We establish the following max-plus analogue of Minkowski’s theorem. Any point of a compact max-plus convex subset of (R∪{−∞})n can be written as the max-plus convex combination of at most n + 1 of the extreme points of this subset. We establish related results for closed max-plus convex cones and closed unbounded max-plus convex sets. In particular, we show that a closed max-plus convex set ca...

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...

We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such vector field be a member of the extremal set, the scalar curvature of a Sasaki extremal metric representing it would have the smallest L2-norm among all Sasakian...

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces. Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented. Finally, Kuhn-Tucker conditions of set-valued optimiz...

It is shown that a set-valued map M : R ⇒ R is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replace...

Gingival recession is commonly associated with plaque‐induced inflammation and calculus. A high frenal attachment is more important in gingival recession in the child‐patient. A healthy child‐patient with impeccable oral hygiene presented with localized gingival recession without plaque‐induced inflammation which led to the exploration of other possible etiologies. Multiple factors appeared to ...

Objectives: The aim of this study was to investigate whether altering the labial-lingual position of lower incisors in adolescents might predispose to the development of gingival recession. Methods: Records from 189 Caucasian adolescents (107 female and 81 male) pre and post orthodontic treatment were selected. Patients yielded mean ± SD values of initial records age 11.2 ± 1.9 years and final ...

This paper estimates a Structural Dynamic Factor Model on a panel of 102 US quarterly series. We model economic comovements by means of 5 underlying structural shocks (oil price, productivity, aggregate demand, monetary policy, and housing demand). The results of the benchmark model (impulse responses and variance decompositions) are in line with those predicted by economic theory and usually e...

The Great Recession was a deep downturn with long-lasting e ects on credit markets, labor markets and output. While narratives about what caused the recession abound, the persistence of GDP below its pre-crisis trend is puzzling. We propose a simple persistence mechanism that can be easily quanti ed and combined with existing models, even complex ones. Our solution rests on the premise that no ...