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 the present work, a Z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles. In this technique, a pulsed second harmonic Nd :YAG laser at wavelength 532 nm was used. The results show that the nonlinear refractive index and nonlinear absorption coefficients of the Ag nanoparticles are found to be dependent on the size these nanoparticles.
In this paper, the Normality set will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of .
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New microphotometer was constructed in our Laboratory Which deals with the determination of Molybdenum (VI) through its Catalysis effect on Hydrogen peroxide and potasum iodide Reaction in acid medium H2SO4 0.01 mM. Linearity of 97.3% for the range 5- 100 ppm. The repeatability of result was better than 0.8 % 0.5 ppm was obtanined as L.U. (The method applied for the determination of Molybdenum (VI) in medicinal Sample (centrum). The determination was compared well with the developed method the conventional method.
An analytical procedure has been carried out to measure the charge that may be trapped in an insulator sample of scanning electron microscope. It mainly concerns the determination of the deduced polarization charges by means of mirror effect phenomenon. Several relations related to such issue have been modified so as to be applicable for regarding charges due to polarization in linear and isotropic material. Consequently, the potential arises as a result for both trapped free and polarization charges which is set up. Actually the well-known magnification factor method is adopted to be a case study to implement the introduced approach. Results have clearly showed that the polarization charge significantly influences the Coul
... Show MoreLet M be a prime Γ-ring satisfying abc abc for all a,b,cM and
, with center Z, and U be a Lie (Jordan) ideal. A mapping d :M M
is called Γ- centralizing if u d u Z [ , ( )] for all uU and .In this paper
, we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ -
centralizing derivations on U.
In this paper, we introduce the concepts of higher reverse left (resp.right) centralizer, Jordan higher reverse left (resp. right) centralizer, and Jordan triple higher reverse left (resp. right) centralizer of G-rings. We prove that every Jordan higher reverse left (resp. right) centralizer of a 2-torsion free prime G-ring M is a higher reverse left (resp. right) centralizer of M.
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With the quick grow of multimedia contents, from among this content, face recognition has got a lot of significant, specifically in latest little years. The face as object formed of various recognition characteristics for detect; so, it is still the most challenge research domain for researchers in area of image processing and computer vision. In this survey article, tried to solve the most demanding facial features like illuminations, aging, pose variation, partial occlusion and facial expression. Therefore, it indispensable factors in the system of facial recognition when performed on facial pictures. This paper study the most advanced facial detection techniques too, approaches: Hidden Markov Models, Principal Component Analysis (PCA)
... Show More
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In this study, we investigate about the estimation improvement for Autoregressive model of the third order, by using Levinson-Durbin Recurrence (LDR) and Weighted Least Squares Error ( WLSE ).By generating time series from AR(3) model when the error term for AR(3) is normally and Non normally distributed and when the error term has ARCH(q) model with order q=1,2.We used different samples sizes and the results are obtained by using simulation. In general, we concluded that the estimation improvement for Autoregressive model for both estimation methods (LDR&WLSE), would be by increasing sample size, for all distributions which are considered for the error term , except the lognormal distribution. Also we see that the estimation improve
... Show MoreOur goal from this work is to find the linear prediction of the sum of two Poisson process
) ( ) ( ) ( t Y t X t Z + = at the future time 0 ), ( ≥ + τ τ t Z and that is when we know the values of
) (t Z in the past time and the correlation function ) (τ βz
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