The preservation of surface shape is important in geometric modelling and approximation theory. In geometric modelling one would like to manipulate the shape of the surface being modelled by the simpler task of manipulating the control points. In scattered data approximation one might wish to approximate bivariate data sampled from a function with a shape property by a spline function sharing t...

On the domain of cooperative transferable utility games, we investigate if there are single valued solutions that reconcile rationality, consistency and monotonicity (with respect to the worth of the grand coalition) properties. This paper collects some impossibility results on the combination of core selection with either complement or projected consistency, and core selection, max consistency...

We consider global stability of a flow network model for vehicular traffic. Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions. In this paper, we show that the network model nonetheless exhibits a mixed monotonicity property. Mixed monotonicity allows us to prove global asymptotic stability...

In this article, we derive the distribution of partially exchangeable binary random variables, generalizing the distribution of exchangeable binary random variables and hence the binomial distribution. The distribution can also be viewed as a mixture of Markov chains. We introduce rectangular complete monotonicity and show that partial exchangebility can be characterized by rectangular complete...

Abstract. In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two ...

Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...

In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total variation bounded (TVB) property. In the analysis the multistep methods are considered in combination with suitable starting proc...

Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio...

A new approach to Markov chain Monte Carlo simulation was recently proposed by Propp and Wilson. This approach, unlike traditional ones, yields samples which have exactly the desired distribution. The Proppp Wilson algorithm requires this distribution to have a certain structure called monotonicity. In this paper, it is shown how the algorithm can be extended to the case where monotonicity is r...

Monotonicity is a major property of entropy measures. In this paper, we focus on measures for intuitionistic fuzzy sets and interval-valued sets. We consider their polar representation which provides an easy interpretation monotonicity several introduced in the literature. Moreover, enables us to propose two new kinds such entropies, that offer more understandable way explain differences entrop...