In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

We give further results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper [6], and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.

Many researchers have attempted to predict the Enron corporate hierarchy from the data. This work, however, has been hampered by a lack of data. We present a new, large, and freely available gold-standard hierarchy. Using our new gold standard, we show that a simple lower bound for social network-based systems outperforms an upper bound on the approach taken by current NLP systems.

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individ...

Alcohol consumption is often linked to a broad range of social and health problems, yet alcohol also plays a fundamental role in social bonding between people. This paper considers the potential of social marketing to contribute to alcohol consumption reduction and reframe social norms that encourage „problem‟ drinking. Based on qualitative research with a variety of Scottish drinkers, the pape...

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.