Search results for: A. Beltagy

Authors: Waheed Zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

Abstract:

In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, shishkin mesh, two small parameters, exponential spline, interval analysis, sensitivity analysis

Procedia PDF Downloads 246

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

Abstract:

So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

Procedia PDF Downloads 131

Authors: M. Ahmed Eldesouky, S. Nasr, A. Beltagy

Abstract:

Groundwater is generally considered as the best source for aquaculture as it is well protected from contamination. The most common problem limiting the use of groundwater in Egypt is its high iron, manganese and ammonia content. This problem is often overcome by applying the treatment before use. Aeration in many cases is not enough to oxidize iron and manganese in complex forms with organics. Most of the treatment we use potassium permanganate as an oxidizer followed by a pressurized closed green sand filter. The aim of present study is to investigate the optimum characteristics of groundwater to give lowest iron, manganese and ammonia, maximum production and quality of fish in aquaculture in El-Max Research Station. The major design goal of the system was determined the optimum time for harvesting the treated water, pH, and Glauconite weight to use it for aquaculture process in the research site and achieve the Egyptian law (48/1982) and EPA level required for aquaculture. The water characteristics are [Fe = 0.116 mg/L, Mn = 1.36 mg/L,TN = 0.44 mg/L , TP = 0.07 mg/L , Ammonia = 0.386 mg/L] by using the glauconite filter we obtained high efficiency for removal for [(Fe, Mn and Ammonia] ,but in the Lab we obtained result for (Fe, 43-97), ( Mn,92-99 ), and ( Ammonia, 66-88 )]. We summarized the results to show the optimum time, pH, Glauconite weight, and the best model for design in the region.

Keywords: aquaculture, ammonia in groundwater, groundwater, iron and manganese in water, groundwater treatment

Procedia PDF Downloads 198

Authors: Aliaa M. El-Borai, Ehab A. Beltagy, Eman E. Gadallah, Samy A. ElAssar

Abstract:

Bioremediation technology is now used for treatment instead of traditional metal removal methods. A strain was isolated from Marsa Alam, Red sea, Egypt showed high resistance to high lead concentration and was identified by the 16S rRNA gene sequencing technique as Halomonas sp. ES015. Medium optimization was carried out using Plackett-Burman design, and the most significant factors were yeast extract, casamino acid and inoculums size. The optimized media obtained by the statistical design raised the removal efficiency from 84% to 99% from initial concentration 250 ppm of lead. Moreover, Box-Behnken experimental design was applied to study the relationship between yeast extract concentration, casamino acid concentration and inoculums size. The optimized medium increased removal efficiency to 97% from initial concentration 500 ppm of lead. Immobilized Halomonas sp. ES015 cells on sponge cubes, using optimized medium in loop bioremediation column, showed relatively constant lead removal efficiency when reused six successive cycles over the range of time interval. Also metal removal efficiency was not affected by flow rate changes. Finally, the results of this research refer to the possibility of lead bioremediation by free or immobilized cells of Halomonas sp. ES015. Also, bioremediation can be done in batch cultures and semicontinuous cultures using column technology.

Keywords: bioremediation, lead, Box–Behnken, Halomonas sp. ES015, loop bioremediation, Plackett-Burman

Procedia PDF Downloads 166

Authors: Mai A. Ibrahim, Mohammed El-Beltagy, Motaz Khorshid

Abstract:

Emerging Markets return distributions have shown significance departure from normality were they are characterized by fatter tails relative to the normal distribution and exhibit levels of skewness and kurtosis that constitute a significant departure from normality. Therefore, the classical Markowitz Mean-Variance is not applicable for emerging markets since it assumes normally-distributed returns (with zero skewness and kurtosis) and a quadratic utility function. Moreover, the Markowitz mean-variance analysis can be used in cases of moderate non-normality and it still provides a good approximation of the expected utility, but it may be ineffective under large departure from normality. Higher moments models and median models have been suggested in the literature for asset allocation in this case. Higher moments models have been introduced to account for the insufficiency of the description of a portfolio by only its first two moments while the median model has been introduced as a robust statistic which is less affected by outliers than the mean. Tail risk measures such as Value-at Risk (VaR) and Conditional Value-at-Risk (CVaR) have been introduced instead of Variance to capture the effect of risk. In this research, higher moment models including the Mean-Variance-Skewness (MVS) and Mean-Variance-Skewness-Kurtosis (MVSK) are formulated as single-objective non-linear programming problems (NLP) and median models including the Median-Value at Risk (MedVaR) and Median-Mean Absolute Deviation (MedMAD) are formulated as a single-objective mixed-integer linear programming (MILP) problems. The higher moment models and median models are compared to some benchmark portfolios and tested on real financial data in the Egyptian main Index EGX30. The results show that all the median models outperform the higher moment models were they provide higher final wealth for the investor over the entire period of study. In addition, the results have confirmed the inapplicability of the classical Markowitz Mean-Variance to the Egyptian stock market as it resulted in very low realized profits.

Keywords: Egyptian stock exchange, emerging markets, higher moment models, median models, mixed-integer linear programming, non-linear programming

Procedia PDF Downloads 284