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.

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

This study refers to the development and characterization of silver oxide nanoparticles obtained by X-ray diffraction, nanostructured silver oxide was used in order to calculate the micro strain and crystal size by Halder-Wagner method and by relying on X-ray diffraction diagram of the nonstructural silver oxide, where the results of the crystal size and the micro-strain were 4nm and 0.33 respectively. Other analysis techniques, such as the Size-strain plot, The X-ray diffraction study confirmed that the crystalline nature of silver oxide nanoparticles has a cubic structure. Through the X-ray diffraction results, the crystal size was calculated using Debye-Scherrer and Williamson-Hall methods. Halder-Wagner (HW), Size-strain plot, D

This research explores the obstacles teachers encounter in executing the smart schools initiative within the framework of Iraq, where educational facilities and digital preparedness are still at an early stage. Although worldwide trends reveal the growing use of smart technologies in education, Iraq has been hindered by systemic barriers, such as archaic curricula, restricted access to technologies, and an unqualified teaching staff. Data were collected using a validated questionnaire on 122 public school teachers working in Baghdad with a descriptive-analytical methodology. The study divided challenges into five areas: infrastructure, teacher preparedness, administrative support, curricular adaptation and cultural resistanc

Cognitive-behavioral therapy is one of the most important relatively recent; treatment programs that attempt to modify behavior and control psychological disorders by modifying the individual's thinking style and awareness of himself and his environment, and cognitive reconstruction by replacing negative thoughts with positive ones. The current study aimed to know the effectiveness of a cognitive behavioral treatment program in reducing nervous fatigue among mothers of children with cerebral palsy. The sample on which the nervous fatigue scale was applied consisted of (30) mothers whose son suffers from cerebral palsy, and the results indicated that (24) mothers suffer from nervous fatigue. This sample was divided

This study investigated the application of the crystallization process for oilfield produced water from the East Baghdad oilfield affiliated to the Midland Oil Company (Iraq). Zero liquid discharge system (ZLD) consists of several parts such as oil skimming, coagulation/flocculation, forward osmosis, and crystallization, the crystallization process is a final part of a zero liquid discharge system. The laboratory-scale simple evaporation system was used to evaluate the performance of the crystallization process. In this work, sodium chloride solution and East Baghdad oilfield produced water were used as a feed solution with a concentration of 177 and 220 g/l. The impact of temperature (70, 80, and 90 °C), mixing speed (300, 400, and 500