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 work focused on principle of higher order mode excitation using in- line Double Clad Multi-Mode Mach-Zehnder Interferometer (DC-MM-MZI). The DC-MM-MZI was designed with 50 cm etched MMF. The etching length is 5cm. The tenability of this interferometer was studied using opt grating ver.4.2.2 and optiwave
ver. 7 simulator. After removing (25, 35, 45, 55) μm from MMF and immersing this segment of MMF with water bath contained distilled water and ethanol, in addition to, air. Pulsed laser source centered at 1546.7nm ,pulse width 10ns and peak power 1.33mW was propagated via this interferometer Maximum modes were obtained in case of air surrounded media which are 9800 and 25 um removed cladding layer, with peak power 49.800 m
In this article, we investigate the heat transfer on nanoparticles Jeffrey Hamel flow problem between two rigid plane walls. Water is used as a main fluid using four different types of nanoparticles, namely aluminum, cuprous, titanium, and silver. The results of nonlinear transformational equations with boundary conditions are solved analytically and numerically. The perturbation iteration scheme (PIS) is used for the analytic solution, while for determining the numerical results, the Rang-Kutta of the four-order scheme (RK4S) is used. The effects on the behavior of non-dimensional velocity and temperature distributions are presented in the form of tables and graphs for different values of emerging physical parameters (Rey
... Show MoreEverybody is connected with social media like (Facebook, Twitter, LinkedIn, Instagram…etc.) that generate a large quantity of data and which traditional applications are inadequate to process. Social media are regarded as an important platform for sharing information, opinion, and knowledge of many subscribers. These basic media attribute Big data also to many issues, such as data collection, storage, moving, updating, reviewing, posting, scanning, visualization, Data protection, etc. To deal with all these problems, this is a need for an adequate system that not just prepares the details, but also provides meaningful analysis to take advantage of the difficult situations, relevant to business, proper decision, Health, social media, sc
... Show MoreThe present study is concerned with the writer's ideologies towards violence against women. The study focuses on analyzing violence against women in English novel to see the extent the writers are being affected and influenced by their genders. It also focuses on showing to what extent the writer's ideologies are reflected in their works. Gender influences social groups ideologies; therefore, when a writer discusses an issue that concerns the other gender, they will be either subjective or objective depending on the degree of influence, i.e., gender has influenced their thoughts as well as behaviors. A single fact may be presented differently by different writers depending on the range of a
... Show MoreUndoubtedly, Road Traffic Accidents (RTAs) are a major dilemma in term of mortality and morbidity facing the road users as well as the traffic and road authorities. Since 2002, the population in Iraq has increased by 49 percent and the number of vehicles by three folds. Consequently, these increases were unfortunately combined with rising the RTAs number, mortality and morbidity. Alongside the humanitarian tragedies, every year, there are considerable economic losses in Iraq lost due to the epidemic of RTAs. Given the necessity of understanding the contributory factors related to RTAs for the implementation by traffic and road authorities to improve the road safety, the necessity have been a rise for
... Show MoreMalaysia has been supported by one of the high-speed fiber internet connections called TM UniFi. TM UniFi is very familiar to be used as a medium to apply Small Office Home Office (SOHO) concept due to the COVID-19 pandemic. Most of the communication vendors offer varieties of network services to fulfill customers' needs and satisfaction during the pandemic. Quality of Services is queried by most users by the fact of increased on users from time to time. Therefore, it is crucial to know the network performance contrary to the number of devices connected to the TM UniFi network. The main objective of this research is to analyze TM UniFi performance with the impact of multiple device connections or users' services. The study was conducted
... Show MoreLanguage plays a major role in all aspects of life. Communication is regarded as the most important of these aspects, as language is used on a daily basis by humanity either in written or spoken forms. Language is also regarded as the main factor of exchanging peoples’ cultures and traditions and in handing down these attributes from generation to generation. Thus, language is a fundamental element in identifying peoples’ ideologies and traditions in the past and the present. Despite these facts, the feminist linguists have objections to some of the language structures, demonstrating that language is gender biased to men. That is, language promotes patriarchal values. This pushed towards developing extensive studies to substantiate s
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