2,147 research outputs found

    Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

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    We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

    Transverse maxillary deficiency in Class II and Class III malocclusions: a cephalometric and morphometric study on postero-anterior films

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71585/1/j.1601-6343.2004.00312.x.pd

    Tensor vastus intermedius: a review of its discovery, morphology and clinical importance

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    Background: This review aims to summarise the relevant literature surrounding the tensor vastus intermedius, a newly discovered muscle, and to discuss its morphology and potential clinical importance. No such review currently exists in the literature. Materials and methods: A comprehensive literature search regarding the tensor vastus intermedius was performed using PubMed and Google Scholar in July 2020. Principles of Evidence-Based Anatomy and the Anatomical Quality Assessment Tool were employed to ensure a high-level review. All relevant papers were included and citation tracking was performed to uncover further publications. Results: The tensor vastus intermedius is found in the anterior compartment of the thigh and has a similar morphology to the other vasti muscles. It has four main variations and a consistent neurovascular supply. The muscle has been implicated in a number of case reports and surgical procedures, which are described in detail in this paper. Conclusions: In the four years since the tensor vastus intermedius was formally described, a significant amount of work has been done to help us understand its structure and function. Further efforts are needed to gain a full picture as to its clinical importance. As such, it is recommended that this muscle should be acknowledged in anatomical education

    Treatment and posttreatment skeletal effects of rapid maxillary expansion studied with low-dose computed tomography in growing subjects

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    Introduction: The aim of this study was to apply low-dose computed tomography (CT) to evaluate treatment and posttreatment effects produced by rapid maxillary expansion (RME) at the levels of the midpalatal suture and the pterygoid processes. Methods: A sample of 17 subjects (7 boys, 10 girls; mean age, 11.2 years) was analyzed. Multi-slice CT scans were taken before RME, at the end of the active expansion phase, and after a retention period of 6 months. Statistical analysis was performed with ANOVA for repeated measures with post-hoc tests. Results: The amounts of opening of the midpalatal suture during the active phase of expansion were 3.01, 2.17, and 1.15 mm for the anterior, middle, and posterior suture widths, respectively. Pterygoid width also showed a statistically significant increase (1.49 mm). In the postretention period, all transverse measurements had significant decreases except for pterygoid width. Conclusions: At the end of the retention phase after RME therapy, the transverse width of the midpalatal suture was similar to the pretreatment width, whereas the width between the pterygoid processes was significantly increased
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