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

The objective of this article is to delve into the intricate dynamics of marriage relationships, exploring the impact of emotions such as fear, love, financial considerations and likability. In our investigation, we adopt a perspective that acknowledges the nonlinear nature of interactions among individuals. Diverging from certain prior studies, we propose that the fear element within the context of marriage is not a singular, isolated factor but rather a manifestation resulting from the amalgamation of numerous social issues. This, in turn, contributes to the emergence of strained and unsuccessful relationships. Unlike conventional approaches, we extensively examine the conditions essential for the existence of all socially signifi

Objectives: The purpose of this in vitro study was to compare the effect of adding poloxamer surfactant to irrigant solutions on the penetration de..

Phoenix dactylifera l. pinnae (the green leaves of dates palm) were used as natural reinforcing (strengthening) fibers to improve the mechanical properties of polyester as a matrix material, the fibers of the green leaves of dates palm were used in two lengths, 10 and 20mm with five rates of 0, 2.5, 5, 10, and 20% , where the reinforcing with the leaves fibers increases the hardness strength from 76.5 to be about 86.55 , the Impact value raised from about 0.313 to 0.461 , in addition to that the flexural strength from 2.66 to be about 55 , and the thermal conductivity increases from 2.54 𝑤∕𝑚.℃ to 5.41 𝑤∕𝑚.℃. The results of the present search explains that the composite samples reinforced at rate 20% and 10mm fiber length

Numerous drilling additives and materials are used continuously because they are necessary to support and give the required properties of the drilling fluid so that to ensure the stability of the borehole. This paper aspires to evaluate the rheological properties of bentonite (montmorillonite) Trefawey as an alternative to using commercial bentonite. Monitoring and evaluating of the rheological and filtration properties were prepared. This exertion aims to focus on the effect of hematite, and barite on the rheological properties of the three aforementioned bentonite types. An improvement in the rheological properties of bentonite (montmorillonite). Trefawey was observed after adding the previous heavy materials. Hematite has by some

Generally the a.c. conductivity shows a power law in frequency s  ()  where the exponent s ≤ 1. As the frequency goes to zero the conductivity become frequency independent. The a.c. conductivity was studied for the Ge1-xSex thin films to see how the selenium contents affect the permittivity and the permeability for the Ge1-x Sex. The thin films prepared by thermal evaporation at room temperature and under vacuum (~2 x10-5toor) using Edward coating unit model 306A. From the relation between ln conductivity and ln w, the effect of selenium contents in Ge1-x Sex thin films on the exponent value, the relaxation time and the maximum barrier height. An algebric fitting method for circles and circular arcs was used to find the permit

The structural, optical and electrical properties of ZnS films prepared by vacuum evaporation technique on glass substrate at room temperature and treated at different annealing temperatures (323, 373, 423)K of thickness (0.5)µm have been studied. The structure of these films is determined by X-ray diffraction (XRD). The X-ray diffraction studies show that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (111). The optical properties investigated which include the absorbance and transmittance spectra, energy band gab, absorption coefficient, and other optical constants. The results showed that films have direct optical transition. The optical band gab was found to be in the range t

A Laced Reinforced Concrete (LRC) structural element comprises continuously inclined shear reinforcement in the form of lacing that connects the longitudinal reinforcements on both faces of the structural element. This study conducted a theoretical investigation of LRC deep beams to predict their behavior after exposure to fire and high temperatures. Four simply supported reinforced concrete beams of 1500 mm, 200 mm, and 240 mm length, width, and depth, respectively, were considered. The specimens were identical in terms of compressive strength (  40 MPa) and steel reinforcement details. The same laced steel reinforcement ratio of 0.0035 was used. Three specimens were burned at variable durations and steady-state temperatures (one