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Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations
Tarek M. A. El-Mistikawy
Advances in Numerical Analysis , 2013, DOI: 10.1155/2013/563872
Abstract:
Modular Analysis of Sequential Solution Methods for Almost Block Diagonal Systems of Equations
Tarek M. A. El-Mistikawy
Advances in Numerical Analysis , 2013, DOI: 10.1155/2013/563872
Abstract: Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods. It also allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. The outcome of the analysis and implementation is to discover new methods that outperform a well-known method, a modification of which is, therefore, advocated. 1. Introduction Systems of equations with almost block diagonal (ABD) matrix of coefficients are frequently encountered in numerical solutions of sets of ordinary or partial differential equations. Several such situations were described by Amodio et al. [1], who also reviewed sequential and parallel solvers to ABD systems and came to the conclusion that sequential solution methods needed little further study. Traditionally, sequential solution methods of ABD systems performed decompositions of the matrix of coefficients through either band (scalar) elimination or block tridiagonal elimination. The famous COLROW algorithm [2], which is highly regarded for its performance, was incorporated in several applications [3–7]. It utilizes Lam’s alternating column/row pivoting [8] and Varah’s correspondingly alternating column/row scalar elimination [9]. The efficient block tridiagonal methods included Keller’s Block Tridiagonal Row (BTDR) elimination method [10, Section 5, case i] and El-Mistikawy’s Block Tridiagonal Column (BTDC) elimination method [11]. Both methods could apply a suitable form of Keller’s mixed pivoting strategy [10], which is more expensive than Lam’s. The present paper is intended to explore other variants of the decomposition of . It does not follow the traditional approaches of treating the matrix of coefficients as a banded matrix or casting it into a block tridiagonal form. It, rather, adopts a new approach, modular analysis, which offers a simple and unified way of expressing and assessing solution methods for ABD systems. The matrix of coefficients (or, more specifically, its significant part containing the nonzero blocks) is disassembled into an ordered set of modules. (In fact, two different sets of modules are identified.) Each module is an entity that has a head and a tail. By arranging the modules in such a way that the head of a module is added to the tail of the next, the significant part of can be reassembled. The module exemplifies the matrix, but is much easier to analyze. All possible methods of decomposition of could be formulated as decompositions
Note on "A. Gorguis, A reliable approach to the solution of Navier-Stokes equations, Appl. Math. Lett. 25 (2012) 2015-2017"
Tarek M. A. El-Mistikawy
Physics , 2012,
Abstract: Gorguis' claim of being able to transform Navier-Stokes equations into linear ones through the Cole-Hopf transformation is disputed. It is shown that the cases treated by Gorguis are intrinsically linear; involving a velocity potential (psi) that is governed by Laplace's equation. They require the external force to be conservative and the initial and boundary conditions to admit such cases of fluid flow. The pressure cannot be known a priori, as suggested by Gorguis, but is determined so that it can be consistent with (psi). Other errors in the cited article are also indicated.
Supersonic triple deck flow past a flat plate with an elastic stretch
Tarek M. A. El-Mistikawy
Physics , 2012,
Abstract: The steady laminar supersonic flow past a flat plate having a stretch of an elastic membrane, the pressure on the other side of which is adjustable, is studied within the framework of the triple deck theory. The resulting lower deck problem is supplemented with a membrane equation relating the pressure difference across the membrane to its curvature. By pressurizing or depressurizing the membrane, it assumes the form of a hump or a dent that alters the flow characteristics. Numerical solutions obtained, in either case, give plausible account of the interaction between the membrane and the flow.
Motion of a spherical solid particle in Couette flow: exact solution vs. homotopy perturbation approximation with and without Pade approximants
Tarek M. A. El-Mistikawy
Physics , 2012,
Abstract: The motion of a spherical solid particle in plane Couette flow is governed by a linear problem that has a simple exact solution. As such, there is no need for an approximate analytical representation of the solution; specially when it is tedious, complicated, and requires hairy terms to give accurate results only at small or moderate values of the time.
Modular Analysis of Almost Block Diagonal Systems of Equations
Tarek M. A. El-Mistikawy
Computer Science , 2013,
Abstract: Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategy- local pivoting. Extension of modular analysis to bordered systems is also included.
Isolation, Biochemical Characterization and DNA Identification of Yogurt Starters Streptococcus thermophilus & Lactobacillus delbrueckii ssp. bulgaricus in Gaza Strip  [PDF]
Kamal E. M. El Kahlout, Ismail M. El Quqa, Mahmoud W. El Hindi, Tarek A. El Bashiti
Advances in Microbiology (AiM) , 2018, DOI: 10.4236/aim.2018.812068
Abstract: Background: Milk is a healthy human nutrient, which is fermented to yogurt by lactic acid bacteria, mainly Streptococcus salivarius ssp, thermophilus and Lactobacillus. delbrueckii ssp. bulgaricus. This study aimed to isolate thermophilic starter bacteria from homemade yogurt made in Gaza Strip. The study sought to define both the biochemical and molecular characteristics of the isolated bacteria. Results: Three of the isolates were identified as Streptococcus thermophiles while two isolates were recognized as Lactobacillus delbrueckii ssp. bulgaricus. All five identified isolates showed worthy acidification capacity. Based on these characters, strains were applied for making yogurt either as single pure cultures or as mixed cultures. When using mixed cultures from S. thermophiles and L. bulgaricus, all tested combinations showed positive results. Conclusion: Isolated strains showed remarkable biotechnological characters. The isolates are expected to stimulate and improve quality of the yogurt when they are used as mixed starter cultures.
Distribution of Different Organotin and Organolead Compounds in Sediment of Suez Gulf  [PDF]
Mohamed A. Shreadah, Tarek O. Said, Safaa A. Abd El Ghani, Abd El Moniem M. Ahmed
Journal of Environmental Protection (JEP) , 2011, DOI: 10.4236/jep.2011.25063
Abstract: Organotin and organolead compounds were determined in sediments of the Suez Gulf The concentrations of Tributyltin (TBT) ranged from 0.27 to 2.77 with an average value of 1.37 µgg-1; dry wt. However, the concentrations of dibutyltin (DBT) ranged from 0.07 to 2.27 with an average value of 0.58 µgg-1; dry wt. A significant correlation was found between TBT and DBT with r = 0.82, (p = 0.05) indicating that the occurrence of DBT is mainly related to the degradation of TBT. Generally, the high concentration of TBT was attributed to shipping activity in harbours. In addition, Diphenyltin (DPhT) concentrations ranged from not detected to 2.09 with an average of 1.10 µgg-1 dry wt. Antifouling agents, industrial discharge and the influence of sewage discharge are the main sources of pollution by DPhT compounds in Suez Gulf. On the other side, organolead (OLC) concentrations ranged from 10.88 - 440.2 with an average of 168.7 ngg-1; dry wt. A significant setting of OLC recorded in sediments of Suez Gulf was mainly attributed to cars exhaust and/or spelling and direct evaporation of fuels.
N-Terminal Pro-BNP in Acute Coronary Syndrome Patients with ST Elevation versus Non ST Elevation Myocardial Infarction  [PDF]
Ragaa H. M Salama, Alaa E. A El- Moniem, Nour El-Hefney, Tarek Samor
International Journal of Clinical Medicine (IJCM) , 2011, DOI: 10.4236/ijcm.2011.23036
Abstract: The study aimed to evaluate the differences in secretion of NT-proBNP and conventional cardiac markers in patients with STE-ACS vs NSTE-ACS as a trial to solve the dilemma of the early detection of myocardial ischemia in NSTE-ACS. Sixty two patients with acute coronary syndrome (ACS) divided into 2 groups according to ECG: group1 with elevated ST segment in ECG (STE-ACS) and group 2 with non elevated ST segment (NSTE-ACS).Twenty healthy subjects with matched age and sex were enrolled as control group in this study. In the sera of all subjects, levels of NT –proBNP, CK-MB and troponin-T were measured by different kits. CK-MB and TnT were both significantly higher in STE-ACS patients compared to NSTE-ACS patients. Conversely, NT-proBNP was significantly higher in NSTE-ACS patients than STE-ACS especially within 4 hours from onset of chest pain. Comparison between NT-proBNP, TnT and CK-MB levels by ROC curves revealed area under the curves = 0.68, 0.31, 0.17 respectively. NT-proBNP at cutoff 415 pg/mL in NSTE-ACS patients had higher sensitivity and specificity (92%, 39%; respectively) than other markers that will help in earl diagnosis of NSTE-ACS.
A Theoretical Study of Light Absorption in Self Assembled Quantum Dots  [PDF]
Tarek A. Ameen, Yasser M. El-Batawy, A. A. Abouelsaood
Optics and Photonics Journal (OPJ) , 2013, DOI: 10.4236/opj.2013.32B057
Abstract:

Self assembled quantum dots have shown a great promise as a leading candidate for infrared detection at room temperature. In this paper, a theoretical model of the absorption coefficient of quantum dot devices is presented. Both of bound to bound absorption and bound to continuum absorption are taken into consideration in this model. This model is based on the effective mass theory and the Non Equilibrium Greens Function (NEGF) formalism. NEGF formalism is used to calculate the bound to continuum absorption coefficient. The results of the model have been compared with a published experimental work and a good agreement is obtained. Based on the presented model, the bound to bound absorption coefficient component is compared to the bound to continuum absorption coefficient component. In addition, the effects of the dot dimensions and electron filling on the bound to continuum absorption coefficient are also investigated. In general, increasing the dot filling increases the absorption and decreasing the dots dimensions will increase the absorption and move the absorption peak towards longer wavelengths.

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