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

Virtual reality, VR, offers many benefits to technical education, including the delivery of information through multiple active channels, the addressing of different learning styles, and experiential-based learning. This paper presents work performed by the authors to apply VR to engineering education, in three broad project areas: virtual robotic learning, virtual mechatronics laboratory, and a virtual manufacturing platform. The first area provides guided exploration of domains otherwise inaccessible, such as the robotic cell components, robotic kinematics and work envelope.  The second promotes mechatronics learning and guidance for new mechatronics engineers when dealing with robots in a safe and interactive manner. And the thir

The shortage in surface water quantities led to a shift in dependence on the groundwater as an alternative water source in southern parts of Iraq. The groundwater is decreasing in quantity and water quality is degrading due to different factors. Therefore, it is important to assess the groundwater quality of the Missan Governorate of the country by analyzing the physicochemical parameters and distinguishing the probable sources of contaminants in the area. The present study used water quality diagrams and statistical methods such as factor analysis and agglomerative cluster analysis to determine the sources of chemical ions in the forty-four groundwater samples collected from wells in the study area. In addition, the Water Quality Index (WQ

The overlap between science and knowledge is a feature of the 21st century. This integration, which crosses the traditional boundaries between academic disciplines, has occurred because of the emergence of new needs and new professions. This overlap has overshadowed the arts in general and design in particular. The Design achievements have not been far away from the attempts of integration of more than one type or design application to produce new outputs unique in its functional and aesthetic character, including the terms of internal graphic design.

The researcher raises the question of the functional dimension of graphic design in the internal space, in order to answer it through the methodological framework, which includes th

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Analyzing plantar pressure trajectories is crucial for assessing foot behavior in dynamic gait stability. We propose the identification of foot symmetry and the detection of deformities by analyzing the trajectories of the center of pressure (CoP) and peak pressure (PP). First, using a foot pressure mapping system, plantar pressure data are acquired during a normal gait cycle. After the data have been acquired, post processing extracts both the CoP and PP trajectories over the spatiotemporal domain of foot motion for each foot independently. For this purpose, we used the optical flow technique which accurately estimates the direction of foot motion. The extracted trajectories of each foot are then segmented into, the medial and lateral regi