Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang-Mills connections with the same Morse index.Comment: 58 pages, 3 figure

The resection angle in apical surgery: a CBCT assessment.

OBJECTIVES The primary objective of the present radiographic study was to analyse the resection angle in apical surgery and its correlation with treatment outcome, type of treated tooth, surgical depth and level of root-end filling. MATERIALS AND METHODS In the context of a prospective clinical study, cone beam computed tomography (CBCT) scans were taken before and 1 year after apical surgery to measure the angle of the resection plane relative to the longitudinal axis of the root. Further, the surgical depth (distance from the buccal cortex to the most lingual/palatal point of the resection plane) as well as the level of the root-end filling relative to the most coronal point of the cut root face was determined. Treated teeth were categorized into four groups (maxillary and mandibular anterior and posterior teeth). The final material comprised 62 treated roots in 55 teeth. RESULTS The mean calculated resection angle of all roots was 17.7° ± 11.4° (range -9.6° to 43.4°). Anterior maxillary roots presented the highest mean angle (25.8° ± 10.3°) that was significantly different from the mean angle in posterior maxillary roots (10.7° ± 9.4°; p 20°), however without reaching statistical significance (p = 0.0905). Angles did not correlate either with the surgical depth or with the retrofilling length. CONCLUSIONS Statistically significant differences were observed comparing resection angles of different tooth groups. However, the angle had no significant effect on treatment outcome. CLINICAL RELEVANCE Contrary to common belief, the resection angle in maxillary anterior teeth was greater than in the other teeth. The surgeon is advised to pay attention to the resection angle when bevelling maxillary anterior teeth in apical surgery

Quasi Regular Polyhedra and Their Duals with Coxeter Symmetries Represented by Quaternions I

In two series of papers we construct quasi regular polyhedra and their duals which are similar to the Catalan solids. The group elements as well as the vertices of the polyhedra are represented in terms of quaternions. In the present paper we discuss the quasi regular polygons (isogonal and isotoxal polygons) using 2D Coxeter diagrams. In particular, we discuss the isogonal hexagons, octagons and decagons derived from 2D Coxeter diagrams and obtain aperiodic tilings of the plane with the isogonal polygons along with the regular polygons. We point out that one type of aperiodic tiling of the plane with regular and isogonal hexagons may represent a state of graphene where one carbon atom is bound to three neighboring carbons with two single bonds and one double bond. We also show how the plane can be tiled with two tiles; one of them is the isotoxal polygon, dual of the isogonal polygon. A general method is employed for the constructions of the quasi regular prisms and their duals in 3D dimensions with the use of 3D Coxeter diagrams.Comment: 22 pages, 16 figure

Reducing the positional modulation of NbO6-octahedra in SrxBa1-xNb2O6 by increasing the Barium content: A single crystal neutron diffraction study at ambient temperature for x=0.61 and x=0.34

We report on the influence of the Barium content on the modulation amplitude in SrxBa1-xNb2O6 compounds by comparing Sr0.61Ba0.39Nb2O6 (SBN61) and Sr0.34Ba0.66Nb2O6 (SBN34). Our single crystal neutron diffraction results demonstrate that the amplitude of the positional modulation of the NbO6 octahedra is reduced with increasing barium content, indicating that the origin of the modulation is the partial occupation of the pentagonal channels by Sr and Ba atoms. By increasing the Sr content the bigger Ba atoms are replaced by the smaller Sr atoms, which leads to a larger deformation of the surrounding lattice and hence to a larger modulation amplitude. The more homogeneous the filling of these channels with one atomic type (Ba) the lower the modulation amplitude. Our results also show that the structure can be described with a two-dimensional incommensurate harmonic modulation. No second order modulation has been observed, both by single crystal diffraction measurements and q-scans. The positional modulation of the Nb atoms is much smaller than that of the oxygen atoms, such that the modulation can be seen as a rotational modulation of almost rigid NbO6-octahedra

Error-Free 10.7 Gb/s Digital Transmission over 2 km Optical Link Using an Ultra-Low-Voltage Electro-Optic Modulator

We demonstrate the feasibility of 10.7 Gb/s error-free (BER < 10-12) optical transmission on distances up to 2 km using a recently developed ultra-low-voltage commercial Electro-Optic Modulator (EOM) that is driven by 0.6 Vpp and with an optical input power of 1 mW. Given this low voltage operation, the modulator could be driven directly from the detectors’ board signals without the need of any further amplification reducing significantly the power dissipation and the material budget

Calcium-phosphate glass-based bioresorbable fibre optics for light and drug delivery

Calcium-phosphate glasses (CPGs) are commonly used as scaffolds in tissue engineering. A novel formulation of optically transparent CPG has been recently developed to be used as an optical fibre for biomedical implantable devices. Its purpose is to combine the bioresorbability of CPGs with optical features, thus extending the applications of bioresorbable sensors for in-body monitoring or diagnostics. Modifications of the glass composition or post-treatments on the fibres can tailor the dissolution time and the interaction of the glass with different stimuli as well as with specific cells. The tested glasses both in bulk and fibre shapes showed good strength (from 200 to 350 MPa) with values that are lower than standard silica glass and much higher than common bioresorbable polymers. CPG fibres were also implanted in living rats for several weeks and no clinical signs of any adverse effect have been found. We will present our latest results on these subjects starting from the characterisation of the CPGs by means of dissolution tests, in-vitro, and ex-vivo experiments

Inter-site Coulomb interaction and Heisenberg exchange

Based on exact diagonalization results for small clusters we discuss the effect of inter-site Coulomb repulsion in Mott-Hubbard or charge transfer insulators. Whereas the exchange constant J for direct exchange is substantially enhanced by inter-site Coulomb interaction, that for superexchange is suppressed. The enhancement of J in the single-band models holds up to the critical value for the charge density wave (CDW) instability, thus opening the way for large values of J. Single-band Hubbard models with sufficiently strong inter-site repulsion to be near a CDW instability thus may provide `physical' realizations of t-J like models with the `unphysical' parameter ratio J/t=1.Comment: Revtex file, 4 PRB pages, with 5 embedded ps-files. To appear in PRB, rapid communications. Hardcopies of figures or the entire manuscript may also be obtained by e-mail request to: [email protected]

Wigner's Spins, Feynman's Partons, and Their Common Ground

The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless particle is isomorphic to the two-dimensional Euclidean group with one rotational and two translational degrees of freedom. The rotational degree corresponds to the helicity, and the translational degrees to the gauge degree of freedom. The question then is whether these two different symmetries can be united. Another hard-pressing problem is Feynman's parton picture which is valid only for hadrons moving with speed close to that of light. While the hadron at rest is believed to be a bound state of quarks, the question arises whether the parton picture is a Lorentz-boosted bound state of quarks. We study these problems within Einstein's framework in which the energy-momentum relations for slow particles and fast particles are two different manifestations one covariant entity.Comment: LaTex 12 pages, 3 figs, based on the lectures delivered at the Advanced Study Institute on Symmetries and Spin (Prague, Czech Republic, July 2001

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating