Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries

Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Coleman-Weinberg mechanism in a three-dimensional supersymmetric Chern-Simons-matter model

Using the superfield formalism, we study the dynamical breaking of gauge symmetry and super-conformal invariance in the N = 1 three-dimensional supersymmetric Chern-Simons model, coupled to a complex scalar superfield with a quartic self-coupling. This is an analogue of the conformally invariant Coleman-Weinberg model in four spacetime dimensions. We show that a mass for the gauge and matter superfields are dynamically generated after two-loop corrections to the effective superpotential. We also discuss the N = 2 extension of our work, showing that the Coleman-Weinberg mechanism in such model is not feasible, because it is incompatible with perturbation theory.

Finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory

Within the superfield approach, we prove the absence of UV/IR mixing in the three-dimensional noncommutative supersymmetric Maxwell-Chern-Simons theory at any loop order and demonstrate its finiteness in one, three, and higher loop orders.

Is there a connection between long airplane flight, venous thromboembolism, and sleep-disordered breathing?

Commercial passenger flights have been increasing around the world. The effect of these flights on health is unclear. Venous thromboembolism has been noted after recent long-distance airplane flight, even in the absence of other risk factors. Hypoxia caused by the low ambient pressure during flights could contribute, and individuals with obstructive sleep apnea may be particularly vulnerable. The association between the effects of long airplane travel and sleep-disordered breathing deserves further study. (C) 2008 Elsevier B.V. All rights reserved.

Connection Admission Control for a WDM Optical Network Based on Traffic Monitoring and Bandwidth Release

We proposed a connection admission control (CAC) to monitor the traffic in a multi-rate WDM optical network. The CAC searches for the shortest path connecting source and destination nodes, assigns wavelengths with enough bandwidth to serve the requests, supervises the traffic in the most required nodes, and if needed activates a reserved wavelength to release bandwidth according to traffic demand. We used a scale-free network topology, which includes highly connected nodes ( hubs), to enhance the monitoring procedure. Numerical results obtained from computational simulations show improved network performance evaluated in terms of blocking probability.

Analysis of a semi-rigid connection for precast concrete

This paper presents a study of a specific type of beam-to-column connection for precast concrete structures. Furthermore, an analytical model to determine the strength and the stiffness of the connection, based on test results of two prototypes, is proposed. To evaluate the influence of the strength and stiffness of the connection on the behaviour of the structure, the results of numerical simulations of a typical multi-storey building with semi-rigid connections are also presented and compared with the results using pinned and rigid connections. The main conclusions are: (a) the proposed design model can reasonably evaluate the studied connection strength; (b) the evaluation of strength is more accurate than that of stiffness; (c) for a typical structure, it is possible to increase the number of storeys of the structure from two to four with lower horizontal displacement at the top, and only a small increase of the column base bending moment by replacing the pinned connections with semi-rigid ones; and (d) although there is significant uncertainty in the connection stiffness, the results show that the displacements at the top of the structure, and the column base moments present low susceptibility deviations to this parameter.

Column connection detail, Kangaroo Point House

Hand-made spotted gum column on edge of outdoor room.

Post and beam connection, PNG Coffee Industry Board Office and Warehouse, Goroka

Detailed view of cast iron brackets connecting beams and posts.

Post and beam connection, PNG Coffee Industry Board Office and Warehouse, Goroka

Detailed view of cast iron brackets connecting beams and posts.

Corner connection detail, Sunshine Coast University Library, Maroochydore

Detailed external view of north-west elevation corner.

North-east verandah connection, Sunshine Coast University Library, Maroochydore

View of underside of verandah corrugated steel roofing, polycarbonate sheeting and north-east glass and floor connection.

Intracardiac Cavopulmonary Connection in Patients with Univentricular Heart Using Intra-atrial Lateral Tunnel and Intra-atrial Conduit Techniques

Background: In this study, we analyzed the time course of hemodynamic efficiency and follow-up in Fontan candidates who underwent the bidirectional Glenn procedure for staged intracardiac cavopulmonary connection (ICPC). Methods: Between 1991 and 2008, 52 patients with univentricular heart (mean age, 3.3 years; range, 2-8 years; 27 female patients [51.9%]) underwent ICPC. The cardiac malformations were as follows: tricuspid atresia, 25 cases (48.0%); common ventricle, 16 cases (30.7%); and pulmonary atresia with intact ventricular septum, 11 cases (21.1%). The intracardiac cavopulmonary procedure was indicated for all 52 cases. In 42 patients (80.7%), an intra-atrial lateral tunnel was constructed with a bovine pericardium patch. In the last 10 consecutive cases (19.3%), we performed a modified surgical technique in which we implanted an intra-atrial corrugated bovine pericardium tube sutured around the superior and inferior vena cava ostium. In all cases, a 4-mm fenestration was made to reduce the intratunnel pressure. All 52 patients had previously undergone a Glenn operation. Results: There were 2 hospital deaths (3.8%) and no recorded late deaths. During the follow-up, all patients were medicated with antiplatelet drugs. To evaluate the hemodynamic performance, we used Doppler echocardiography, computed tomography, and magnetic nuclear resonance studies. There were no prosthesis thromboses during this follow-up period. To evaluate cardiac arrhythmias, we conducted a Holter study. The last 10 patients with an intra-atrial conduit (IAC) presented with sinus rhythm and no arrhythmias during the last 4 years. The 50 surviving patients (96.1%) have been followed up for 6 to 204 months; all these patients are free of reoperation. Conclusion: The Glenn operation, which is performed at an early age, prepares the pulmonary bed to receive the ICPC. The midterm results of the intracardiac Fontan procedure seem to be good. The modified surgical procedure (IAC) can be a good alternative technique to the Fontan procedure in suitable patients.