This paper is devoted to the fast and exact diameter computation in graphs with n vertices and m edges, if the diameter is a large fraction of n. We give an optimal O(m+n) time algorithm for diameters above n/2. The problem changes its structure at diameter value n/2, as large cycles may be present. We propose a randomized O(m + n logn) time algorithm for diameters above (1/3 + )n for constant ...

We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d ≥ 4 and n sufficiently large, depending on d. As a corollary we determine the exact maximum number of unit distances for all even d ≥ 6, and the exact maximum number of diameters for all d ≥ 4, for all n suffi...

Numerical solutions of the.fourth-moment differential equation are obtained for a finite, initially Gaussian beam propagating in a. two-dimensional homogeneous and isotropic random medium with a Gaussian correlation function. In addition to the covariance of the intensity fluctuations, the full spatial dependence of the fourth moment of the propagating field is described for several beam diamet...

Nearly monodisperse iron nanoclusters have been used to define the diameters of carbon nanotubes grown by chemical vapor deposition (CVD). Iron nanoparticles with average diameters of 3, 9, and 13 nm were used to grow carbon nanotubes with average diameters of 3, 7, and 12 nm, respectively. Transmission electron microscopy studies of the nanotubes show that the as-grown nanotubes are single-wal...

In this paper circuit implementations of cellular processor arrays intended for image processing applications are discussed. It is demonstrated that a departure form the standard CNN model can lead to a significant improvement when processing binary (black/white) images. An asynchronous cellular logic array circuit is presented, which is capable of simulating trigger-waves in an excitable mediu...

background: the aim of this in vitro study was to evaluate the effect of shape, diameter and length of implants on their primary stability based on resonance frequency analysis. materials and methods: replace select tapered and branemark mk iii implants were selected. each of these two selected groups was divided into nine subgroups based on the implant length (il) (short, medium and long) and ...

by determining normal ranges of spinal canal diameters we can make early diagnosis in persons who have lower diameters of spinal canal. these persons are predisposed to spinal canal stenosis that is a major cause of spinal radiculopathies. in different studies performed in several countries, minimum and maximum ranges of spinal canal diameters were different for each population. in this study, ...