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.
In this article, the additivity of higher multiplicative mappings, i.e., Jordan mappings, on generalized matrix algebras are studied. Also, the definition of Jordan higher triple product homomorphism is introduced and its additivity on generalized matrix algebras is studied.
The Disi water samples were collected from different Disi aquifer wells in Jordan using a clean polyethylene container of 10-liter size. A hyper-pure germanium (HPGe) detector with high- resolution gamma-ray spectroscopy and a low background counting system was used for the identification of unknown gamma-rays emitting from radionuclides in the environmental samples. The ranges of specific activity concentrations of 226Ra and 228Ra in the Disi aquifer water were found to be from 0.302 ± 0.085 to 0.723 ± 0.207 and from 0.047 ± 0.010 to 0.525 ± 0.138 Bq L−1, with average values of 0.516 ± 0.090 and 0.287 ± 0.091 Bq L−1, respectively. The average combined radium (226Ra + 228Ra) activity and radium activity ratio (228Ra/226Ra) in Disi
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Bivariate time series modeling and forecasting have become a promising field of applied studies in recent times. For this purpose, the Linear Autoregressive Moving Average with exogenous variable ARMAX model is the most widely used technique over the past few years in modeling and forecasting this type of data. The most important assumptions of this model are linearity and homogenous for random error variance of the appropriate model. In practice, these two assumptions are often violated, so the Generalized Autoregressive Conditional Heteroscedasticity (ARCH) and (GARCH) with exogenous varia
... Show MoreGlobally, Sustainability is very quickly becoming a fundamental requirement of the construction industry as it delivers its projects; whether buildings or infrastructures. Throughout more than two decades, many modeling schemes, evaluation tools, and rating systems have been introduced en route to realizing sustainable construction. Many of these, however, lack consensus on evaluation criteria, a robust scientific model that captures the logic behind their sustainability performance evaluation, and therefore experience discrepancies between rated results and actual performance. Moreover, very few of the evaluation tools available satisfactorily address infrastructure projects. The res
Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing flower pollination algorithm in the environmental field to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement. We estimate the regression function of the semi-parametric model by estimating the parametric model and estimating the non-parametric model, the parametric model is estimated by using an instrumental variables method (Wald method, Bartlett’s method, and Durbin
... Show MoreMultiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of
... Show MoreSignature verification involves vague situations in which a signature could resemble many reference samples or might differ because of handwriting variances. By presenting the features and similarity score of signatures from the matching algorithm as fuzzy sets and capturing the degrees of membership, non-membership, and indeterminacy, a neutrosophic engine can significantly contribute to signature verification by addressing the inherent uncertainties and ambiguities present in signatures. But type-1 neutrosophic logic gives these membership functions fixed values, which could not adequately capture the various degrees of uncertainty in the characteristics of signatures. Type-1 neutrosophic representation is also unable to adjust to various
... Show MoreThe Internet of Things (IoT) has great importance in the medical industry. The creation of intelligent sensors, intelligent machines, and superior algorithms for lightweight communication made it feasible to connect medical equipment in order to monitor biomedical signals and also to detect illnesses in patients without human intervention. This new IoT and medical equipment connection is called IoMT. This IoMT model is most adapted to this pandemic since every human being has to be interconnected and monitored via a larger communication network. Hence, this article provides an overview of remote healthcare systems, monitoring ingestible sensors, mobile health, smart hospitals, and improved chronic disease management focused on t
... Show MoreABSTRACT Background: The main goal of chemomechanical endodontic treatment is the reduction or elimination of microorganisms from root canal system. The intracanal medicaments were used to enhance the disinfection process. This study was conducted to evaluate the antibacterial effect of thymus vulgaris, tea tree essential oils and cold pressed black seed oil (BSO) against E.faecalis. Materials and methods: E.faecalis was isolated from ten patients in need for endodontic treatment. The sensitivity of E.faecalis to the tested oils was evaluated in different concentrations in agar well diffusion method and compared with calcium hydroxide. The sensitivity of E.faecalis to vapor of the tested oils was also evaluated, in disk vaporization method
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