Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

The objective of this work is to study the influence of end milling cutting process parameters, tool material and geometry on multi-response outputs for 4032 Al-alloy. This can be done by proposing an approach that combines Taguchi method with grey relational analysis. Three cutting parameters have been selected (spindle speed, feed rate and cut depth) with three levels for each parameter. Three tools with different materials and geometry have been also used to design the experimental tests and runs based on matrix L9. The end milling process with several output characteristics is solved using a grey relational analysis. The results of analysis of variance (ANOVA) showed that the major influencing parameters on multi-objective response w

The present paper focuses on the nature of the different interactions between cometary nucleus and tail with solar wind. The dynamics of the comet will impose many features that provide unique behavior of the comet when entering the solar system. These features are reviewed in this paper and few investigations are made. The calculations made in this work represent the analysis and interpretation of the different features of the comet, such as perihelion and eccentricity dependence on the gas production rate, and the dependence of the latter on the composition of the comet nucleus. The dependences of the heliocentric, bow shock, contact surface, and stand-off distances with gas production rate for many types of comets that cover linear and n

The voice had a special place in the writting of the Andalusian poet (Ibn al-Abar ) , which aroused my attention because of the sonic capacity of the lettering inside the poetic at Ibn al-Abar poems . So Istudied the qualities of the lettering , structures and their exits . Scientists have not been able to determine the musical from the nonmusical sound , but we find the innate ability of Ibn al-Abar , which was able to determine this by using the lettering the right places and to revival the life to reflect the moments of his life , therefore came votes to express his purposes of praise and pride Etc. The poet Ibn al-Abar could exploit the lettering features in the effect of bilateral – static and moving and its ability to e

Failure in asphalt mixture and distress in pavement are major issues to roads infrastructure. Selecting an appropriate chemical composition of asphalt cement is a key component in avoiding these issues. This work aimed to investigate the effect of the chemical composition of different polar fractions on the rheological and physical properties of asphalt cement. Four types of asphalt cement with penetration grades of 20/30, 40/50, 60/70 and 85/100 were divided into four fractions. Complex shear modules, rutting resistance and rotational viscosity of the asphalt cement were determined by using a Dynamic Shear Rheometer and a Rotation Viscometer, respectively. The results show that an increase in the asphaltene content and Gastel index resulte

The durability of asphalt concrete is highly dependent on the geometry and mineralogy of coarse aggregates, yet their combined influence on mechanical and moisture resistance properties is still not fully understood. This study evaluates the effects of coarse aggregate geometry, specifically flat and elongated particle ratios and angularity, as well as mineral composition (quartz versus calcite), on asphalt mixture durability. The durability of mixtures was evaluated through Marshall properties as well as moisture susceptibility indicators, including the tensile strength ratio (TSR) and index of retained strength (IRS). Statistical analyses (ANOVA and t-tests) were also conducted to confirm the significance of the observed effects.