Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Histomorphometric Evaluation of Bioceramic Molecular Impregnated and Dual Acid-Etched Implant Surfaces in the Human Posterior Maxilla

Background: Physical and bioceramic incorporation surface treatments at the nanometer scale showed higher means of bone-to-implant contact (BIC) and torque values compared with surface topography at the micrometer scale; however, the literature concerning the effect of nanometer scale parameters is sparse. Purpose: The aim of this study was to evaluate the influence of two different implant surfaces on the percentage bone-to-implant contact (BIC%) and bone osteocyte density in the human posterior maxilla after 2 months of unloaded healing. Materials and Methods: The implants utilized presented dual acid-etched (DAE) surface and a bioceramic molecular impregnated treatment (Ossean(R), Intra-Lock International, Boca Raton, FL, USA) serving as control and test, respectively. Ten subjects (59 1 9 years of age) received two implants (one of each surface) during conventional implant surgery in the posterior maxilla. After the non-loaded period of 2 months, the implants and the surrounding tissue were removed by means of a trephine and were non-decalcified processed for ground sectioning and analysis of BIC%, bone density in threaded area (BA%), and osteocyte index (Oi). Results: Two DAE implants were found to be clinically unstable at time of retrieval. Histometric evaluation showed significantly higher BIC% and Oi for the test compared to the control surface (p < .05), and that BA% was not significantly different between groups. Wilcoxon matched pairs test was used to compare the differences of histomorphometric variables between implant surfaces. The significance test was conducted at a 5% level of significance. Conclusion: The histological data suggest that the bioceramic molecular impregnated surface-treated implants positively modulated bone healing at early implantation times compared to the DAE surface.

Efficacy of high intensity diode laser as an adjunct to non-surgical periodontal treatment: a randomized controlled trial

The high intensity diode laser has been studied in periodontics for the reduction of subgingival bacteria in non-surgical treatment. Our study evaluated the bacterial effect as well as changes in periodontal clinical parameters promoted by root scaling and planing associated with this wavelength. Twenty-seven patients randomly assigned in two groups underwent root scaling and planing on the tested sites, and only the experimental group received the diode laser irradiation. Among the clinical parameters studied, the clinical probing depth (CPD) and the clinical attachment level (CAL) resulted in significant enhancement in the control group when compared with the experimental group (P = 0.014 and P = 0.039, respectively). The results were similar for both groups regarding the plaque index (PI) and bleeding on probing (BP). No significant difference in the microbiological parameters was observed between the control and experimental groups. It was possible to conclude that the high power diode laser adjunct to the non-surgical periodontal treatment did not promote additional effects to the conventional periodontal treatment.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

Rotation effect on geodesic and zonal flow modes in tokamak plasmas with isothermal magnetic surfaces

The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model including heat flux to compensate for the non-adiabatic pressure distribution along the magnetic surfaces in plasmas with poloidal rotation. Instead of two standard geodesic modes, three geodesic continua are found. The two higher branches of the geodesic modes have a small frequency up-shift from ordinary geodesic acoustic and sonic modes due to rotation. The lower geodesic continuum is a newzonal flowmode (geodesic Doppler mode) in plasmas with mainly poloidal rotation. Limits to standard geodesic modes are found. Bifurcation of Alfven continuum by geodesic modes at the rational surfaces is also discussed. Due to that, the frequency of combined geodesic continuum extends from the poloidal rotation frequency to the ion-sound band that can have an important role in suppressing plasma turbulence.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.