Abstract: The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimat...

Abstract In this paper we introduce the concept of conical behaviour, a complete time invariant cones of trajesctories. We focus our attention on the cones as subsets of autonomous linear system. We give geometrical conditions that such cones admit a non negative state realization. In addition we consider the closed sets of trajectories of a autoregressive scalar model on wich are imposed inequ...

We show that in reflexive Banach spaces there are two classes of closed cones (consumption sets) i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. We prove that in the first category of these cones the demand correspondence of any upper semicontinuous preference relation exists and we show also that this property characterizes the reflexive spaces. Moreover...

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = ∏ i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for R+. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence ...

The scanning electron microscope was used to examine the growth cones of sensory neurites on the basal lamina of the trunk skin and on the myotomes in dissected embryos of the amphibian, Xenopus laevis. On the myotomes growth cones are large and flat with extensive lamellipodia and many filopodia. On the skin growth cones are smaller and have simpler processes particularly in more ventral posit...