This paper investigates the following question: Given an integer grid , where is a proper subset of the integer plane or a proper subset of the integer 3d space, which graphs admit straight-line crossing-free drawings with vertices located at the grid points of ? We characterize the trees that can be drawn on a two dimensional c n k grid, where k and c are given integer constants, and on a two ...

Based on first-principles calculations and effective model analysis, all possible straight nodal-line phonons in symmorphic space groups are uncovered. A classification of two-band ${\textbf{k}}\cdot {\textbf{p}}$ models at an arbitrary point the nodal lines is carried out, these found to locate along high symmetry Brillouin zone. According our classification, there two types groups. The first ...

introduction: an overlooked but important part of successful root canal treatment is a straight-line access (sla). the purpose of this in vitro study was to compare the efficacy of introfile and prerace rotary instruments with gates glidden (gg) drills in gaining sla by cone-beam computed tomography (cbct). methods and materials: a total of forty five extracted mandibular first molars were sele...