In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

Stone Matrix Asphalt (SMA) is a gap-graded asphalt concrete hot blend combining high-quality coarse aggregate with a rich asphalt cement content. This blend generates a stable paving combination with a powerful stone-on-stone skeleton that offers excellent durability and routing strength. The objectives of this work are: Studying the durability performance of stone matrix asphalt (SMA) mixture in terms of moisture damage and temperature susceptibility and Discovering the effect of stabilized additive (Fly Ash ) on the performance of stone matrix asphalt (SMA) mixture. In this investigation, the durability of stone matrix asphalt concrete was assessed in terms of temperature susceptibility, resistance to moisture damage, and sensitivity t

This research aims to study and evaluate the reality of the Iraqi banks in terms of how they cope with the risks of the banking business, specifically banking operational risks, and to develop a model integrated to define, identify, measure and mitigate the impact of these risks on according to the Basel Committee requirements II about the dangers of Alchgal.uchir major search to the presence of weak results in the Iraqi banks in understanding and defining and measuring operational risks and not hedged properly, which avoids those banks operating losses as well as the results show there is a shortage in the equation of capital adequacy applied by the Iraqi banks because of non-observance of the minimum capital required to counter the ris

In this paper, an exact stiffness matrix and fixed-end load vector for nonprismatic beams having parabolic varying depth are derived. The principle of strain energy is used in the derivation of the stiffness matrix.
The effect of both shear deformation and the coupling between axial force and the bending moment are considered in the derivation of stiffness matrix. The fixed-end load vector for elements under uniformly distributed or concentrated loads is also derived. The correctness of the derived matrices is verified by numerical examples. It is found that the coupling effect between axial force and bending moment is significant for elements having axial end restraint. It was found that the decrease in bending moment was
in the

Elzaki Transform Adomian decomposition technique (ETADM), which an elegant combine, has been employed in this work to solve non-linear Riccati matrix differential equations. Solutions are presented to demonstrate the relevance of the current approach. With the use of figures, the results of the proposed strategy are displayed and evaluated. It is demonstrated that the suggested approach is effective, dependable, and simple to apply to a range of related scientific and technical problems.