The boundaries of quantum materials can host a variety exotic effects such as topologically robust edge states or anyonic quasiparticles. Here, we show that fermionic systems graphene admit low energy Dirac description exhibit counterintuitive relativistic at their boundaries. As an example, consider carbon nanotubes and demonstrate bulk spinor have non zero charge density on the boundaries, in...

Let H be a graph. If G is an n-vertex simple graph that does not contain H as a minor, what is the maximum number of edges that G can have? This is at most linear in n, but the exact expression is known only for very few graphs H . For instance, when H is a complete graph Kt, the “natural” conjecture, (t− 2)n− 12(t− 1)(t− 2), is true only for t ≤ 7 and wildly false for large t, and this has rat...

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...

Edges of an image are considered a crucial type of information. These can be extracted by applying edge detectors with different methodology. Edge detection is a vital step in computer vision tasks, because it is an essential issue for pattern recognition and visual interpretation. In this paper, we propose a new method for edge detection in images, based on the estimation by kernel of the prob...

We hypothesized that edge density more strongly influences species abundances in more productive environments. To test this hypothesis we collected songbird point count data across broad biophysical gradients and gradients in forest patch edge density in thewest and east slopes of the CascadeMountains of Oregon and Washington, U.S.A., which differ in ecological productivity. We then analyzed bi...

This paper gives new constructions of k-chromatic critical graphs with high minimum degree and high edge density, and of vertex-critical graphs with high edge density. c © 2002 Elsevier Science B.V. All rights reserved.