The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
This paper presents a method to organize memory chips when they are used to build memory systems that have word size wider than 8-bit. Most memory chips have 8-bit word size. When the memory system has to be built from several memory chips of various sizes, this method gives all possible organizations of these chips in the memory system. This paper also suggests a precise definition of the term “memory bank” that is usually used in memory systems. Finally, an illustrative design problem was taken to illustrate the presented method practically.
Polarization modulation plays an important role in polarization encoding in quantum key distribution. By using polarization modulation, quantum key distribution systems become more compact and more vulnerable as one laser source is used instead of using multiple laser sources that may cause side-channel attacks. Metasurfaces with their exceptional optical properties have led to the development of versatile ultrathin optical devices. They are made up of planar arrays of resonant or nearly resonant subwavelength pieces and provide complete control over reflected and transmitted electromagnetic waves opening several possibilities for the development of innovative optical components. In this work, the Si nanowire metasurface grating polarize
... Show MoreThe Yamama Formation is characterized by a wide geographic extension of southern Iraq. Microfacies analysis of this formation was studied in six wells distributed in six fields: Fayhaa, Sindbad, Siba, Zubair, Ratawi and West Qurna. This research aims to determine paleoenvironments by diagnosing biofacies and lithofacies. Miscellaneous marine fauna of foraminifera and calcareous algae, mainly green algae (dasycladacean.) and skeletal bioclasts from gastropods, pelecypods, bryozoans, sponge spicules, and echinoderms were found. Petrographic studies and well logs interpretations led to the identification of five main Microfacies ( Mudstone, Wackestone, Packestone, Grainestone and Rudstone and twelve submicrofacies (Foraminiferal-
... Show MoreThis study was undertaken to diagnose routine settling problems within a third-party oil and gas companies’ Mono-Ethylene Glycol (MEG) regeneration system. Two primary issues were identified including; a) low particle size (<40 μm) resulting in poor settlement within high viscosity MEG solution and b) exposure to hydrocarbon condensate causing modification of particle surface properties through oil-wetting of the particle surface. Analysis of oil-wetted quartz and iron carbonate (FeCO₃) settlement behavior found a greater tendency to remain suspended in the solution and be removed in the rich MEG effluent stream or to strongly float and accumulate at the liquid-vapor interface in comparison to naturally water-wetted particles. As su
... Show MoreIn this study, successive electrocoagulation (EC) and electro-oxidation (EO) processes were used to minimize some of the major pollutants in real wastewater, such as organics (detected by chemical oxygen demand (COD)), and turbidity. The wastewater utilized in the present study was collected from the Midland Refinery Company in Baghdad-Iraq. The performance of the successive batch EC-EO processes was studied by utilizing Graphite and Aluminum (Al) as monopolar anode electrodes and stainless steel (st.st.) as the cathode. The Taguchi experimental design approach was used to attain the best experimental conditions for COD reduction as a major response. Starting from chemical oxygen demand COD of (600 ppm), the effects of current density (C
... Show MoreIn this study, successive electrocoagulation (EC) and electro-oxidation (EO) processes were used to minimize some of the major pollutants in real wastewater, such as organics (detected by chemical oxygen demand (COD)), and turbidity. The wastewater utilized in the present study was collected from the Midland Refinery Company in Baghdad-Iraq. The performance of the successive batch EC-EO processes was studied by utilizing Graphite and Aluminum (Al) as monopolar anode electrodes and stainless steel (st.st.) as the cathode. The Taguchi experimental design approach was used to attain the best experimental conditions for COD reduction as a major response. Starting from chemical oxygen demand COD of (600 ppm), the effects of current densi
... Show More