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  .

Praise to Allah, Lord of the Worlds. Thank you very much. Blessed. As his face should be majestic and great. His authority, and may peace and blessings be upon our master Muhammad, a perpetual blessing until the Day of Judgment

And upon the God of purity, His righteous companions, and those who follow them in righteousness until the Day of Judgment. But after:-

Anyone who looks into the history of nations, peoples, and the conditions of human beings will see that naturalization as a person’s affiliation to a particular state is something that happened only in recent centuries. In ancient times, a person’s loyalty was to the tribe to which the person belonged, and he was integrated into it and attributed to it, and in

This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

The development of new building materials, able of absorbing more energy is an active research area. Engineering Cementitious Composite (ECC) is a class of super-elastic fiberreinforced cement composites characterized by high ductility and tight crack width control. The use of bendable concrete produced from Portland Limestone Cement (PLC) may lead to an interest in new concrete mixes. Impact results of bendable concrete reinforced with steel mesh and polymer fibers will provide data for the use of this concrete in areas subject to impact loading. The experimental part consisted of compressive strength and impact resistance tests along with a result comparison with unreinforced concrete. Concrete samples, with dimensions of 100×

This paper is devoted to investigate the effect of internal curing technique on the properties of self-compacting concrete (SCC). In this study, SCC is produced by using silica fume (SF) as partial replacement by weight of cement with percentage of (5%), sand is partially replaced by volume with saturated fine lightweight aggregate (LWA) which is thermostone chips as internal curing material in three percentages of (5%, 10% and 15%) for SCC, two external curing conditions water and air. The experimental work was divided into three parts: in the first part, the workability tests of fresh SCC were conducted. The second part included conducting compressive strength test and modulus of rupture test at ages of (7, 28 and 90). The third part i

This paper introduces a Laplace-based modeling approach for the study of transient converter-grid interactions. The proposed approach is based on the development of two-port admittance models of converters and other components, combined with the use of numerical Laplace transforms. The application of a frequency domain method is aimed at the accurate and straightforward computation of transient system responses while preserving the wideband frequency characteristics of power components, such as those due to the use of high frequency semiconductive switches, electromagnetic interaction between inductive and capacitive components, as well as wave propagation and frequency dependence in transmission systems.

The Corrosion protection effectiveness of Alimina(Al2O3,50nm)and Zinc oxide (ZnO,30nm) nanoparticales were studied on carbon steel and 316 stainless steel alloys in saline water (3.5%NaCl)at four temperatures: (20,30,40,50 OC)using three electrodes potentiostat. An average corrosion protection efficiencies of 65 %and 80% was achieved using Al2O3 NP's on carbon steel and stainless steel samples respectively, and it seems that no effect of rising temperature on the performances of the coated layers. While ZnO NP'S showed protection efficiency around 65% for the two alloys and little effected by temperature rising on the performanes of the coated layers. The morphology of the coated spesiemses was examined by Atomic force microscope.

Galvanic corrosion of stainless steel 316 (SS316) and carbon steel (CS) coupled in 5% wt/v sulfuric acid solution at agitation velocity was investigated. The galvanic behavior of coupled metals was also studied using zero resistance ammeter (ZRA) method. The effects of agitation velocity, temperature, and time on galvanic corrosion current and loss in weight of both metals in both free corrosion and galvanic corrosion were investigated. The trends of open circuit potential (OCP) of each metal and galvanic potential (E_g) of the couple were, also, determined. Results showed that SS316 was cathodic relative to CS in galvanic couple and its OCP was much more positive than that of CS for all investigated ranges of