We study the Minkowski length L(P ) of a lattice polytope P , which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P . The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P , and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a...

A total of 78 orthodontic patients participated in a study of the degree of decalcification inhibition induced by daily treatment with 0.4% SnF2 gel. Control patients (n = 39) were managed exactly as were the test patients (n = 39) except that the latter were instructed to brush at bedtime each day with the gel. In the nongel users, 24 (64.1%) developed decalcification after 18-24 months bandin...

abstract to evaluate the effect of sowing date and weed interference on growth indices of red bean cultivars with different growth habit, a field experiment was carried out during the spring 2009 at university of zanjan as a factorial split plot on the basis of randomized complete block design, with three replications. main plots included factorial of three red bean cultivars (derakhshan (stand...

chickpea (cicer arietinum) is the third most important pulse crop in the world, grown widely across asia and the middle east. weed is one of the main limiting factors in chickpea (cicer arietinum) production. several characteristics of chickpea (cicer arietinum), such as slow plant emergence, short plant height, and chickpea morphology allow weeds to compete effectively. to investigate the effe...

In all, 182 and 220 replies were received from patients in group A and B, respectively. Early complications included haematoma in five (2%) and two (0.9%) patients, respectively, and wound infection in 24 (13%) and 17 (7.7%). Eight patients who had scrotal pain even before vasectomy were excluded from the analysis (two in group A and six in group B). In group A, 25 of 180 (13.8%) had a new onse...

Objective: Field experiment was conducted in 2009 to investigate the effects of plant density and weed interference on morphological characteristics and yield of corn (Zea Mays, L.) at Research Station of University of Tabriz, Tabriz, Iran. Methods: The experiment was arranged as split plot based on randomized complete block design with three replications. Plant density (D1, D2, D3 and D4: 5, 7...

Objective: Field experiment was conducted in 2009 to investigate the effects of plant density and weed interference on morphological characteristics and yield of corn (Zea Mays, L.) at Research Station of University of Tabriz, Tabriz, Iran. Methods: The experiment was arranged as split plot based on randomized complete block design with three replications. Plant density (D1, D2, D3 and D4: 5, 7...

We investigate the structure of the Minkowski sum of standard simplices in R. In particular, we investigate the one-dimensional structure, the vertices, their degrees and the edges in the Minkowski sum polytope. 2000 MSC: 52B05, 52B11, 05C07.