Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

GeoGebraTUTOR : développement d’un système tutoriel autonome pour l’accompagnement d’élèves en situation de résolution de problèmes de démonstration en géométrie plane et genèse d’un espace de travail géométrique idoine

Travaux d'études doctorales réalisées conjointement avec les travaux de recherches doctorales de Nicolas Leduc, étudiant au doctorat en génie informatique à l'École Polytechnique de Montréal.

Comparison of two methods for measuring the pubococcygeal line from sagittal-plane magnetic resonance imaging

Aims The pubococcygeal line (PCL) is an important reference line for determining measures of pelvic organ support on sagittal-plane magnetic resonance imaging (MRI); however, there is no consensus on where to place the posterior point of the PCL. As coccyx movement produced during pelvic floor muscle (PFM) contractions may affect other measures, optimal placement of the posterior point is important. This study compared two methods for measuring the PCL, with different posterior points, on T2-weighted sagittal MRI to determine the effect of coccygeal movement on measures of pelvic organ support in older women. Methods MRI of the pelvis was performed in the midsagittal plane, at rest and during PFM contractions, on 47 community-dwelling women 60 and over. The first PCL was measured to the tip of the coccyx (PCLtip) and the second to the sacrococcygeal joint (PCLjnt). Four measures of pelvic organ support were made using each PCL as the reference line: urethrovesical junction height, uterovaginal junction height, M-line and levator plate angle. Results During the PFM contraction the PCLtip shortened and lifted (P < 0.001); the PCLjnt did not change (P > 0.05). The changes in the four measures of pelvic organ support were smaller when measured relative to the PCLtip as compared to those to the PCLjnt (P < 0.001). Conclusions Coccyx movement affected the length and position of the PCLtip, which resulted in underestimates of the pelvic-organ lift produced by the PFM contraction. Therefore, we recommend that the PCL be measured to the sacrococcygeal joint and not to the tip of the coccyx

Light polarization sensitive photodetectors with m- and r-plane homoepitaxial ZnO/ZnMgO quantum wells

Homoepitaxial ZnO/(Zn,Mg)O multiple quantum wells (MQWs) grown with m- and r-plane orientations are used to demonstrate Schottky photodiodes sensitive to the polarization state of light. In both orientations, the spectral photoresponse of the MQW photodiodes shows a sharp excitonic absorption edge at 3.48 eV with a very low Urbach tail, allowing the observation of the absorption from the A, B and C excitonic transitions. The absorption edge energy is shifted by ∼30 and ∼15 meV for the m- and r-plane MQW photodiodes, respectively, in full agreement with the calculated polarization of the A, B, and C excitonic transitions. The best figures of merit are obtained for the m-plane photodiodes, which present a quantum efficiency of ∼11%, and a specific detectivity D* of ∼6.4 × 1010 cm Hz1/2/W. In these photodiodes, the absorption polarization sensitivity contrast between the two orthogonal in-plane axes yields a maximum value of (R⊥/R||)max ∼ 9.9 with a narrow bandwidth of ∼33 meV.

Space density distribution of galaxies in the absolute magnitude - rotation velocity plane: a volume-complete Tully-Fisher relation from CALIFA stellar kinematics

We measured the distribution in absolute magnitude - circular velocity space for a well-defined sample of 199 rotating galaxies of the Calar Alto Legacy Integral Field Area Survey (CALIFA) using their stellar kinematics. Our aim in this analysis is to avoid subjective selection criteria and to take volume and large-scale structure factors into account. Using stellar velocity fields instead of gas emission line kinematics allows including rapidly rotating early-type galaxies. Our initial sample contains 277 galaxies with available stellar velocity fields and growth curve r-band photometry. After rejecting 51 velocity fields that could not be modelled because of the low number of bins, foreground contamination, or significant interaction, we performed Markov chain Monte Carlo modelling of the velocity fields, from which we obtained the rotation curve and kinematic parameters and their realistic uncertainties. We performed an extinction correction and calculated the circular velocity v_circ accounting for the pressure support of a given galaxy. The resulting galaxy distribution on the M-r - v(circ) plane was then modelled as a mixture of two distinct populations, allowing robust and reproducible rejection of outliers, a significant fraction of which are slow rotators. The selection effects are understood well enough that we were able to correct for the incompleteness of the sample. The 199 galaxies were weighted by volume and large-scale structure factors, which enabled us to fit a volume-corrected Tully-Fisher relation (TFR). More importantly, we also provide the volume-corrected distribution of galaxies in the M_r - v_circ plane, which can be compared with cosmological simulations. The joint distribution of the luminosity and circular velocity space densities, representative over the range of -20 > M_r > -22 mag, can place more stringent constraints on the galaxy formation and evolution scenarios than linear TFR fit parameters or the luminosity function alone.

X Factors (Rebecca's Mermaid and Sonja's Plane)

Combined media on photographic paper.

Plane

Mixed media. 23" x 19", Complexity Series.

Linguística e Semiótica Contemporâneas: A Relação Entre Hjelmslev e Zilberberg

Tivemos como objetivo compreender o papel da teoria hjelmsleviana na concepção da tensividade, uma vertente atual da semiótica discursiva, proposta por Claude Zilberberg. Para isso, retomamos algumas das ideias apresentadas pelo mestre dinamarquês que foram cruciais para o desenvolvimento da teoria do semioticista francês nessas últimas três décadas. Nesse movimento da volta, partimos do modelo de silabação, proposto no CLG, a partir dos cursos ministrados por Saussure, até chegar nas contribuições de Hjelmslev, as quais abriram caminho para os estudos da foria e da tensividade. O corpus consiste nas principais obras de cada um dos teóricos, entre elas Le langage (1966), Ensaios Linguísticos (1991), Prolegômenos (1953), de Hjelmslev, e também Razão e Poética do sentido (1988), Des formes de vie aux valeurs (2011) e La structure tensive (2012), escritas por Zilberberg. Do linguista dinamarquês, Zilberberg aproveita os pares intenso vs. extenso e instensivo vs. extensivo, o que lhe permite compreender a tensividade como o lugar de encontro entre uma intensidade e uma extensidade, pressuposto central no desenvolvimento de sua teoria. Outro princípio hjelmsleviano tomado emprestado por Zilberberg é o da processualidade, necessário para se possa compreender a continuidade e a gradação das grandezas no campo de presença. Em nossa análise, ficou evidente que há uma relação entre Hjelmslev e Zilberberg, pois essa vertente da semiótica atual continua a revisitar os escritos do linguista da glossemática. http://dx.doi.org/10.5935/1981-4755.20170024

The Behavior of Hydroxyl Units of Synthetic Goethite and its Dehydroxylated Product Hematite

The behavior of the hydroxyl units of synthetic goethite and its dehydroxylated product hematite was characterized using a combination of Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) during the thermal transformation over a temperature range of 180-270 degrees C. Hematite was detected at temperatures above 200 degrees C by XRD while goethite was not observed above 230 degrees C. Five intense OH vibrations at 3212-3194, 1687-1674, 1643-1640, 888-884 and 800-798 cm(-1), and a H2O vibration at 3450-3445 cm(-1) were observed for goethite. The intensity of hydroxyl stretching and bending vibrations decreased with the extent of dehydroxylation of goethite. Infrared absorption bands clearly show the phase transformation between goethite and hematite: in particular. the migration of excess hydroxyl units from goethite to hematite. Two bands at 536-533 and 454-452 cm(-1) are the low wavenumber vibrations of Fe-O in the hematite structure. Band component analysis data of FTIR spectra support the fact that the hydroxyl units mainly affect the a plane in goethite and the equivalent c plane in hematite.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Mapping of indoor environments by robots using low-cost vision sensors

For robots to operate in human environments they must be able to make their own maps because it is unrealistic to expect a user to enter a map into the robot’s memory; existing floorplans are often incorrect; and human environments tend to change. Traditionally robots have used sonar, infra-red or laser range finders to perform the mapping task. Digital cameras have become very cheap in recent years and they have opened up new possibilities as a sensor for robot perception. Any robot that must interact with humans can reasonably be expected to have a camera for tasks such as face recognition, so it makes sense to also use the camera for navigation. Cameras have advantages over other sensors such as colour information (not available with any other sensor), better immunity to noise (compared to sonar), and not being restricted to operating in a plane (like laser range finders). However, there are disadvantages too, with the principal one being the effect of perspective. This research investigated ways to use a single colour camera as a range sensor to guide an autonomous robot and allow it to build a map of its environment, a process referred to as Simultaneous Localization and Mapping (SLAM). An experimental system was built using a robot controlled via a wireless network connection. Using the on-board camera as the only sensor, the robot successfully explored and mapped indoor office environments. The quality of the resulting maps is comparable to those that have been reported in the literature for sonar or infra-red sensors. Although the maps are not as accurate as ones created with a laser range finder, the solution using a camera is significantly cheaper and is more appropriate for toys and early domestic robots.

A study of vibration and vibration control of ship structures

This paper examines the vibration characteristics and vibration control of complex ship structures. It is shown that input mobilities of a ship structure at engine supports, due to out-of-plane force or bending moment excitations, are governed by the flexural stiffness of the engine supports. The frequency averaged input mobilities of the ship structure, due to such excitations, can be represented by those of the corresponding infinite beam. The torsional moment input mobility at the engine support can be estimated from the torsional response of the engine bed section under direct excitation. It is found that the inclusion of ship hull and deck plates in the ship structure model has little effect on the frequency-averaged response of the ship structure. This study also shows that vibration propagation in complex ship structures at low frequencies can be attenuated by imposing irregularities to the ring frame locations in ships. Vibration responses of ship structures due to machinery excitations at higher frequencies can be controlled by structural modifications of the local supporting structures such as engine beds in ships.

Raman spectroscopic study of the magnesium carbonate minerals– artinite and dypingite

Magnesium minerals are important in the understanding of the concept of geosequestration. The two hydrated hydroxy magnesium carbonate minerals artinite and dypingite have been studied by Raman spectroscopy. Intense bands are observed at 1092 cm-1 for artinite and at 1120 cm-1 for dypingite attributed CO32- ν1 symmetric stretching mode. The CO32- ν3 antisymmetric stretching vibrations are extremely weak and are observed at1412 and 1465 cm-1 for artinite and at 1366, 1447 and 1524 cm-1 for dypingite. Very weak Raman bands at 790 cm-1 for artinite and 800 cm-1 for dypingite are assigned to the CO32- ν2 out-of-plane bend. The Raman band at 700 cm-1 of artinite and at 725 and 760 cm-1 of dypingite are ascribed to CO32- ν2 in-plane bending mode. The Raman spectrum of artinite in the OH stretching region is characterised by two sets of bands: (a) an intense band at 3593 cm-1 assigned to the MgOH stretching vibrations and (b) the broad profile of overlapping bands at 3030 and 3229 cm-1 attributed to water stretching vibrations. X-ray diffraction studies show the minerals are disordered. This is reflected in the difficulty of obtaining Raman spectra of reasonable quality and explains why the Raman spectra of these minerals have not been previously or sufficiently described.