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.

The early childhood stage, which is usually described as establishing the development and growth of most of the child’s mental, psychological, moral, and physical abilities, so scientists and researchers have been interested in the growth and upbringing of the child, especially for the specified period between (6 until the age of 11) due to the importance of education in this stage. The age stage in terms of developing the child’s senses and experiences, because he is by nature inclined to play and draw in his instinctive activity, according to which his natural responses to stimuli and his contemplation of what surrounds him change. Since drawing plays an important role in raising a child from an emotional and intellectual point of vie

Abiotic stress-induced genes may lead to understand the response of plants and adaptability to salinity and drought stresses. Differential display reverse transcriptase – polymerase chain reaction (DDRT-PCR) was used to investigate the differences in gene expression between drought- and salinity-stressed plantlets of Ruta graveolens. Direct and stepwise exposures to drought- or salt-responsive genes were screened in R. graveolens plantlets using the DDRT technique. Gene expression was investigated both in the control and in the salt or drought-stressed plantlets and differential banding patterns with different molecular sizes were observed using the primers OPA-01 (646,770 and 983 pb), OPA-08 (593 and 988 pb), OPA-11 (674 and 831 pb

The study was conducted to determine the effect Toxoplasma gondii and the efficacy of azithromycin and garlic tablets on the treatment of acute murine toxoplasmosis and observe the histopathological changes due to infection. 60 Albino mice were divided into six groups, and their survival rate, pathology, bioassay trial and immunofluorescence were observed. Results revealed that azithromycin (250 mg/kg/day) given to infected mice increased the survival rate (90% on day 7 PI) and decreased the histopathological changes when compared with the control groups. Garlic tablets (500 mg/kg/day) had lesser effect on infected mice, and the survival rate (40% at days 6 and 7 PI) was lower than the groups treated with azithromycin. The group treated wit

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