In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

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.

Surge pressure is supplemental pressure because of the movement of the pipes downward and the swab pressure is the pressure reduction as a result of the drill string's upward movement. Bottom hole pressure is reduced because of swabbing influence. An Investigation showed that the surge pressure has great importance for the circulation loss problem produced by unstable processes in the management pressure drilling (MPD) actions. Through Trip Margin there is an increase in the hydrostatic pressure of mud that compensates for the reduction of bottom pressure due to stop pumping and/or swabbing effect while pulling the pipe out of the hole. This overview shows suggested mathematical/numerical models for simulating surge pressure problems ins

Various of 2,5- disubstituted 1,3,4-oxadiazole (Schiff base, ?- lactam and azo) were synthesized from 2,5-di (4,4?-amino-1,3,4-oxadiazole which usequently synth-esized from mixture of 4- amino benzoic acid and hydrazine arch of polyphosphorus acid. The synthesized compounds were cherecterized by using some spectral data (UV, FT-IR , and 1H-NMR)

The present study was designed to investigate the effect of different concentrations of Maxxthor on some hematological and oxidative stress parameters in male albino rats.Twenty male rats with age of 6-8 weeks and weight of 200-250gm were equally divided into four groups as follow:G1 treated with normal saline as control group,while G2,G3andG4groups were treated with(0.01,0.1,1)mg\kg body weight of Maxxthor respectively for 40 days.The following hematological parameters were measured: red blood cell(RBC),hemoglobin (Hb),white blood cell(WBC), platelets(PLT),malondialdehyde(MDA),glutathione(GSH),catalase and vitamin E. The hematological parameters results revealed highly significant(p<0.01)decreasein RBC and H,while a highly significant(p<0.