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.
The researcher was interested in studying a crucial aspect of the systematic world music culture. He highlights the analysis of the harmonic construction in the musical compositions of the artist Khalil Ismail, where harmony is a significant Western musical science, a pillar of the structure of instrumental and vocal music.
It depends on the compositions of vertical sounds performed simultaneously, as tones coincide and are sometimes dissonant to give sound resonance that enriches musical work and attracts recipients. Hence, the researcher has many questions, including: Can the composition of the writings of the artist Khalil Ismail determine in an objective research framework? Is there a study on this subject in some detail? whic
In this article, Pb2Ba1.7Sr0.3Ca2Cu3O10+δ superconductor material was synthesized using conventional solid-state reaction method. X-ray diffraction (XRD) analysis demonstrated one dominant phase 2223 and some impurities in the product powder. The strongest peaks in the XRD pattern were successfully indexed assuming a pseudo-tetragonal cell with lattice constants of a = 3.732, b = 3.733 and c = 14.75 Å for a Pb-Based compound. The crystallite size and lattice strain between the layers of the studied compound were estimated using several methods, namely the Scherrer, Williamson-Hall (W.H), sizestrain plot (SSP) and Halder Wagner (H.W) approach. The values of crystallite size, calculated by Scherrer, W.H, SSP and H.W methods, were 89.454077
... Show MoreIn this paper, the Monte Carlo N-Particle extended computer code (MCNP) were used to design a model of the European Sodium-cooled Fast Reactor. The multiplication factor, conversion factor, delayed neutrons fraction, doppler constant, control rod worth, sodium void worth, masses for major heavy nuclei, radial and axial power distribution at high burnup are studied. The results show that the reactor breeds fissile isotopes with a conversion ratio of 0.994 at fuel burnup 70 (GWd/T), and minor actinides are buildup inside the reactor core. The study aims to check the efficiency of the model on the calculation of the neutronic parameters of the core at high burnup.
As cultures are mainly divided into collectivistic and individualistic, members tend to emphasize, through communication, either their position as part of their group or their independence from the group. This emphasis is manifested in using the pragmatic concepts of positive politeness and negative politeness. The present study looks into the reflection of these two cultures in Rockstar’s renowned video game, Red Dead Redemption 2 (2018). It aims at identifying the two cultures as present in the game and showing their significance to its narrative. It fills the gap in the studies of language used within video games as well as its cultural reflections. The study addresses the following question: What are the positive and negative
... Show MoreBackground: This study aimed to determine the cephalometric values of tetragon analysis on a sample of Iraqi adults with normal occlusion. Material and methods: Forty digital true lateral cephalometric radiographs belong to 20 males and 20 females having normal dental relation were analyzed using AutoCAD program 2009. Descriptive statistics and sample comparison with Fastlicht norms were obtained. Results: The results showed that maxillary and mandibular incisors were more proclined and the maxillary/mandibular planes angle was lower in Iraqi sample than Caucasian sample. Conclusion: It's recommended to use result from this study when using tetragon analysis for Iraqis to get more accurate result.
A water resources management for earthen canal/stream is introduced through creating a combination procedure between a field study and the scientific analytical concepts that distinguish the hydraulic problems on this type of stream with using the facilities that are available in HECRAS software; aiming to point the solutions of these problems. Al Mahawil stream is an earthen canal which is subjected to periodic changes in cross sections due to scour, deposition, and incorrect periodic dredging processes due to growth of the Ceratophyllum plants and weeds on the bed and banks of the stream; which affect the characteristics of the flow. This research aims to present a strategy of water resources management through a field study that conducte
... Show MoreFind the impediments Activity vital and important, but focuses a bancassurance activity, diagnosis and its impact on the financial ratios indicators for insurance companies. The researcher has adopted in his research on several financial ratios used to analyze the financial performance of a (relative profitability, liquidity ratio and the ratio of solvency) of the company Iraqi insurance for a period of one year (2009) to a year (2015), based on the annual reports and financial statements (balance sheet revealed income), financial statements for insurance premiums for banks research sample of this research has addressed several topics of theoretical and practical body through which the researcher obstacles to banking and insurance experi
... Show MoreThe food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu
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