Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the
KE Sharquie, AA Al-Bayatti, AI Al-Ajeel, AJ Al-Bahar, AA Al-Nuaimy, Saudi medical journal, 2007 - Cited by 63
In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo
... Show MoreA partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.
Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi
... Show MoreThe current work is characterized by simplicity, accuracy and high sensitivity Dispersive liquid - Liquid Micro Extraction (DLLME). The method was developed to determine Telmesartan (TEL) and Irbesartan (IRB) in the standard and pharmaceutical composition. Telmesartan and Irbesartan are separated prior to treatment with Eriochrom black T as a reagent and formation ion pair reaction dye. The analytical results of DLLME method for linearity range (0.2- 6.0) mg /L for both drugs, molar absorptivity were (1.67 × 105- 5.6 × 105) L/ mole. cm, limit of detection were (0.0242and0.0238), Limit of quantification were (0.0821and0.0711), the Distribution coefficient were
... Show MoreBackground: Salivary immunoglobulin IgA plays an essential role in the immune response against dental caries. This studywas conducted to compare the salivary IgA levels and flow rate of stimulated saliva in caries active and caries free children. Materials and methods: The present study included sixty healthy children age 7-10 yearswho were divided into two groups. They were caries free and caries active children (30 children in each group). Assessment and recording of caries – experience were through the application of Decayed, Missing and Filled Tooth Index (DMFT) and (dmft) index, for permanent and deciduous teeth respectively. After dental examination, stimulated saliva samples were collected from the subjects and performed und
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This study investigates the mechanical compression properties of tin-lead and lead-free alloy spherical balls, using more than 500 samples to identify statistical variability in the properties in each alloy. Isothermal aging was done to study and compare the aging effect on the microstructure and properties.
The results showed significant elastic and plastic anisotropy of tin phase in lead-free tin based solder and that was compared with simulation using a Crystal Plasticity Finite Element (CPEF) method that has the anisotropy of Sn installed. The results and experiments were in good agreement, indicating the range of values expected with anisotropic properties.
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... Show MoreBackground: Salivary immunoglobulin IgA plays an essential role in the immune response against dental caries. This studywas conducted to compare the salivary IgA levels and flow rate of stimulated saliva in caries active and caries free children. Materials and methods: The present study included sixty healthy children age 7-10 yearswho were divided into two groups. They were caries free and caries active children (30 children in each group). Assessment and recording of caries – experience were through the application of Decayed, Missing and Filled Tooth Index (DMFT) and (dmft) index, for permanent and deciduous teeth respectively. After dental examination, stimulated saliva samples were collected from the subjects and performed und
... Show More