Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

An outer-independent double Italian dominating function (OIDIDF)on a graph $G$ with vertex set $V(G)$ is a function$f:V(G)longrightarrow {0,1,2,3}$ such that if $f(v)in{0,1}$ for a vertex $vin V(G)$ then $sum_{uin N[v]}f(u)geq3$,and the set $ {uin V(G)|f(u)=0}$ is independent. The weight ofan OIDIDF $f$ is the value $w(f)=sum_{vin V(G)}f(v)$. Theminimum weight of an OIDIDF on a graph $G$ is cal...

without any doubt the value of the securities in the economic analyses isdepending on the origin of assets and they don’t have value themselves. in respect of the rule of paper document in the nature of securities, some of iranian lawyer argues that the right to which the paper document relates materializes in the document and can therefore be transferred according to the rules governing tangib...

The aim of intermediate care, according to the National Service Framework for Older People, is to provide integrated services to promote faster recovery from illness, prevent unnecessary acute hospital admissions, support timely discharge, and maximise independent living. In Hackney, east London, this has resulted in two innovative approaches to meeting the NSF target. Homerton University Hospi...

This article reports on a pilot vocational study programme for provision of antenatal services in the general practice environment. The concurrent evaluation study assessed practice nurses' experiences of undertaking the pilot programme, the level and applicability of the content, and the mode of delivery. General practitioners' understanding of the role of the nurse in providing antenatal serv...

Planning for a successful MIS implementation requires understanding the effects of the introduction of a new system on the work lives of potential adopters. The effects can be assessed by the MIS practitioner/ change agent ff the agent will first obtain a thorough and specific understanding of the task activities performed by potential adopters, the interactions they engage in as they perform t...

This note investigates the noncooperative foundations of von Neumann-Morgenstern (vN-M) stable sets in voting games. To do so, we study subgame perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following results emerge from such an exercise: Every stable set of the underlying simple game is the limit set of undominated pure-strategy Markov...