Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.

   In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all .

In this article four samples of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ were prepared and irradiated with different doses of gamma radiation 6, 8 and 10 Mrad. The effects of gamma irradiation on structure of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ samples were characterized using X-ray diffraction. It was concluded that there effect on structure by gamma irradiation. Scherrer, crystallization, and Williamson equations were applied based on the X-ray diffraction diagram and for all gamma doses, to calculate crystal size, strain, and degree of crystallinity. I

In this paper, we will introduce a new concept of operators in b-Hilbert space, which is respected to self- adjoint operator and positive operator. Moreover we will show some of their properties as well as the relation between them.

Naturally occurring radioactive materials (NORM) contaminated sites at Al-Rumaila Iraqi oil fields have been characterized as a part of soil remediation project. Activity of radium isotopes in contaminated soil have been determined using gamma spectrometer High Purity Germanium detector (HPGe) and found to be very high for Al-Markezia, Al-Qurainat degassing stations and storage area at Khadhir Almay region. The activity concentration of samples ranges from 6474.11±563.8 Bq/kg to 1232.5±60.9 Bq/kg with mean value of 3853.3 Bq/kg for ²²⁶Ra, 843.59±8.39 Bq/kg to 302.2±9.2 Bq/kg  with mean value of 572.9 Bq/kg for ²³²Th and 294.31±18.56 Bq/kg to 156.64±18.1 Bq/kg with mean value of 225.5 for ⁴⁰K. S

Radiological assessment due to existing of natural occurring radioactive materials
(NORM) in South Rumaila oil field was achieved in this study. Different samples
including soil, sludge, scale, oil, and water were collected from different stages of
oil and gas production in Markazia Degassing Station (SDS) in South Rumaila oil
field. Radioactivity of Ra-226, Th-232 and K-40 were measured using gamma
spectrometry system based on HPGe detector with efficiency of 30%. The results
show that some locations within SDS are contaminated with NORM. The activity of
Ra-226, Th-232 and K-40 range between 18.4 to 312.8, 9.4 to 140.8 and 66.4 to
800.8 (Bq/kg) respectively. The places to be more contaminated among the other
p

Concentration of natural occurring radioactive material (NORM) in Markazia Degasing Station in North Rumaila oilfield (NDS) was measured in this study. Then, radiological assessment due to existing of NORM in different samples including soil, sludge, scale, oil, and water collected from different stages of oil and gas production NDS was done. Radioactivity concentration of Ra-226, Th-232 and K-40 were measured using gamma spectrometry system based on HPGe detector with efficiency of 30%. The results show that some locations within NDS are contaminated with NORM. The activity in Bq/kg of Ra-226, Th-232 and K-40 range between 15.19 in oil to 68.73 in sludge, 8.5 in oil to 23.45 in sludge and 80.23 in oil to 319.73 in saline water samples r

Cabrera and Mohammed proved that the right and left bounded algebras of quotients  and  of norm ideal  on a Hilbert space  are equal to  Banach algebra of all bounded linear operators on . In this paper, we prove that  where  is a norm ideal on a complex Banach space .

    The main purpose of the work is to apply a new method, so-called LTAM, which couples the Tamimi and Ansari iterative method (TAM) with the Laplace transform (LT). This method involves solving a problem of non-fatal disease spread in a society that is assumed to have a fixed size during the epidemic period. We apply the method to give an approximate analytic solution to the nonlinear system of the intended model. Moreover, the absolute error resulting from the numerical solutions and the ten iterations of LTAM approximations of the epidemic model, along with the maximum error remainder, were calculated by using MATHEMATICA® 11.3 program to illustrate the effectiveness of the method.

The fuzzy sets theory has been applied in many fields, such as operations research, control theory and management sciences, etc. In particular, an application of this theory in decision making problem is linear programming problems with fuzzy technological coefficients numbers, as well as studying the parametric linear programming problems in the case of changes in the objective function. In this paper presenting a new procedure which connects and makes link between fuzzy linear programming problem with fuzzy technological coefficients numbers and parametric linear programming problem with change in coefficients of the objective function, then develop a numerical example illustrates the steps of solution to this kind of problems.