the first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...

Article history: Received 20 October 2011 Received in revised form 2 July 2012 Accepted 15 July 2012 Available online xxxx

As a sequel to [1], the position of the maximum in a geometrically distributed sample is investigated. Samples of length n are considered, where the maximum is required to be in the first d positions. The probability that the maximum occurs in the first d positions is sought for d dependent on n (as opposed to d fixed in [1]). Two scenarios are discussed. The first is when d = αn for 0 < α ≤ 1,...

In this article, we present the first method to generate plausible sounds while animating crumpling virtual paper in real time. Our method handles shape-dependent friction and crumpling sounds which typically occur when manipulating or creasing paper by hand. Based on a run-time geometric analysis of the deforming surface, we identify resonating regions characterizing the sound being produced. ...