3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Birkhoffian Systems in Infinite Dimensional Manifolds

We generalize the theory of Kobayashi and Oliva (On the Birkhoff Approach to Classical Mechanics. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, 2003) to infinite dimensional Banach manifolds with a view towards applications in partial differential equations.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Effect of propolis gel on the in vitro reduction of dentin permeability

OBJECTIVE: The aim of this study was to evaluate the capacity of potassium oxalate, fluoride gel and two kinds of propolis gel to reduce the hydraulic conductance of dentin, in vitro. MATERIAL AND METHODS: The methodology used for the measurement of hydraulic conductance of dentin in the present study was based on a model proposed in literature. Thirty-six 1-mm-thick dentin discs, obtained from extracted human third molars were divided into 4 groups (n=9). The groups corresponded to the following experimental materials: GI-10% propolis gel, pH 4.1; GII-30% propolis gel; GIII-3% potassium oxalate gel, pH 4,1; and GIV-1.23% fluoride gel, pH 4.1, applied to the dentin under the following surface conditions: after 37% phosphoric acid and before 6% citric acid application. The occluding capacity of the dentin tubules was evaluated using scanning electron microscopy (SEM) at ×500, ×1,000 and ×2,000 magnifications. Data were analyzed statistically by two-way ANOVA and Tukey's test at 5% significance level. RESULTS: Groups I, II, III, IV did not differ significantly from the others in any conditions by reducing in hydraulic conductance. The active agents reduced dentin permeability; however they produced the smallest reduction in hydraulic conductance when compared to the presence of smear layer (P<0.05). The effectiveness in reducing dentin permeability did not differ significantly from 10% or 30% propolis gels. SEM micrographs revealed that dentin tubules were partially occluded after treatment with propolis. CONCLUSIONS: Under the conditions of this study, the application of 10% and 30% propolis gels did not seem to reduce the hydraulic conductance of dentin in vitro, but it showed capacity of partially obliterating the dentin tubules. Propolis is used in the treatment of different oral problems without causing significant great collateral effects, and can be a good option in the treatment of patients with dentin sensitivity.

Comparasion of two minimally invasive methods on the longevity of glass ionomer cement restorations: short-term results of a pilot study

The purpose of this study was to evaluate the clinical performance of glass ionomer cement (GIC) restorations comparing two minimally invasive methods in permanent teeth after 12 months. Fifty pregnant women (second trimester of pregnancy), mean age 22 ± 5.30 years, were treated by two previously trained operators. The treatment approaches tested were: chemomechanical method (CarisolvTM; MediTeam) and atraumatic restorative treatment (ART). A split-mouth study design was used in which the two treatments were randomly placed in 50 matched pairs of permanent teeth. The chemomechanical method (CM) was the test group and the ART was the control group. The treatments were performed in Public Health Centers. The tested restorative material was a high-strength GIC (Ketac Molar; 3M/ESPE). The restorations were placed according to the ART guidelines. Two calibrated independent examiners evaluated the restorations in accordance with ART criteria. The inter-examiner kappa was 0.97. Data were analyzed using 95% confidence interval on the binomial distribution and Fisher's exact test at 5% significance level. In a 12-month follow-up, 86% of the restorations were evaluated. In the test group (CM), 100% (CI=93.3-100%) of the restorations were considered successful. In the control group (ART) 97.6% (CI=87.4-99.9%) of the restorations were considered successful and 2.4% unsuccessful (marginal defect >0.5 mm). There was no statistically significant difference between the 12-mounth success rate for both groups (Fisher's exact test: P=0.49) and between the two operators (Fisher's exact test: P=1.00). Both minimally invasive methods, chemomechanical method and ART, showed a similar clinical performance after 12 months of follow up.

Scanning electron microscopic study of the in situ effect of salivary stimulation on erosion and abrasion in human and bovine enamel

This in situ study investigated, using scanning electron microscopy, the effect of stimulated saliva on the enamel surface of bovine and human substrates submitted to erosion followed by brushing abrasion immediately or after one hour. During 2 experimental 7-day crossover phases, 9 previously selected volunteers wore intraoral palatal devices, with 12 enamel specimens (6 human and 6 bovine). In the first phase, the volunteers immersed the device for 5 minutes in 150 ml of a cola drink, 4 times a day (8h00, 12h00, 16h00 and 20h00). Immediately after the immersions, no treatment was performed in 4 specimens (ERO), 4 other specimens were immediately brushed (0 min) using a fluoride dentifrice and the device was replaced into the mouth. After 60 min, the other 4 specimens were brushed. In the second phase, the procedures were repeated but, after the immersions, the volunteers stimulated the salivary flow rate by chewing a sugar-free gum for 30 min. Enamel superficial alterations of all specimens were then evaluated using a scanning electron microscope. Enamel prism core dissolution was seen on the surfaces submitted to erosion, while on those submitted to erosion and to abrasion (both at 0 and 60 min) a more homogeneous enamel surface was observed, probably due to the removal of the altered superficial prism layer. For all the other variables - enamel substrate and salivary stimulation -, the microscopic pattern of the enamel specimens was similar.

The influence of residual salivary fluoride from dentifrice on enamel erosion: an in situ study

The objective of this study was to assess the salivary residual effect of fluoride dentifrice on human enamel subjected to an erosive challenge. This crossover in situ study was performed in two phases (A and B), involving ten volunteers. In each phase, they wore acrylic palatal appliances, each containing 3 human enamel blocks, during 7 days. The blocks were subjected to erosion by immersion of the appliances in a cola drink for 5 minutes, 4 times a day. Dentifrice was used to brush the volunteers’ teeth, 4 times a day, during 1 minute, before the appliance was replaced into the mouth. In phases A and B the dentifrices used had the same formulation, except for the absence (PD) or presence (FD) of fluoride, respectively. Enamel alterations were determined using profilometry, microhardness (%SMHC), acid- and alkali-soluble F analysis. The data were tested using ANOVA (p < 0.05). The concentrations (mean ± SD) of alkali- and acid-soluble F (µgF/cm²) were, respectively, PD: 1.27ª ± 0.70/2.24A ± 0.36 and FD: 1.49ª ± 0.44/2.24A ± 0.67 (p > 0.05). The mean wear values (± SD, µm) were PD: 3.63ª ± 1.54 and FD: 3.54ª ± 0.90 (p > 0.05). The mean %SMHC values (± SD) were PD: 89.63ª ± 4.73 and FD: 87.28ª ± 4.01 (p > 0.05). Thus, we concluded that the residual fluoride from the fluoride-containing dentifrice did not protect enamel against erosion.

Effect of cyclic load on vertical misfit of prefabricated and cast implant single abutment

OBJECTIVES: The purpose of this in vitro study was to evaluate misfit alterations at the implant/abutment interface of external and internal connection implant systems when subjected to cyclic loading. MATERIAL AND METHODS: Standard metal crowns were fabricated for 5 groups (n=10) of implant/abutment assemblies: Group 1, external hexagon implant and UCLA cast-on premachined abutment; Group 2, internal hexagon implant and premachined abutment; Group 3, internal octagon implant and prefabricated abutment; Group 4, external hexagon implant and UCLA cast-on premachined abutment; and Group 5, external hexagon implant and Ceraone abutment. For groups 1, 2, 3 and 5, the crowns were cemented on the abutments and in group 4 crowns were screwed directly on the implant. The specimens were subjected to 500,000 cycles at 19.1 Hz of frequency and non-axial load of 133 N in a MTS 810 machine. The vertical misfit (μm) at the implant/abutment interface was evaluated before (B) and after (A) application of the cyclic loading. Data were analyzed statistically by using two-away ANOVA and Tukey's post-hoc test (p<0.05). RESULTS: Before loading values showed no difference among groups 2 (4.33±3.13), 3 (4.79±3.43) and 5 (3.86±4.60); between groups 1 (12.88±6.43) and 4 (9.67±3.08), and among groups 2, 3 and 4. However, groups 1 and 4 were significantly different from groups 2, 3 and 5. After loading values of groups 1 (17.28±8.77) and 4 (17.78±10.99) were significantly different from those of groups 2 (4.83±4.50), 3 (8.07±4.31) and 5 (3.81±4.84). There was a significant increase in misfit values of groups 1, 3 and 4 after cyclic loading, but not for groups 2 and 5. CONCLUSIONS: The cyclic loading and type of implant/abutment connection may develop a role on the vertical misfit at the implant/abutment interface.

Influence of different catilever extensions and glass or polyamaramid reinforcement fibers on fracture strength of implant-supported temporary

In long-term oral rehabilitation treatments, resistance of provisional crowns is a very important factor, especially in cases of an extensive edentulous distal space. The aim of this laboratorial study was to evaluate an acrylic resin cantilever-type prosthesis regarding the flexural strength of its in-balance portion as a function of its extension variation and reinforcement by two types of fibers (glass and polyaramid), considering that literature is not conclusive on this subject. Each specimen was composed by 3 total crowns at its mesial portion, each one attached to an implant component (abutment), while the distal portion (cantilever) had two crowns. Each specimen was constructed by injecting acrylic resin into a two-part silicone matrix placed on a metallic base. In each specimen, the crowns were fabricated with either acrylic resin (control group) or acrylic resin reinforced by glass (Fibrante, Angelus) or polyaramide (Kevlar 49, Du Pont) fibers. Compression load was applied on the cantilever, in a point located 7, 14 or 21 mm from the distal surface of the nearest crown with abutment, to simulate different extensions. The specimen was fixed on the metallic base and the force was applied until fracture in a universal test machine. Each one of the 9 sub-groups was composed by 10 specimens. Flexural strength means (in kgf) for the distances of 7, 14 and 21 mm were, respectively, 28.07, 8.27 and 6.39 for control group, 31.89, 9.18 and 5.16 for Kevlar 49 and 30.90, 9.31 and 6.86 for Fibrante. Data analysis ANOVA showed statistically significant difference (p<0.05) only regarding cantilever extension. Tukey's test detected significantly higher flexural strength for the 7 mm-distance, followed by 14 and 21 mm. Fracture was complete only on specimens of non-reinforced groups.

Effect of cement type and water storage time on the push-out bond strength of a glass fiber post

This study investigated the effects of the cement type and the water storage time on the push-out bond strength of a glass fiber post. Glass fiber posts (Fibrekor, Jeneric Pentron) were luted to post spaces using a self-cured resin cement (C&B Cement [CB]), a glass ionomer cement (Ketac Cem [KC]) or a resin-modified glass ionomer cement (GC FujiCEM [FC]) according to the manufacturers’ instructions. For each luting agent, the specimens were exposed to one of the following water storage times (n=5): 1 day (T1), 7 days (T7), 90 days (T90) and 180 days (T180). Push-out tests were performed after the storage times. Control specimens were not exposed to water storage, but subjected to the push-out test 10 min after post cementation. Data (in MPa) were analyzed by Kruskal-Wallis and Dunn`s test (α=0.05). Cement type and water storage time had a significant effect (p<0.05) on the push-out bond strength. CB showed significantly higher values of retention (p<0.05) than KC and FC, irrespective of the water storage time. Water storage increased significantly the push-out bond strength in T7 and T90, regardless of the cement type (p<0.05). The results showed that fiber posts luted to post spaces with the self-cured resin cement exhibited the best bonding performance throughout the 180-day water storage period. All cements exhibited a tendency to increase the bond strength after 7 and 90 days of water storage, decreasing thereafter.