A. A. Ibrahim

Publications

1 On Algebraic Structure of Improved Gauss-Seidel Iteration

Authors: O. M. Bamigbola, A. A. Ibrahim

Abstract:

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: Convergence, Gauss-Seidel iteration, algebraic structure, Linear system of equations

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Abstracts

3 Iron Catalyst for Decomposition of Methane: Influence of Al/Si Ratio Support

Authors: A. S. Al-Fatesh, A. A. Ibrahim, A. M. AlSharekh, F. S. Alqahtani, S. O. Kasim, A. H. Fakeeha

Abstract:

Hydrogen is the expected future fuel since it produces energy without any pollution. It can be used as a fuel directly or through the fuel cell. It is also used in chemical and petrochemical industry as reducing agent or in hydrogenation processes. It is produced by different methods such as reforming of hydrocarbon, electrolytic method and methane decomposition. The objective of the present paper is to study the decomposition of methane reaction at 700°C and 800°C. The catalysts were prepared via impregnation method using 20%Fe and different proportions of combined alumina and silica support using the following ratios [100%, 90%, 80%, and 0% Al₂O₃/SiO₂]. The prepared catalysts were calcined and activated at 600 OC and 500 OC respectively. The reaction was carried out in fixed bed reactor at atmospheric pressure using 0.3g of catalyst and feed gas ratio of 1.5/1 CH₄/N₂ with a total flow rate 25 mL/min. Catalyst characterizations (TPR, TGA, BET, XRD, etc.) have been employed to study the behavior of catalysts before and after the reaction. Moreover, a brief description of the weight loss and the CH₄ conversions versus time on stream relating the different support ratios over 20%Fe/Al₂O₃/SiO₂ catalysts has been added as well. The results of TGA analysis provided higher weights losses for catalysts operated at 700°C than 800°C. For the 90% Al₂O₃/SiO₂, the activity decreases with the time on stream using 800°C reaction temperature from 73.9% initial CH₄ conversion to 46.3% for a period of 300min, whereas the activity for the same catalyst increases from 47.1% to 64.8% when 700°C reaction temperature is employed. Likewise, for 80% Al₂O₃/SiO₂ the trend of activity is similar to that of 90% Al₂O₃/SiO₂ but with a different rate of activity variation. It can be inferred from the activity results that the ratio of Al₂O₃ to SiO₂ is crucial and it is directly proportional with the activity. Whenever the Al/Si ratio decreases the activity declines. Indeed, the CH₄ conversion of 100% SiO₂ support was less than 5%.

Keywords: Hydrogen, Iron, SiO2, Al2O3, CH₄ decomposition

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2 Some Factors Affecting Reproductive Traits in Nigerian Indigenous Chickens under Intensive Management System

Authors: J. Aliyu, A. O. Raji, A. A. Ibrahim

Abstract:

The study was carried out to assess the fertility, early and late embryonic mortalities as well as hatchability by strain, season and hen’s weight in Nigerian indigenous chickens reared on deep litter. Four strains (normal feathered, naked neck, frizzle and dwarf) of hens maintained at a mating ratio of 1 cock to 4 hens, fed breeders mash and water ad libitum were used in a three year experiment. The data generated were subjected to analysis of variance using the SAS package and the means, where significant, were separated using the least significant difference (LSD). There were significant effects (P < 0.05) of strain on all the traits studied. Fertility was generally high (84.29 %) in all the strains. Early embryonic mortality was significantly lowest (P < 0.01) in naked neck which had the highest late embryonic mortality (P < 0.001). Hatchability was significantly highest (P < 0.01) in normal feathered (80.23 %) and slightly depressed in frizzle (74.95 %) and dwarf (72.27 %) while naked neck had the lowest (60.80 %). Season of the year had significant effects on early embryonic mortality. Dry hot season significantly (P < 0.05) depressed fertility while early embryonic mortality was depressed in the wet season (15.33 %). Early and late embryonic mortalities significantly increased (P < 0.05) with increasing weight of hen. Dwarf, frizzle and normal feathered hens could be used to improve hatchability as well as reduce early and late embryonic mortalities in Nigerian indigenous chickens.

Keywords: Indigenous, Fertility, Chicken, strain, hatchability

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1 On Algebraic Structure of Improved Gauss-Seide Iteration

Authors: O. M. Bamigbola, A. A. Ibrahim

Abstract:

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: Convergence, linear algebraic system, Gauss-Seidel iteration, algebraic structure

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