We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

Abstract

This research aims to identify the challenges faced by families of children with intellectual disabilities and to identify the impact of the challenges facing them on the mental health of their children with intellectual disabilities. Based on the following questions: What is the nature of the challenges faced by families of children with disabilities and how do these challenges affect the mental health of their children with intellectual disabilities? The study was conducted on a sample of four families of six children with intellectual disabilities, depending on the degree and type of disability. To achieve the study's objectives, the qualitative approach was used, Because of the importance of accessin

In the current study, remote sensing techniques and geographic information systems were used to detect changes in land use / land cover (LULC) in the city of Al Hillah, central Iraq for the period from 1990 - 2022. Landsat 5 TM and Landsat 8 OLI visualizations, correction and georeferencing of satellite visuals were used. And then make the necessary classifications to show the changes in LULC in the city of Al Hillah. Through the study, the results showed that there is a clear expansion in the urban area from 20.5 km2 in 1990 to about 57 km2 in 2022. On the other hand, the results showed that there is a slight increase in agricultural areas and water. While the arid (empty) area decreased from 168.7 km 2 to 122 km 2 in 2022. Long-term ur

Fiscal policy is one of the important economic tools that affect economic development in general and human development in particular through its tools (public revenues, public expenditures, and the general budget).

It was hoped that the effects of fiscal policy during the study period (2004-2007) will positively reflect on human development indicators (health, education, income) by raising these indicators on the ground. After 2003, public revenues in Iraq increased due to increased revenues. However, despite this increase in public budgets, the actual impact on human development and its indicators was not equivalent to this increase in financial revenues. QR The value of the general budget allocations ha

   Phenol is one of the worst-damaging organic pollutants, and it produces a variety of very poisonous organic intermediates, thus it is important to find efficient ways to eliminate it. One of the promising techniques is sonoelectrochemical processing. However, the type of electrodes, removal efficiency, and process cost are the biggest challenges. The main goal of the present study is to investigate the removal of phenol by a sonoelectrochemical process with different anodes, such as graphite, stainless steel, and titanium. The best anode performance was optimized by using the Taguchi approach with an L16 orthogonal array. the degradation of phenol sonoelectrochemically was investigated with three process parameters: current de