We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors. In its simplest instances, this algorithm works by finding the minimal position of the two curves. We achieve this by phrasing the problem as a collection of...

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supp...

Edges are important visual features, providing many cues to the three-dimensional structure of the world. One of these cues is edge blur. Sharp edges tend to be caused by object boundaries, while blurred edges indicate shadows, surface curvature, or defocus due to relative depth. Edge blur also drives accommodation and may be implicated in the correct development of the eye's optical power. Her...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

Graphene is an ideal thin membrane substrate for creating molecule-scale devices. Here we demonstrate a scalable method for creating extremely small structures in graphene with atomic precision. It consists of inducing defect nucleation centers with energetic ions, followed by edge-selective electron recoil sputtering. As a first application, we create graphene nanopores with radii as small as ...

Edge detection is one of the most principal techniques for detecting discontinuities in the gray levels of image pixels. The Modulation Transfer Function (MTF) is one of the main criteria for assessing imaging quality and is a parameter frequently used for measuring the sharpness of an imaging system. In order to determine the MTF, it is essential to determine the best edge from the target imag...

Multiple resonances of the ELM frequency caused by application of low n (= 1 or 2) magnetic perturbations for Edge Localized Mode (ELM) control has been observed on JET. With a low n field applied, a strong increase in ELM frequency, fELM , by a factor of ∼ 4.5 was found in many separated narrow windows of q95 (resonant q95), while the fELM increased only by a factor of ∼ 2 for non-resonant q95...

Tuning the electronic structure of metal-organic frameworks is the key to extending their functionality to the photocatalytic conversion of absorbed gases. Herein we discuss how the band edge positions in zeolitic imidazolate frameworks (ZIFs) can be tuned by mixing different imidazole-based linkers within the same structure. We present the band alignment for a number of known and hypothetical ...

In this paper, the breakdown characteristic of 4H-SiC pn diode using Internal Ring(IR) termination technique is investigated. N-type 4H-SiC wafer having a 10um epilayer with a doping concentration of 5.4×10 15 /cm 3 was used to fabricate the pn diodes with one or two IRs. IR was formed by boron implantation of single energy of 360keV with 5×10 14 /cm 2 dose and activation annealing at 1700 o C ...

Let C be a uniform clutter and let I = I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C1. For arbitrary edge ideals of clutters we prove that the normality property is closed under parallelizat...