Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

LHC discovery potential for supersymmetry with root s=7 TeV and 5-30 fb(-1)

We extend our earlier results delineating the supersymmetry reach of the CERN Large Hadron Collider operating at a center-of-mass energy root s = 7 TeV to integrated luminosities in the range 5-30 fb(-1). Our results are presented within the paradigm minimal supergravity model or constrained minimal supersymmetric standard model. Using a six-dimensional grid of cuts for the optimization of signal to background ratio-including missing E-T-we find for m((g) over tilde) similar to m((q) over tilde) an LHC 5 sigma supersymmetry discovery reach of m((g) over tilde) similar to 1:3, 1.4, 1.5, and 1.6 TeV for 5, 10, 20, and 30 fb(-1), respectively. For m((q) over tilde) >> m((g) over tilde), the corresponding reach is instead m((g) over tilde) similar to 0: 8, 0.9, 1.0, and 1.05 TeV, for the same integrated luminosities.

Influence of anatomical barriers on maxillary incisor root resorption after orthodontic treatment with premolar extractions

INTRODUCTION: Apical root resorption is a frequent and occasionally critical problem in orthodontic patients undergoing induced tooth movement. One of the factors that might influence prognosis, especially in maxillary incisors, which most frequently present resorptions, are the so-called the anatomical barriers; that is, proximity of the buccal and palatal cortical bones to the maxillary incisor roots. OBJECTIVE: The purpose of this research was to investigate whether patients with excessive vertical growth really present a small distance between the alveolar cortical bones and the maxillary incisor roots, and whether there is a correlation between this distance and the root resorption index in comparison with patients presenting horizontal growth. METHODS: The sample comprised orthodontic records of 18 patients with extraction planning of first maxillary premolars and treatment by the standard and/or preadjusted edgewise brackets. Their initial and final periapical radiographs were evaluated to determine the amount of root resorption that occurred. RESULTS: On the palatal side, patients with excessive vertical growth (Group 2 - SN-GoGn > 43º) showed a narrower alveolar bone than the horizontal growth patients (Group 1 - SN-GoGn < 29º). However, the distance between the buccal cortical bone and the central incisor root apex showed no significant difference between Groups 1 and 2; CONCLUSIONS: It was concluded that there are no correlations between the proximity of buccal cortical bone, maxillary incisor roots and the root resorption index.