Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

Changes in Complete Blood Count in Patients With Surgically Treated Facial Fractures

The purpose of this prospective study was to verify the changes in the preoperative and postoperative complete blood counts of patients with surgically treated facial fractures. Fifty consecutive patients with a mean age of 34 years who presented facial fractures and underwent surgical treatment were included. A complete blood count was performed, comprising the red and white blood cell count (cells/mu L), hemoglobin (g/dL), and hematocrit (%) levels. These data were obtained preoperatively and postoperatively during a 6-week period. Statistical analyses were performed using the Kruskal-Wallis and Mann-Whitney tests to identify the possible differences among the groups and among the periods of observation using the Friedman and Wilcoxon matched-pairs signed-ranks tests. The most common location of the fractures was the mandible (42.3%), followed by the zygomatic-orbital (36.5%) and associated locations (21.2%). Leukocytosis was associated with neutrophilia in the immediate postoperative period in all of the groups. There were no values below the reference limits of the values of hemoglobin, hematocrit, and erythrocytes, and no values above the reference limits for the remaining white blood cells, although significant differences among periods were observed in most cells, depending on the type of fracture. The primary findings were leukocytosis associated with neutrophilia, verified in the immediate postoperative period in all of the groups, and the influence of the type of fracture on the significant alterations observed among studied periods on the values of hemoglobin, hematocrit, erythrocytes, leukocytes, neutrophils, and lymphocytes.

Pretherapeutic Expression of the hOCT1 Gene Predicts a Complete Molecular Response to Imatinib Mesylate in Chronic-Phase Chronic Myeloid Leukemia

In this retrospective study we evaluated the pretherapeutic mRNA expression of the hOCT1 (human organic cation transporter 1) gene in patients with chronic-phase (CP) chronic myeloid leukemia (CML) who varied in terms of their response to imatinib (IM). hOCT1 mRNA was quantified by real-time PCR. Patients were classified as expressing either high (n = 44) or low hOCT1 mRNA (n = 44). The complete cytogenetic response rates observed at 6, 12 and 18 months were 47.7, 84.1 and 91%, respectively, in patients with high hOCT1 mRNA and 47.5, 81.8 and 86.3%, respectively, in patients with low hOCT1 transcripts. The major molecular response rates were not significantly different between patients with high and low hOCT1 mRNA after 6 months of therapy (22.7 vs. 9.1%; p = 0.07), but they were significantly different after 12 months (54.5 vs. 31.8%; p = 0.026) and 18 months (77.2 vs. 56.8%; p = 0.034). Complete molecular responses were observed in 5 patients with low and 17 patients with high hOCT1 mRNA (p = 0.003). The 5-year event-free and overall survival analyses revealed no significant differences between the groups. These data imply that knowledge of the pretherapeutic level of hOCT1 could be a useful marker to predict IM therapy outcome in treatment-naive CP CML patients. Copyright (C) 2012 S. Karger AG, Basel

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

Complete Sequence of Broad-Host-Range Plasmid pRIO-5 Harboring the Extended-Spectrum-beta-Lactamase Gene bla(BES-1)

Broad-host-range plasmid pRIO-5, harboring the extended-spectrum beta-lactamase bla(BES-1) gene in Serratia marcescens, was fully sequenced. Analysis of the 12,957-bp sequence of this IncP6-type plasmid revealed that the bla(BES-1) gene was associated with two copies of the insertion sequence IS26. The promoter responsible for the bla(BES-1) expression was hybrid, made of a - 35 box located inside the inverted repeat of IS26 and a - 10 box inside a remnant of an insertion sequence.

Evaluation of Complete Denture Quality and Masticatory Efficiency in Denture Wearers

Purpose: This study aimed to investigate (1) the influence of complete denture quality and years of denture use on masticatory efficiency and (2) the relationship between complete denture quality and years of use. Materials and Methods: A cross-sectional study was conducted with 93 edentulous patients (mean age: 65.6 years) wearing both mandibular and maxillary dentures. Patients were classified into two categories according to years of denture use: <= 2 years and >= 5 years. Masticatory efficiency was evaluated via the colorimetric method with beads as the artificial test food. A reproducible method for objective evaluation of the technical quality of complete dentures was employed. The association between denture quality and years of denture use was analyzed using chi-square and Fisher exact tests. The results of masticatory efficiency testing were analyzed using two-way analysis of variance (with the Tukey post hoc test) in terms of years of denture use <= 2 years, >= 5 years) and denture quality (poor, average, good). Results: A significant relationship was found between denture quality and years of denture use (P < .05). Masticatory efficiency differed significantly (P < .05) between patients with <= 2 years of denture use (0.101 +/- 0.076 absorbance) and >= 5 years of use (0.068 +/- 0.076 absorbance). Masticatory efficiency was not influenced by denture quality. Conclusions: Complete denture quality and masticatory efficiency significantly decreased over time. However, complete denture quality did not influence masticatory efficiency. Int J Prosthodont 2012;25:625-630.

Complete denture wear during sleep in elderly sleep apnea patients-a preliminary study

There is no consensus in the literature about the impact of complete denture wear on obstructive sleep apnea (OSA). The goal of this randomized clinical study was to assess if complete denture wear during sleep interferes with the quality of sleep. Elderly edentulous OSA patients from a complete denture clinic were enrolled and received new complete dentures. An objective sleep analysis was determined with polysomnography performed at the sleep laboratory for all patients who slept either with or without their dentures. Twenty-three patients (74% females) completed the study with a mean age of 69.6 years and a mean body mass index of 26.7 kg/m(2). The apnea and hypopnea index (AHI) was significantly higher when patients slept with dentures compared to without (25.9 +/- 14.8/h vs. 19.9 +/- 10.2/h; p > 0.005). In the mild OSA group, the AHI was significantly higher when patients slept with the dentures (16.6 +/- 6.9 vs. 8.9 +/- 2.4; p < 0.05), while in moderate to severe OSA patients, the AHI was not significantly different when sleeping with dentures (.30.8 +/- 15.6 vs. 25.7 +/- 7.5; p = 0.2). The supine AHI in mild patients was related to a higher increase in AHI while wearing dentures (12.7 +/- 8.4/h vs. 51.9 +/- 28.6/h; p < 0.001). A limitation of the study is that the mild OSA patients had a higher BMI when compared to the moderate to severe OSA patients. Ten out of 14 patients who preferred to sleep with their upper and lower dentures showed an increase in their AHI while wearing dentures to sleep. Contrary to previous studies, we found that OSA patients may experience more apneic events if they sleep with their dentures in place. Specifically, in mild OSAS patients, the use of dentures substantially increases the AHI especially when in the supine position.

A cross-over randomised clinical trial of eccentric occlusion in complete dentures

The objective of this study is to compare the effects of canine guidance (CG) and bilateral balanced occlusion (BBO) on denture satisfaction and kinesiographic parameters of complete denture wearers, by means of a cross-over trial. Fifty edentulous patients received new maxillary and mandibular complete dentures. After the intra-oral adjustments and adaptation period, 44 participants were enrolled in the trial and randomly received a sequence of occlusal schemes: BBO followed by CG, or CG followed by BBO. Outcomes were assessed after 30 days of each occlusal scheme. Participants answered a denture satisfaction questionnaire and a kinesiograph instrument recorded mandibular physiologic movements and pattern of maxillary denture movement during chewing. Wilcoxon test and paired sample t-test were used to compare satisfaction levels and kinesiographic data for each occlusal scheme, respectively (a = 0.05). The results showed no differences between occlusal schemes on participants satisfaction and in any of the kinesiographic parameters studied, except for the vertical intrusion of the maxillary complete denture during chewing, which was lower with CG. It can be concluded that the occlusal scheme did not influence on satisfaction and kinesiographic parameters evaluated, as long as volume and resilience of residual edentulous ridges of the participants were normal. Clinical Trial Registration Identifier: NC.T01420536.

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' threshold theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Restoration of the rabbit corneal surface after total epithelial debridement and complete limbal excision

How is the corneal epithelium restored when all of it plus the limbus have been eliminated? This investigation explored the possibility that this may be achieved through the conjunctival epithelium. The corneal epithelium of the right eye of 12 rabbits (Oryctolagus cuniculus) was totally scraped followed by surgical excision of the limbus plus 1.0-1.5 mm of the adjacent conjunctiva. Antibiotics and corticosteroids were applied for 1 week after surgery. Histological and immunohistochemical techniques were used to monitor the events taking place on the eye surface 2 weeks and 1, 3 and 6 months thereafter. Initially, the corneal surface was covered by conjunctival-like epithelium. After 1 month and more prominently at 3 and 6 months an epithelium displaying the morphological features of the cornea and reacting with the AE5 antibody was covering the central region. It is likely that the corneal epithelium originated from undifferentiated cells of the conjunctiva interacting with the corneal stroma.

BIOCIVILIZACAO: OVERVIEW AND BACKGROUND TO COMPLETE OUR independence

Latin American countries have a privileged position to tackle the environmental crisis, producing a new framework of relations and interdependencies: a biocivilizacao. Inspired by the ideas and Gourou Sachs, founded in centralities other than those of the "global market", and fed by other "sources" than those of high-carbon, embodied in examples like those provided by the Amazons, that teach us how the interaction between cultural and natural elements can produce the main source of biodiversity on the planet and your invaluable environmental service. Countries that share, if you can settle in other conditions (have) dependencies, guided references and values different from those that have chaired the hegemonic order. But for that, the paths that lead only to "cooperate" with the construction of "common markets", which will be replaced by others, eg, dialogues between the Organization of the Amazon Cooperation Treaty and Pan Amazonian Social Forum.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.