Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Virtual reality, VR, offers many benefits to technical education, including the delivery of information through multiple active channels, the addressing of different learning styles, and experiential-based learning. This paper presents work performed by the authors to apply VR to engineering education, in three broad project areas: virtual robotic learning, virtual mechatronics laboratory, and a virtual manufacturing platform. The first area provides guided exploration of domains otherwise inaccessible, such as the robotic cell components, robotic kinematics and work envelope.  The second promotes mechatronics learning and guidance for new mechatronics engineers when dealing with robots in a safe and interactive manner. And the thir

Corruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.

      According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.

      Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.

      Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside

Total Quality Assurance Concept have appeared in Higher Education Institutions as a result of the continuous criticism for the lower quality of the outputs of these institutions and their inappropriacy to the needs of the job market. The faculty, i.e. teaching staff member, is one of the most important output for his/her responsibility to achieve the stated goals in higher education. This represents a problem that may influence the construction of society which has to limit his tasks, responsibilities, and competencies that should be found in a faculty, and evaluating his teaching profession in light of the prerequisites of the century to become an input to achieve quality assurance in Higher Education. Therefore, the present study aims

The modification of hydrophobic rock surfaces to the water-wet state via nanofluid treatment has shown promise in enhancing their geological storage capabilities and the efficiency of carbon dioxide (CO2) and hydrogen (H2) containment. Despite this, the specific influence of silica (SiO2) nanoparticles on the interactions between H2, brine, and rock within basaltic formations remains underexplored. The present study focuses on the effect of SiO2 nanoparticles on the wettability of Saudi Arabian basalt (SAB) under downhole conditions (323 K and pressures ranging from 1 to 20 MPa) by using the tilted plate technique to measure the contact angles between H2/brine and the rock surfaces. The findings reveal that the SAB's hydrophobicity intensif