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 ...

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...

Field Ion Microscopy (FIM) and Scanning Tunneling Microscopy (STM) have found a wide application in nanotechnology. These microscopes use a metallic nanotip for image acquisition. Resolution of FIM and STM images depends largely on the radius of nanotip apex; the smaller the radius the higher the resolution. In this research, for tungsten nanotip fabrication, electrochemical etching of tungsten...

during endodontic treatment, clinicians may face endodontic procedural mishaps such as broken instruments, which is a complex situation especially when the file breaks beyond the apex. this condition is associated with potential risk of contamination, which compromises the healing process. management of a broken instrument beyond the apex is difficult and time consuming and requires creativity ...

PURPOSE Recent work has shown the safety and efficacy of halo-gravity traction as an operative adjunct. However, there are no reports specifically looking at halo-gravity traction in patients with skeletal dysplasia. Our purpose was to assess the safety and efficacy of traction in children with skeletal dysplasia who present with severe kyphoscoliosis. METHODS We retrospectively reviewed eigh...

Highly ionic beams of several hundred μA per cm 2 have been measured from porous glass ionic liquid electrospray sources fabricated using a conventional mill. The thrust output from three prototype devices, two emitting the ionic liquid EMI-Im and one emitting EMI-BF 4, was measured directly using a precise balance. Thrusts up to 50 μN were measured when emitting EMI-Im in a bipolar, alternatin...

The spreading of the water droplets falling on surfaces with a contact angle from 0 to 160° was investigated in this work. Superhydrophilicity surface is achieved by laser treatment, and hydrophobization then applying fluoropolymer coating different thicknesses. chosen approach makes it possible obtain wettability, but same morphology. parameter t* corresponding time when capillary wave reaches...

(2) The angle made by the blade with the surface of the globe, i.e., the degree of obliquity of the incision. From the same external site an incision perpendicular to the scleral surface may penetrate the ciliary body, whereas a slanting incision parallel to the iris surface would enter the anterior chamber (Swan, 1959). Much controversy still exists concerning some of the external landmarks of...