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, ...

one of the goals of financial reporting is to provide the useful information in order to facilitate the decision making. accounting information system is of high importance for the users to make specific decisions. the information should be analyzed to present the valuable information to the investors so that in this paper, the relative content and return additive with cash recovery have been a...

OBJECTIVES This article presents five-year relative survival rates for prostate, breast, colorectal and lung cancer diagnosed in 1992. Provincial variations are also examined. DATA SOURCES Data are from the Canadian Cancer Registry, the National Cancer Incidence Reporting System, the Canadian Mortality Data Base, and life tables. ANALYTICAL TECHNIQUES Analysis was conducted using the maximu...

biological and demographic parameters of the mealybug ladybird, cryptolaemus montrouzieri (mulsant) were evaluated on citrus mealybug, planococcus citri (risso) and obscure mealybug, pseudococcus viburni (signoret) under 24 ± 2 ºc, 80 ± 5% relative humidity and a photoperiod of 16:8 (l: d) h. the mealybugs had a significant effect on developmental time and reproductive and demographic parameter...