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

The relation between faithful, finitely generated, separated acts and the one-to-one operators was investigated, and the associated S-act of coshT and its attributes have been examined. In this paper, we proved for any bounded Linear operators T, VcoshT is faithful and separated S-act, and if a Banach space V is finite-dimensional, VcoshT is infinitely generated.

Linear attenuation coefficient of polymer composite for beta particles and bremsstrahlung ray were investigated as a function of the absorber thickness and energy. The attenuation coefficient were obtained using NaI(Tl) energy selective scintillation counter with ⁹⁰Sr/⁹⁰Y beta source having an energy range from 0.1-1.1 MeV. The present results show the capability of this composite to absorber beta particles and bremsstrahlung ray that yield from it. That’s mean it is useful to choice this composite for radiation shielding of beta ray with low thickness.

     Detection moving car in front view is difficult operation because of the dynamic background due to the movement of moving car and the complex environment that surround the car, to solve that, this paper proposed new method based on linear equation to determine the region of interest by building more effective background model to deal with dynamic background scenes. This method exploited the permitted region between cars according to traffic law to determine the region (road) that in front the moving car which the moving cars move on. The experimental results show that the proposed method can define the region that represents the lane in front of moving car successfully with precision over 94%and detection rate 86

In this paper, a hybrid image compression technique is introduced that integrates discrete wavelet transform (DWT) and linear polynomial coding. In addition, the proposed technique improved the midtread quantizer scheme once by utilizing the block based and the selected factor value. The compression system performance showed the superiority in quality and compression ratio compared to traditional polynomial coding techniques.

Many of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence

The current research examines the employment of indicators of stereotypes and the dimensions of organizational clarification to achieve planned organizational behaviour on a sample of employees in a number of departments of the Faculties of Engineering, University of Kufa, for a sample of (122) teaching staff. This research proposes the use of positive indicators of stereotypes for both the organization and employees and their awareness of what they want to obtain and what should be done for both parties and the removal of organizational clarity represented by the functional dimension that explores to what degree the employee's understanding of the internal strategy of the organization and the strategic dimension that searches fo

Molar conductance (Λ) of ionizable side chains amino acids, lysine (Lys) and arginine (Arg) with dehydroascorbic acid (DHA) in water and in NaCl solutions was measured at temperatures range 298 K to 313 K. The limited molar conductance (Λo) and the constant of the ions association (KA) are calculated using the Shedlovsky techniques. The dynamic radius of the concerned ion (R) is calculated by used Stokes–Einstein relation. The heat of association, the Gibbs free energy, the change of entropy and activation energy (ΔHo/ kJ mol-1, ΔGo/ kJ mol-1, ΔSo/J K-1 mol-1, and ΔES/ kJ mol-1) respectively), also calculated. The data show increases the molar conductance with increas