In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

Background: Among individuals who have a stenotic aortic valve, a precise assessment of aortic valve area is essential for clinical judgment. So far, no studies have been conducted to investigate and assess the role of the three dimensional echo-cardiography in the assessment of the valve stenosis. This study aims to compare and assess the precision of the measurement of the stenosis area of the aortic valve by 2D versus 3D echo-cardiography.

The study included a statement toxicity of some heavy metals individually and collectively and the existence of plant nutrients in the center Agirenk bluish green moss growth and Askhaddm biomass as an indicator of the study, in addition to portability moss on the accumulation of the metal

Abstract:

Viral marketing has become one of the modern strategies adopted by organizations in the marketing of products and services. The idea of viral marketing focuses on the social relations between individuals and groups. As a result of the technological development, most organizations have resorted to using the Internet and its applications and social media to market and promote their products. To reach the largest number of consumers to display their products and services in many ways, including text, audio, visual or video and thus affect the behavior of the consumer.

The problem of the study was the following question (do viral marketing technologies have an impact on consumer behavior?)

Experimental densities, viscosities η, and refractive indices n_D data of the ternary  ethanol+ n-hexane + 3-methyl pentane system have been determined at temperatures 293.15,303.15 and 313.15 K and at atmospheric pressure then these properties were calculated theoretically by using mixing rules for densities, viscosities and refractive indices .After that the theoretical data and the experimental data were compared due to the high relative errors in viscosities an equation of viscosity was proposed to decrease the relative errors.

The experiment was conducted to study the effect of leaves extract of Salvia sclarea , Rosmarinus officinalis and Thymus vulgaris with 10% and 30% concentration on germination of seeds and growth of seedlings . The effect of these extracts on infection percentage of seeds decay and surface growth of Rhizoctonia solani . The results showed that the three extracts effected significantly to reduced percentage of seeds germination, acceleration of germination , promoter indicator , infection percentage of seeds decay and surface growth of R. solani especially in 30% concentration .