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

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. analytical solution the problem unachievable with famous Chandrasekhar–Von-Neumann results up to present time. alternative methods are connected modeling a real ion field by approximate models. One most accurate theories ions in plasmas Frequency Fluctuation Model (FFM) tested comparison microfield n...

We isolated and characterized 33 novel, polymorphic microsatellite loci from the social sponge-dwelling snapping shrimp Zuzalpheus brooksi. We screened all 33 loci in approximately 31 individuals from a population of Z. brooksi from the Florida Keys, USA and found an average of 16 alleles per locus. Approximately 25% of the loci showed more than two bands per individual, suggesting evidence of ...

The effect of an additional chromosome 6 upon recombination in chromosome 9 was investigated in maize. Trisomic 6 plants and their disomic sibs, heterozygous for three loci of chromosome 9 (yg, sh and wx), were testcrossed, and recombination in the regions yg-sh and sh-wx was analyzed. Single exchanges in the sh-wx region and double exchanges were more frequent in trisomics, particularly in fem...

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, ...

Although many mathematics-based and heuristic approaches have been recently developed on optimally allocation of TCSCs for lines overloads reduction and buses voltage stability enhancement during fault conditions, the works on the TCSCs efficiency to achieve the abovementioned goals are rare. This idea that TCSCs can surely enhance the system’s security must be comprehensively investigated. In ...