Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Apical seal of root canals with gutta-percha points with calcium hydroxide

Foi propósito deste trabalho observar se o uso de cones de guta-percha contendo Ca(OH)2, promove melhora no selamento marginal apical e, também, se apenas o cone principal contendo essa droga produz esse efeito. Assim, dentes humanos extraídos foram preparados biomecânicamente e obturados pela técnica da condensação lateral com OZE e cones de guta-percha contendo ou não Ca(OH)2. Após imersão dos espécimes em azul de metileno a 2%, em ambiente com vácuo, observou-se diferença estatisticamente significante entre os espécimes obturados com cones contendo Ca(OH)2, comparativamente aos casos obturados com cones de guta percha comuns (p=0.01). Os resultados obtidos permitiram concluir que esses cones tornam as obturações mais herméticas e que esse efeito também pode ser obtido com o emprego do cone principal da mesma fórmula, aliado a cones acessórios comuns (p=0.05).

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.

Limit weierstrass points on nodal reducible curves

In the 1980s D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The use of the challenge test to analyse preservative efficiency in non-sterile cosmetic and health products: applications and critical points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has nontrivial fixed points, they will correspond to extrema of the vacuum energy. This relationship provides a different method to determine fixed points.

Uses of QCD sumrules (QCDSR) from different points of view

We support the idea that the baryon, B with mass MB, couples to its current with a coupling λ2 B ∼ 0.71 M6 B from an analysis of magnetic moment sum rules. And we find a sum rule among the experimental magnetic moments which is independent of the parameters of QCDSR. © 1998 Elsevier Science B.V. All rights reserved.

In vitro antimicrobial activity of different gutta-percha points and calcium hydroxide pastes

The aim of this study was to evaluate the antimicrobial activity of different trademarks and compositions of gutta-percha points and calcium hydroxide pastes used in endodontic therapy. The evaluated material consisted of gutta-percha points containing calcium hydroxide (Roeko™), gutta-percha points containing chlorhexidine (Roeko™), two convencional gutta-percha points (Endo Points™ and Roeko™) and two calcium hydroxide pastes (Calen™ and Calen/PMCC™). Antimicrobial tests included five species of microorganisms: Escherichia coli (ATCC10538), Staphylococcus epidermidis (ATCC12228), Staphylococcus aureus (ATCC6538), Pseudomonas aeruginosa (ATCC27853), and Micrococcus luteus (ATCC9341). The Agar difusion method was employed. The plates were kept at room temperature for 2 h for prediffusion and then incubated at 37°C for 24 h. The triphenyltetrazolium chloride gel was added for optimization and the zones of inhibition were measured. Statistical evaluation was carried out using analysis of variance and Tukey Test. The obtained results showed that all microbial species used in the study were inhibited by the gutta-percha points containing chlorhexidine and by the calcium hydroxide pastes (Calen™ and Calen/ PMCC™), with similar results (p > 0.05). No antimicrobial activity was observed for the other groups. It was concluded that the gutta-percha points containing chlorhexidine presented antimicrobial activity, whereas the gutta-percha points containing calcium hydroxide did not.

Influence of brush type as a carrier of adhesive solutions and paper points as an adhesive-excess remover on the resin bond to root dentin

Purpose: To evaluate the influence of the brush type as a earner of priming adhesive solutions and the use of paper points as a remover of the excess of these solutions on the push-out bond strength of resin cement to bovine root dentin. The null hypotheses were that brush type and the use of paper points do not affect the bond strength. Materials and Methods: The canals of 80 single-root bovine roots (16 mm in length) were prepared at 12 mm using the preparation drill (FRC Postec Plus, Ivoclar). Half of each root was embedded in acrylic resin and the specimens were divided into 8 groups, considering the factors brush type (4 levels) and paper point (2 levels) (n = 10): Gr 1: small microbrush (Cavi-Tip, SDI); Gr 2: Microbrush (Dentsply); Gr 3: Endobrush (Bisco); Gr 4: conventional brush (Bisco); Gr 5: Cavi-Tip (SDI) + paper points; Gr 6: Microbrush (Dentsply) + paper points; Gr 7: Endobrush (Bisco) + paper points; Gr 8: conventional brush (Bisco) + paper points. The root dentin was treated with a multistep total-etch adhesive system (All Bond 2). The adhesive system was applied using each microbrush, with and without using paper points. One fiber post was molded with addition silicon and 80 posts were made of resin cement (Duolink), The resin posts were luted (Duolink resin cement), and the specimens were stored for 24 h in water at 37°C. Each specimen was cut into 4 disk-shaped samples (1.8 mm in thickness), which were submitted to the push-out test. Results: The brush type (p < 0.0001) (small microbrush > microbrush = endobrush = conventional brush) and the use of paper points (p = 0.0001) (with > without) influenced the bond strength significantly (two-way ANOVA). The null hypotheses were rejected. Conclusion: The smallest brush (Cavi-Tip) and the use of paper points significantly improved the resin bond to bovine root dentin.

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.