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 research aims to develop physical exercises with auxiliary training tools that work to develop the explosive power of the arms and legs, and then find out their effect on the accuracy of shooting from free throw and correction from jumping of advanced basketball players, as the researchers found a problem that these players have weakness in the skill of throwing Free throwing and shooting by jumping calculated with two points as a result of adopting unhealthy physical and technical positions, which led to a lack of focus and accuracy, and thus negatively affected the performance technique of free throw and jump shot, as most teams use traditional exercises without the use of auxiliary training tools, and this topic gave researchers the

The corrosion behavior of copper and carbon steel in 1M concentration of hydrochloric acid (HCl) and sulphuric acid (H2SO4) has been studied. The corrosion inhibition of copper and carbon steel in 1M concentration of hydrochloric acid (HCl) and sulphuric acid (H2SO4) by Ciprofloxacin has been investigated. Specimens were exposed in the acidic media for 7 hours and corrosion rates evaluated by using the weight loss method. The effect of temperature (from 283 ºK to 333 ºK), pH (from 1to 6), inhibitor concentration (10-4 to 10-2) has been studied. It was observed that sulphuric acid environment was most corrosive to the metals because of its oxidizing nature, followed by hydrochloric acid. The rate of metal dissolution increased with incre

Flexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec