Curves in homogeneous spaces and their contact with 1-dimensional orbits

Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with alpha. In this paper, we give various important properties of the sequence of subspaces G superset of S(1)(alpha) superset of S(2)(alpha) superset of S(3)(alpha) superset of ... In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with alpha.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

In-hospital and 1-year mortality in patients undergoing early surgery for prosthetic valve endocarditis.

IMPORTANCE: There are limited prospective, controlled data evaluating survival in patients receiving early surgery vs medical therapy for prosthetic valve endocarditis (PVE). OBJECTIVE: To determine the in-hospital and 1-year mortality in patients with PVE who undergo valve replacement during index hospitalization compared with patients who receive medical therapy alone, after controlling for survival and treatment selection bias. DESIGN, SETTING, AND PARTICIPANTS: Participants were enrolled between June 2000 and December 2006 in the International Collaboration on Endocarditis-Prospective Cohort Study (ICE-PCS), a prospective, multinational, observational cohort of patients with infective endocarditis. Patients hospitalized with definite right- or left-sided PVE were included in the analysis. We evaluated the effect of treatment assignment on mortality, after adjusting for biases using a Cox proportional hazards model that included inverse probability of treatment weighting and surgery as a time-dependent covariate. The cohort was stratified by probability (propensity) for surgery, and outcomes were compared between the treatment groups within each stratum. INTERVENTIONS: Valve replacement during index hospitalization (early surgery) vs medical therapy. MAIN OUTCOMES AND MEASURES: In-hospital and 1-year mortality. RESULTS: Of the 1025 patients with PVE, 490 patients (47.8%) underwent early surgery and 535 individuals (52.2%) received medical therapy alone. Compared with medical therapy, early surgery was associated with lower in-hospital mortality in the unadjusted analysis and after controlling for treatment selection bias (in-hospital mortality: hazard ratio [HR], 0.44 [95% CI, 0.38-0.52] and lower 1-year mortality: HR, 0.57 [95% CI, 0.49-0.67]). The lower mortality associated with surgery did not persist after adjustment for survivor bias (in-hospital mortality: HR, 0.90 [95% CI, 0.76-1.07] and 1-year mortality: HR, 1.04 [95% CI, 0.89-1.23]). Subgroup analysis indicated a lower in-hospital mortality with early surgery in the highest surgical propensity quintile (21.2% vs 37.5%; P = .03). At 1-year follow-up, the reduced mortality with surgery was observed in the fourth (24.8% vs 42.9%; P = .007) and fifth (27.9% vs 50.0%; P = .007) quintiles of surgical propensity. CONCLUSIONS AND RELEVANCE: Prosthetic valve endocarditis remains associated with a high 1-year mortality rate. After adjustment for differences in clinical characteristics and survival bias, early valve replacement was not associated with lower mortality compared with medical therapy in the overall cohort. Further studies are needed to define the effect and timing of surgery in patients with PVE who have indications for surgery.

Parameter estimation using a particle method: inferring mixing coefficients from sea level observations

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

Parameter spaces of environmental fields responsible for cyclone development from tropics to extratropics

Objective cyclone tracking applied to a 30-yr reanalysis dataset shows that cyclone development in the summer and autumn seasons is active in the tropics and extratropics and inactive in the subtropics. To understand this geographically bimodal distribution of cyclone development associated with tropical and extratropical cyclones quantitatively, the direct relationship between cyclone types and their environments are assessed by using a parameter space of environmental variables [environmental parameter space (EPS)]. The number of cyclones is analyzed in terms of two different factors: the environmental conditions favorable for cyclone development and the area size that satisfies the favorable condition. The EPS analysis is mainly conducted for two representative environmental parameters that are commonly used for cyclone analysis: potential intensity for tropical cyclones and baroclinicity for extratropical cyclones. The geographically bimodal distribution is attributed to the high sensitivity of the cyclone development to the change in the environmental fields from tropics to extratropics. In addition, the bimodal distribution is partly attributed to the rapid change in the environmental fields from tropics to extratropics. The EPS analysis also shows that other environmental parameters, including relative humidity and vertical velocity, may enhance the contrast between the tropics (extratropics) and subtropics, whereas they are not essential for determining cyclone types. The relationship between cyclones and their environments is found to be similar between the hemispheres in the EPS, although the geographical distribution, particularly the longitudinal uniformity, is markedly different between the hemispheres.

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Length and caliber of the rectosigmoid colon among patients with Chagas disease and controls from areas at different altitudes

Introduction In this study, we investigated radiological changes in the sigmoid colon in chagasic patients by comparing their colon lengths and caliber with those of non-chagasic living in the same region and non-chagasic living at high altitudes. Methods A total of 317 individuals were evaluated using clinical, serological and radiological methods and divided into three groups: 1) one hundred and nine non-chagasic individuals from Uberaba, Brazil; 2) sixty-one non-chagasic from Puno, Peru; 3) one hundred forty-seven chagasics examined in Uberaba, being 62 without megacolon (3A), 72 with megacolon (3B) and 13 with doubtful diagnosis of megacolon (3C). Results In group 2, the sigmoid colon had a significantly larger caliber (p=0.001) and the rectosigmoid colon was longer (p<0.001) than group 1. In subgroup 3A, the sigmoid colon (p<0.001) and rectum (p<0.001) had a significantly larger caliber and the rectosigmoid was longer (p<0.001) than that of the non-chagasic individuals. In subgroup 3B, the rectosigmoid was longer in all patients, and the caliber of the sigmoid was significantly larger than that of subjects in subgroups 3A and 3C (p<0.001). Conclusions Morphometric analysis confirms that Chagas disease may increase the caliber and length of the rectosigmoid. Our results suggest that altitude, ethnicity and diet may have influenced the size and length of the rectosigmoid of andean patients.

An Autoregressive Spectral Density Estimator at Frequency Zero for Nonstationarity Tests.

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero at some process. Kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression are commonly used. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. in this paper, we first show that this least squares bias induces a significant increase in the bias and mean-squared error of kernel-based estimators.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Coincidence properties for maps from the torus to the Klein bottle

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Campos de Killing, curvatura média e translações

D. Hoffman, R. Osserman e R. Schoen mostraram que se a aplicação de Gauss de uma superfície orientada completa de curvatura média constante M imersa em R³ está contida em um hemisfério fechado de S² (equivalentemente, a função não muda de sinal em M, onde n é um vetor unitário normal de M e v algum vetor não nulo de R³), então M é invariante por um subgrupo a um parâmetro de translações de R³ (aquele determinado por v). Neste trabalho obtemos uma extensão deste resultado para o caso em que o espaço ambiente é uma variedade riemanniana e M uma hipersuperfície em N requerendo que a função não mude de sinal em M, onde V é um campo de Killing em N. Na parte final deste trabalho consideramos uma variedade riemanniana Killing paralelizável N para definir uma translação Y: M -> Rn de uma hipersuperfície M de N que é uma extensão natural da aplicação de Gauss de uma hipersuperfície de Rn. Considerando as mesmas hipóteses para a imagem de y obtemos uma extensão do resultado original de Hoffman-Osserman-Schoen.

Effect of delayed start of light-curing on microtensile bond strengths of two adhesives bonded to dentin

The aim of the present study was to evaluate the microtensile bond strength to dentin (ATBS) of two total-etching adhesives applied with delays of 1-30 s for curing. Fifty extracted molar teeth were used. Occlusal enamel was sectioned to expose flat dentin surface, which was further polished with 600-grit paper for smear layer standardization. The specimens were divided into two groups, G1: Single Bond total-etching adhesive (SB), and G2: Prime & Bond NT total-etching adhesive (PB). Each group was further divided into 5 subgroups according to the delayed light-cure initiation after the adhesive systems application (n=5): Subgroup 1s - 1 s; Subgroup 5s -5 s; Subgroup 10s - 10 s; Subgroup 20s - 20 s; Subgroup 30s - 30 s. Composite resin cones 5 mm height and 10 mm in diameter were fabricated. Specimens were stored in distilled water at 37 degrees C for 24 h and sectioned to obtain 1 x 1 mm(2) transversal specimens. Specimens were thermocycled and mu TBS was measured. Data were submitted to two-way ANOVA (AdhesiveXDelay time) and Tukey's test. The level of significance was set at 5%. The results in mean MPa(+/- SD) for interaction between adhesive and delay time were: PB/1s - 23.82 +/- 2.54a; SB/5s - 19.52 +/- 2.67b; PB/5s - 18.56 +/- 3.06bc; SB/1s - 15.49 +/- 2.69cd; SB/20s - 16.33 +/- 2.55d; SB/10s - 13.88 +/- 1.67d; PB/10s - 11.04 +/- 1.28e; PB/30s - 10.89 +/- 1.31e; PB/20s - 10.24 +/- 2.33e; SB/30s - 9.19 +/- 1.91e. It was concluded that light-cure initiation timing of total-etching adhesives interferes negatively with mu TBS to dentin. (C) 2014 Elsevier Ltd. All rights reserved.

Double point curves for corank 2 map germs from C-2 to C-3

We characterize finite determinacy of map germs f : (C-2, 0) -> (C-3, 0) in terms of the Milnor number mu(D(f)) of the double point curve D(f) in (C-2, 0) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f(t) : (C-2, 0) -> (C-3, 0) is equivalent to the constancy of both mu(D(f(t))) and mu(f(t)(C-2)boolean AND H) with respect to t, where H subset of C-3 is a generic plane. (C) 2011 Elsevier B.V. All rights reserved.