unacceptable social behaviors, particularly withdrawal behavior that appears in children with autism represent a major problem hindering the process of communication with those around them and therefore the process of mergence  with them be difficult.

     The withdrawal causes a real affect deficit for children with autism limits the possibility of development of their intellectual and mental growth due to their solitude and the weakness of their focus in the acquisition of pedagogical skills and lack the necessary social skills to maintain the relations of friendship and enjoyment of them.

      withdrawal children fail to participate

  Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Human beings are greatly inspired by nature. Nature has the ability to solve very complex problems in its own distinctive way. The problems around us are becoming more and more complex in the real time and at the same instance our mother nature is guiding us to solve these natural problems. Nature gives some of the logical and effective ways to find solutions to these problems. Nature acts as an optimized source for solving the complex problems.  Decomposition is a basic strategy in traditional multi-objective optimization. However, it has not yet been widely used in multi-objective evolutionary optimization.   

Although computational strategies for taking care of Multi-objective Optimization Problems (MOPs) h

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Background: Despite the importance of vaccines in preventing COVID-19, the willingness to receive COVID-19 vaccines is lower among RA patients than in the general population. Objective: To determine the extent of COVID-19 knowledge among RA patients and their attitudes and perceptions of COVID-19 vaccines. Methods: A qualitative study with a phenomenology approach was performed through face-to-face, individual-based, semi-structured interviews in the Baghdad Teaching Hospital, Baghdad, Iraq, rheumatology unit. A convenient sample of RA patients using disease-modifying anti-rheumatic drugs was included until the point of saturation. A thematic content analysis approach was used to analyze the obtained data. Results: Twenty-five RA pa