The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .

Community participation is one of the basic pillars of the sustainable development process. It provides opportunities for different groups of society to contribute to the management, preparation and implementation of development plans commensurate with their needs and aspirations. In this context, the study presents a study of the concept of community participation and its importance in sustainable development, In terms of its conditions, requirements and principles, as well as its image, as well as addressing the most important challenges and obstacles facing the participation of citizens in development projects. The research also provides an analysis of a number of international and Arab experiences adopted In its polici

This work comprises the synthesis of new thioxanthone derivatives containing C-substituted thioxanthone. To obtain these derivatives, the o-mercapto benzoic acid was chosen as the starting material, which was reacted with dry benzene in sulfuric acid (98 %) to produce the thioxanthone (1). The 2,7-(disulfonyl phosphine imine) thioxanthone (4-8) were prepared from reaction of compound (1) with chlorosulfonic acid gave 2,7-(disulfonyl chloride) thioxanthone (2). Treatment of (2) with sodium azide to produce 2,7-(disulfonyl azide) thioxanthone (3). Condensation of (3) with phosphorus compounds afforded compounds (4-8). The 2,7-(disulfonamide) thioxanthone (9-21) was obtained when co

Communication is a vital process that needs much more understanding and mutual background knowledge on the part of ESL learners in terms of grammar, meaning and context. Thus, the main aim of the current research paper is to identify and figure out the denotative and connotative meaning of barnyard verbs in English and practically analyzing these verbs to identify the dictionary meaning from connotative one. The main problem of this study is attributed to the fact that ESL learners may not be able to identify and understand the connotative meaning of barnyard verbs since these verbs are onomatopoeic (i.e,) a word that phonetically imitates, or suggests the source of sound that it describes). Consider the following example: the verb "coo" ha

An indoor spraying robot is built in this research to solve numerous challenges associated with manual spraying. The mechanical, hardware and essential technologies used are all detailed and designed. The proposed spraying robot's conceptual design is split into two parts: hardware and software. The mechanical design, manufacturing, electrical, and electronics systems are described in the hardware part, while the control of the robot is described in the software section. This robot's kinematic and dynamic models were developed using three links that move in the x, y, and z directions. The robot was then designed using SolidWorks software to compute each connection's deflection and maximum stresses. The characteristics of the stepper moto

F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds