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.

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

Chemical bath deposition was used to synthesize ZnO nanorods (NRs) on glass and fluorine^_doped tin oxide (FTO) substrates. X-ray diffraction was performed to examine the crystallinity of ZnO nanorod. Results showed that ZnO NRs had a wurtzite crystal structure. Field emission scanning electron microscopy images showed that glass sample had rod-like structure distribution with (50 nm) diameter and average length of approximately (700 nm), whereas the FTO-coated glass sample had 25 nm diameter and average length of approximately 950 nm. The direct optical transition band gaps of the glass and FTO^_coated glass samples were( 4 and 4.43 eV), respectively. The structural and optical properties of the synthesized ZnO p

Four new copolymers were synthesized from reaction of bis acid monomer 3-((4-carboxyphenyl) diazenyl)-5-chloro-2-hydroxybenzoic acid with five diacidhydrazide in presence of poly phosphoric acid. The resulted monomers and copolymers have been characterized by FT-IR, 1H-NMR, 13C-NMR spectroscopy as well as EIMs technique. The number averages of molecular weights of the copolymers are between 4822 and 9144, and their polydispersity indexes are between 1.02 and 2.15. All the copolymers show good thermal stability with the temperatures higher than 305.86 C when losing 10% weight under nitrogen. The cyclic voltammetry (CV) measurement and the electrochemical band gaps (Eg) of these copolymers are found below 2.00 ev.

This research explores the integration of multi-walled carbon nanotubes (MWCNTs) into polyvinyl alcohol (PVA) matrices to enhance their structural, electrical and thermal properties. Fourier-transform infrared spectroscopy analysis confirms the formation of a PVA-MWCNT complex. The incorporation of MWCNTs, even at low concentrations, leads to increased electrical conductivity, making the composite material suitable for applications in flexible electronics and sensors. Dielectric studies reveal frequency-dependent electrical behavior, attributed to interfacial polarization, suggesting potential uses in capacitors and energy storage devices. The introduction of MWCNTs into PVA leads to N-type semiconductor behavior, as indicated by the Hall c

The synthesis and bioactivity of zinc oxide nanoparticles has been extensively studied. The antibacterial activity of different antibiotics individually (ceftriaxone (C), chloramphenicol (CRO), penicillin (P) and amoxicillin (Ax)) and Zinc oxide nanoparticles (60μg/ml) in combination with the previously mentioned antibiotics has been demonstrated in the present study by using the disk diffusion assay method. The results showed a synergistic effect between Zinc oxide nanoparticles (ZnO NPs) and both Ax and P for most of the studied Gram-positive isolates (Staphylococcus aureus1, Staphylococcus aureus2, Staphylococcus epidermidis1, Staphylococcus epidermidis2, Enterococcus faecalis1, Enterococcus faecalis2 ) and between ZnO NPs and both C