wound is damage or disruption to the normal anatomical structure and function. Carrageenan is sulphated polysaccharide found in Gigartina, Chondrus and Eucheuma species in the red algal family. Having anticancer, anti-inflammatory and renewal of tissues. Our study aimed to detect the role of kappa carrageenan in the burned skin wound repair. Skin burn were performed in the right and left cheek of 20 male rats (aged 7-8 weeks weighing 300-350 g). Burned skin rats were categorized into two equal groups. Burned areas of right side were treated with a local application of 1 ml of kappa carrageenan solution once daily (treatment group) and the left side receive no treatment (control group). After 5, and 10 days, 5 rats from each
... Show MoreIn this paper the effect of nonthermal atmospheric argon plasma on the optical properties of the cadmium oxide CdO thin films prepared by chemical spray pyrolysis was studied. The prepared films were exposed to different time intervals (0, 5, 10, 15, 20) min. For every sample, the transmittance, Absorbance, absorption coefficient, energy gap, extinction coefficient and dielectric constant were studied. It is found that the transmittance and the energy gap increased with exposure time, and absorption. Absorption coefficient, extinction coefficient, dielectric constant decreased with time of exposure to the argon plasma
Discrete logarithms are applied in many cryptographic problems . For instance , in public key . and for construction of sets with disti nct sums of k-clcments. The purpose o r this paper
is to modify the method ol' informationl1·iding using discrete logarithms , introduce new properties of St - sets , uscdthe direct product of groups to construct cyclic group and finally, present modified method for knapsack &
... Show MoreIn this paper, the blow-up solutions for a parabolic problem, defined in a bounded domain, are studied. Namely, we consider the upper blow-up rate estimate for heat equation with a nonlinear Neumann boundary condition defined on a ball in Rn.
Breast cancer is one of the most common malignant diseases among women;
Mammography is at present one of the available method for early detection of
abnormalities which is related to breast cancer. There are different lesions that are
breast cancer characteristic such as masses and calcifications which can be detected
trough this technique. This paper proposes a computer aided diagnostic system for
the extraction of features like masses and calcifications lesions in mammograms for
early detection of breast cancer. The proposed technique is based on a two-step
procedure: (a) unsupervised segmentation method includes two stages performed
using the minimum distance (MD) criterion, (b) feature extraction based on Gray