We study geometric hypergrahs in a kinetic setting. That is, the set of vertices of the hypergraph is a set of moving points in R with coordinates that are polynomials in time. The hyperedges are all subsets that can be realized by intersecting the set of points at some fixed time with some “simple” geometric shape, such as, say, a halfspace. We show that for many of the static cases where the ...

background: malocclusion, as a worldwide issue, can cause a lot of problems for patients. panoramic (pr) and lateral cephalometric (lcr) radiographs are both usually indicated for orthodontic treatments. the aim of this study was to analyze vertical and sagittal parameters of both jaws on prs and to compare them on lcrs. materials and methods: in this cross sectional study, 61 samples from all ...

let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, ...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...

Suppose that we have the unit Euclidean ball in R and construct new bodies using three operations linear transformations, closure in the radial metric and multiplicative summation defined by ‖x‖K+0L = p ‖x‖K‖x‖L. We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of ...