Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

Abstract We introduce the concepts of components’ second-order productivities in cooperative games with transferable utility (TU games) a coalition structure (CS and payoffs for one-point solutions CS as generalizations players’ TU (Casajus Discrete Appl Math 304:212–219, 2021). The are conceptualized marginal contributions, that is, how one player affects another player’s contributions to coal...

Abstract We introduce Hyper 2 LTL, a temporal logic for the specification of hyperproperties that allows second-order quantification over sets traces. Unlike first-order logics hyperproperties, such as HyperLTL, LTL can express complex epistemic properties like common knowledge, Mazurkiewicz trace theory, and asynchronous hyperproperties. The model checking problem is, in general, undecidable. ...

In this article, a stochastic algorithm is briefly presented based on the one of second moment applied to a stochastic process model of second order. The design initially consisted in formulating the state equation model and the stochastic outputs, in order to apply the second moment using the internal product of Martingale and the stochastic operators of the expectation, variance and covarianc...