We present a tight bound on the exact maximum complexity of Minkowski sums of polytopes in R. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2, . . . ,mk facets respectively is bounded from above by

We derive tight bounds for the maximum number of k-faces, 0 ≤ k ≤ d − 1, of the Minkowski sum, P1 ⊕ P2, of two ddimensional convex polytopes P1 and P2, as a function of the number of vertices of the polytopes. For even dimensions d ≥ 2, the maximum values are attained when P1 and P2 are cyclic d-polytopes with disjoint vertex sets. For odd dimensions d ≥ 3, the maximum values are attained when ...

Let P and Q be finite sets of points in the plane. In this note we consider the largest cardinality of a subset of the Minkowski sum S ⊆ P ⊕ Q which consist of convexly independent points. We show that, if |P | = m and |Q| = n then |S| = O(m2/3n2/3 + m + n).

A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let δ(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine δ(d, k) for small instances. We show that δ(3, 4) = 7 and δ(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby δ(d, ...

abstract cognizing environment in human vision-system is complex process. part of this process is perceiving image elements and attention signals in general. in the other hand, extracting special description from image elements. it is assumed that the environment scene is a kind of image. according to this description, it is justifiable to interpret image according to the gestalt theory princip...

Background: In this study, Quantitative 32P bremsstrahlung planar and SPECT imaging and consequent dose assessment were carried out as a comprehensive phantom study to define an appropriate method for accurate Dosimetry in clinical practice. Materials and Methods: CT, planar and SPECT bremsstrahlung images of Jaszczak phantom containing a known activity of 32P were acquired. In addition, Phanto...

due to the hard climatic conditions of the yardang region in the lut desert, not much information about land surface temperatures of this region, one of the extremely arid cli-matic zones of iran, has been extracted. therefore, in this study in order to obtain some information about important surface features of the lut desert (marl, grey sand, bright sand and salt affected land), field tempera...