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 work a model of a source generating truly random quadrature phase shift keying (QPSK) signal constellation required for quantum key distribution (QKD) system based on BB84 protocol using phase coding is implemented by using the software package OPTISYSTEM9. The randomness of the sequence generated is achieved by building an optical setup based on a weak laser source, beam splitters and single-photon avalanche photodiodes operating in Geiger mode. The random string obtained from the optical setup is used to generate the quadrature phase shift keying signal constellation required for phase coding in quantum key distribution system based on BB84 protocol with a bit rate of 2GHz/s.
A new attempt is made to determine diosmin (DIO) in its pure form and in dietary supplements by using spectrophotometric flow injection analysis (FIA) assay method conjugated with batch method. The analysis was achieved depending on the oxidative coupling reaction with N, N-dimethyl-p-phenylenediamine (DMPD) to form a green dye which is measured at wavelength of 677 nm. The tested methods were found to be economical, delicate, precise and sturdy. The validation variables of the batch and FIA methods gave linearity in the determination range of DIO (1-35) μg/mL and (5-120) μg/mL demonstrated calibration graphs with linearity coefficient values of r2 =0.9989 and r2 =0.9991, respectively. Limits of quanti
... Show MoreIn this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by for any operators in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.
This research is concerned with the study of (the aesthetic of constructive relations in linear composition) with what distinguished Arabic calligraphy through the style and artistic method in its construction, and the specifications it carries that enabled it to pay attention to building formations to achieve in its total linear ranges aesthetic values and relationships. Through the research, the models and the exploratory study that he obtained, the researcher was able to raise the research problem in the first chapter according to the following question: What is the aesthetic of constructive relations in linear formation?
The importance of the research in achieving the aesthetics of the formations, which is a wide field according t
in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner
As of late, humankind has experienced radiation issues either computerized tomography (CT) or X-rays. In this investigation, we endeavor to limit the effect of examination hardware. To do this the medical image is cropping (cut and zoom) then represented the vascular network as a graph such that each contraction as the vertices and the vessel represented as an edges, the area of the coagulation was processed already, in the current search the shortest distance to reach to the place of the blood vessel clot is computed
Abstract: The aim of the current research is to find out the extent to which systems thinking skills are included in the mathematics textbook scheduled for the third intermediate grade for the academic year (2020-2021) by answering the main research question: What are the systems thinking skills included in the mathematics textbook for middle third grade? The analytical descriptive approach was used, and to achieve the goal of the research, a list of the main systemic thinking skills and sub-skills was prepared, and after analyzing the content of the mathematics textbook, the reliability of the analysis was verified through the analysis over time and through others, and it obtained a reliability rate of 98% us
... Show MoreIn the present work the clathrate hydrate dissociation enthalpies of refrigerant R134a+ water system, and R134a + water + salt system were determined. The heat of dissociation of three types of aqueous salts solutions of NaCl, KBr and NaF at three concentrations (0.09, 0.17and 0.26) mol·kg−1 for each salt type, were enthalpy measured. The Clapeyron equation was used tocalculate heat of dissociation of experimental data for binary and ternary system.In order to find the effect of compressibility factor on heat dissociation enthalpy, the study was conducted by using equation of state proposed by Peng and Robinson Stryjek-Vera (PRSV). The obtained results of dissociation enthalpy for binary system were (143.8) kJ.mol-1
... Show MoreThe growing interest in the use of chaotic techniques for enabling secure communication in recent years has been motivated by the emergence of a number of wireless services which require the service provider to provide low bit error rates (BER) along with information security. This paper investigates the feasibility of using chaotic communications over Multiple-Input-Multiple-Output (MIMO) channels. While the use of Chaotic maps can enhance security, it is seen that the overall BER performance gets degraded when compared to conventional communication schemes. In order to overcome this limitation, we have proposed the use of a combination of Chaotic modulation and Alamouti Space Time Block Code. The performance of Chaos Shift Keying (CSK) wi
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