For a rooted graph G, let EVb(G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We determine the expected value of EVb(G; p) for random trees, and include a connection to unrooted trees. We also consider rooted digraphs, computing the expected value of a random orientation of a rooted graph G in terms of E...

For a rooted graph G, let EV (G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We examine combinatorial properties of this polynomial, proving that G is k-edge connected iff EV ′(G; 1) = · · · = EV k−1(G; 1) = 0. We find bounds on the first and second derivatives of EV (G; p); applications yield character...

OBJECTIVE The objective of this study was to compare the smear layer formed on root canal walls during canal preparation of extracted human teeth by Twisted, Mtwo, and ProTaper rotary nickel titanium instruments. MATERIALS AND METHODS Sixty single rooted human premolar teeth with root curvature <25(0) were selected and randomly divided into three Groups (n= 20 teeth per Group). Three types of...

Background: The most commonly impacted teeth are the third molars, maxillary canines, maxillary central incisors and premolars. Impacted premolars may lead to aesthetic concerns, masticatory inefficiency and oral hygiene difficulties as well as follicle pathology and destruction of adjacent structures, including neighboring teeth, the purpose of this study to shade light on the prevalence of im...

the vast majority of mandibular second molars have two roots with three root canals; however, variations in molar root canal anatomy are not uncommon. to the best of our knowledge, four rooted mandibular second molar with three mesial roots and one distal root has never been reported. herein, we present the endodontic management of a four rooted mandibular second molar tooth, diagnosed with the...

introduction : this in vitro study was designed to measure and compare the amount of temperature rise in the pulp chamber of the teeth exposed to different light curing units (lcu), which are being used for curing composite restorations. methods: the study was performed in two settings; first, an in vitro and second was mimicking an in vivo situation. in the first setup of the study, three grou...