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.
DFT (3-21G, 6-31G and 6-311G/ B3LYP) and Semi-empirical PM3 methods were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) of the Tri-rings layer (6,0) Zigzag single wall carbon nanotube (SWCNT) at their equilibrium geometries which was found to have D6h symmetry point group with C-C bond alternation in all tube rings.as well as mono ring layer. Assignments of the modes of vibration were done depending on the pictures of their modes applying by Gaussian 03 program. The whole relations for the vibration modes were also done including (CH stretching, CC stretching, deformation in plane of the molecule (δCH, δring and δCCC), deformation out of plane of the molecule (CH and
... Show MoreIn this paper, we use the repeated corrected Simpson's 3/8 quadrature method for obtaining the numerical solutions of Fredholm linear integral equations of the second kind. This method is more accurately than the repeated corrected Trapezoidal method and the repeated Simpson's 3/8 method. To illustrate the accuracy of this method, we give a numerical example
Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n2), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ3) were e
... Show MoreA mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc
... Show MoreMany of the dynamic processes in different sciences are described by models of differential equations. These models explain the change in the behavior of the studied process over time by linking the behavior of the process under study with its derivatives. These models often contain constant and time-varying parameters that vary according to the nature of the process under study in this We will estimate the constant and time-varying parameters in a sequential method in several stages. In the first stage, the state variables and their derivatives are estimated in the method of penalized splines(p- splines) . In the second stage we use pseudo lest square to estimate constant parameters, For the third stage, the rem
... Show MoreIn this study, different oil fields in Mesopotamian basin, southern Iraq (Siba, Zubair, Nahr - Umr, Majnoon, Halfaya, Kumait, and Amara) were selected for studying burial history. PetroMod software 1D was used for basin constructing and to evaluate burial history of the basin. Results showed that in the upper Jurassic to the Recent, Mesopotamian Basin exhibited a complex subsidence history over a period of about 152 Ma.There are different periods of subsidence: high, moderate, and slow. High subsidence occurred at upper Jurassic- mid Cretaceous and at Miocene due to Tectonic subsidence. Slow subsidence occurred at upper Cretaceous and moderate subsidence at Paleogene. In the upper Jurassic, rapid subsidence is driven under the effect of
... Show MorePassive optical network (PON) is a point to multipoint, bidirectional, high rate optical network for data communication. Different standards of PONs are being implemented, first of all PON was ATM PON (APON) which evolved in Broadband PON (BPON). The two major types are Ethernet PON (EPON) and Gigabit passive optical network (GPON). PON with these different standards is called xPON. To have an efficient performance for the last two standards of PON, some important issues will considered. In our work we will integrate a network with different queuing models such M/M/1 and M/M/m model. After analyzing IPACT as a DBA scheme for this integrated network, we modulate cycle time, traffic load, throughput, utilization and overall delay
... Show MoreIn this paper, we investigate the behavior of the bayes estimators, for the scale parameter of the Gompertz distribution under two different loss functions such as, the squared error loss function, the exponential loss function (proposed), based different double prior distributions represented as erlang with inverse levy prior, erlang with non-informative prior, inverse levy with non-informative prior and erlang with chi-square prior.
The simulation method was fulfilled to obtain the results, including the estimated values and the mean square error (MSE) for the scale parameter of the Gompertz distribution, for different cases for the scale parameter of the Gompertz distr
... Show MoreThe aim of this paper is to construct the analysis mathematical model for stream cipher cryptosystems in order to be cryptanalysis using the cryptanalysis tools based on plaintext attack (or part from it) or ciphertext only attack, choosing Brüer generator as study case of nonlinear stream cipher system.
The constructing process includes constructing the linear (or non-linear) equations system of the attacked nonlinear generator. The attacking of stream cipher cryptosystem means solving the equations system and that means finding the initial key values for each combined LFSR.
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