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...