Field emission tips with an apex radius of curvature below 100 nm are not adequately described by the standard theoretical models based on Fowler–Nordheim and Murphy–Good formalisms. This is due to breakdown “constant electric field” assumption within tunneling region leading substantial errors in current predictions. A uniformly applicable curvature-corrected field theory requires that potenti...

Aa apex graph is a graph which has a vertex whose removal makes the resulting graph planar. Embeddings of apex graphs having face-width three are characterized. Surprisingly, there are such embeddings of arbitrarily large genus. This solves a problem of Robertson and Vitray. We also give an elementary proof of a result of Robertson, Seymour, and Thomas 5] that any embedding of an apex graph in ...

Labium is a primitive transantarctic genus which parasitizes ground-nesting halictid bees and until now has been known only from the Australian Region. Diagnostic features include its large exposed labrum (as long as clypeus) ; elongate mandible with upper tooth much shorter and smaller than lower tooth; slender 1st gastric tergite with spiracle distad of middle; and short, concealed ovipositor...

The generation of highly collimated electron beams from a double-gate field emitter array with 40000 metallic tips and large collimation gate apertures is reported. Field emission beam measurements demonstrated the reduction of the beam envelope down to the array size by applying a negative potential to the on-chip gate electrode for the collimation of individual field emission beamlets. Owing ...

OBJECTIVE Vaginal apex pain is a subset of chronic pelvic pain commonly treated with surgical excision of the vaginal apex. Our objective was to estimate long-term postoperative pain levels, recovery time, and return to sexual function in women who have undergone vaginal apex repair for chronic vaginal apex pain. METHODS Since 1995, 45 women have undergone vaginal apex repair at our instituti...

If G is a connected graph, then HA(G) = ∑ u6=v(deg(u) + deg(v))/d(u, v) is the additively Harary index and HM (G) = ∑ u6=v deg(u) deg(v)/d(u, v) the multiplicatively Harary index of G. G is an apex tree if it contains a vertex x such that G − x is a tree and is a k-apex tree if k is the smallest integer for which there exists a k-set X ⊆ V (G) such that G − X is a tree. Upper and lower bounds o...

Introduction: The exact measurement of the root canal length is of great importance in root canal therapy. Although, determination of the root canal length through radiography is the most common method, recently electronic apex locators are being used to determine working length and decrease the number of radiographs. The purpose of this study was to compare the accuracy of an electronic apex l...

Abstract The coherent modulation of swift electron beams with strong laser fields has enabled the generation attosecond pulses, opening up new research avenues in ultrafast science. Here we study a comparatively simple alternative, production pulse trains directly at source. In our theory work, show that sub-optical-cycle bursts induced by tunneling photoemission from metal nanotip can retain te...