This is a continuation of our previous work [41]. It is well known that various isoperimetric inequalities imply their functional “counterparts”, but in general this is not an equivalence. We show that under certain convexity assumptions (e.g. for log-concave probability measures in Euclidean space), the latter implication can in fact be reversed for very general inequalities, generalizing a re...

In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of the induced paths is associated with the monophonic convexity ; and there are many other examples. Besides reviewing the path convexities in the literature, ...

Logistic and Gompertz growth equations are the usual choice to model sustainable immoderate causing depletion of resources, respectively. Observing that logistic distribution is geo-max-stable function proportional Gumbel max-stable distribution, we investigate other models either distributions (log-logistic backward log-logistic) or (Fréchet max-Weibull). We show former arise when in hyper-log...

We study the existence of Stackelberg equilibrium points on strategy sets which are geodesic convex in certain Riemannian manifolds by using metric projection arguments. The present results extend those obtained in Nagy [J. Global Optimization (2013)] in the Euclidean context.

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

Two CT features were developed to quantitatively describe lung adenocarcinomas by scoring tumor shape complexity (feature 1: convexity) and intratumor density variation (feature 2: entropy ratio) in routinely obtained diagnostic CT scans. The developed quantitative features were analyzed in two independent cohorts (cohort 1: n = 61; cohort 2: n = 47) of patients diagnosed with primary lung aden...

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...

Many resource allocation problems can be studied within the framework of interference functions. Basic properties of interference functions are non-negativity, scale-invariance, and monotonicity. In this paper, we study interference functions with additional properties, namely convexity, concavity, and log-convexity. Such interference functions occur naturally in various contexts, e.g., adaptiv...

Gordon G Johnson* ([email protected]), Department of Mathematics, University of Houston, Houston, TX 77204-3008. The Closure in a Hilbert Space of a PreHilbert Space CHEBYSHEV Set Fails to be a CHEBYSHEV Set. Preliminary report. E is the real inner product space that is union of all finite-dimensional Euclidean spaces, S is a certain bounded nonconvex set in the E having the property that every...