Geometry of the SL(3,ℂ)-character variety of torus knots.

Let G be the fundamental group of the complement of the torus knot of type (m, n). It has a presentation G = . We find a geometric description of the character variety X(G) of characters of representations of G into SL(3,ℂ), GL(3,ℂ) and PGL(3,ℂ).

Analysis of the spectral response of fractal antennas related with its geometry and current paths

Fractal antennas have been proposed to improve the bandwidth of resonant structures and optical antennas. Their multiband characteristics are of interest in radiofrequency and microwave technologies. In this contribution we link the geometry of the current paths built-in the fractal antenna with the spectral response. We have seen that the actual currents owing through the structure are not limited to the portion of the fractal that should be geometrically linked with the signal. This fact strongly depends on the design of the fractal and how the different scales are arranged within the antenna. Some ideas involving materials that could actively respond to the incoming radiation could be of help to spectrally select the response of the multiband design.

Compositional and Geochemical Signatures for the Sedimentary Evolution of the Middle Triassic–Lower Jurassic Continental Redbeds from Western-Central Mediterranean Alpine Chains

Compositional and chemical analyses suggest that Middle Triassic–Lower Liassic continental redbeds (in the internal domains of the Betic, Maghrebian, and Apenninic chains) can be considered a regional lithosome marking the Triassic-Jurassic rift-valley stage of Tethyan rifting, which led to the Pangaea breakup and subsequent development of a mosaic of plates and microplates. Sandstones are quartzose to quartzolithic and represent a provenance of continental block and recycled orogen, made up mainly of Paleozoic metasedimentary rocks similar to those underlying the redbeds. Mudrocks display K enrichments; intense paleoweathering under a hot, episodically humid climate with a prolonged dry season; and sediment recycling. Redbeds experienced temperatures in the range of 100°–160°C and lithostatic/tectonic loading of more than 4 km. These redbeds represent an important stratigraphic signature to reconstruct a continental block (Mesomediterranean Microplate) that separated different realms of the western Tethys from Middle-Late Jurassic to Miocene, when it was completely involved in Alpine orogenesis.

The influence of magnetic field geometry on magnetars X-ray spectra

Nowadays, the analysis of the X-ray spectra of magnetically powered neutron stars or magnetars is one of the most valuable tools to gain insight into the physical processes occurring in their interiors and magnetospheres. In particular, the magnetospheric plasma leaves a strong imprint on the observed X-ray spectrum by means of Compton up-scattering of the thermal radiation coming from the star surface. Motivated by the increased quality of the observational data, much theoretical work has been devoted to develop Monte Carlo (MC) codes that incorporate the effects of resonant Compton scattering (RCS) in the modeling of radiative transfer of photons through the magnetosphere. The two key ingredients in this simulations are the kinetic plasma properties and the magnetic field (MF) configuration. The MF geometry is expected to be complex, but up to now only mathematically simple solutions (self-similar solutions) have been employed. In this work, we discuss the effects of new, more realistic, MF geometries on synthetic spectra. We use new force-free solutions [14] in a previously developed MC code [9] to assess the influence of MF geometry on the emerging spectra. Our main result is that the shape of the final spectrum is mostly sensitive to uncertain parameters of the magnetospheric plasma, but the MF geometry plays an important role on the angle-dependence of the spectra.

Reverse Geometry Hybrid Contact Lens Fitting in a Case of Donor-Host Misalignment after Keratoplasty

Purpose: To report the successful outcome obtained after fitting a new hybrid contact lens in a cornea with an area of donor-host misalignment and significant levels of irregular astigmatism after penetrating keratoplasty (PKP). Materials and methods: A 41-year-old female with bilateral asymmetric keratoconus underwent PKP in her left eye due to the advanced status of the disease. One year after surgery, the patient referred a poor visual acuity and quality in this eye. The fitting of different types of rigid gas permeable contact lenses was performed, but with an unsuccessful outcome due to contact lens stability problems and uncomfortable wear. Scheimpflug imaging evaluation revealed that a donor-host misalignment was present at the nasal area. Contact lens fitting with a reverse geometry hybrid contact lens (Clearkone, SynergEyes Carlsbad) was then fitted. Visual, refractive, and ocular aberrometric outcomes were evaluated during a 1-year period after the fitting. Results: Uncorrected distance visual acuity improved from a prefitting value of 20/200 to a best corrected postfitting value of 20/20. Prefitting manifest refraction was +5.00 sphere and -5.50 cylinder at 75°, with a corrected distance visual acuity of 20/30. Higher order root mean square (RMS) for a 5 mm pupil changed from a prefitting value of 6.83 µm to a postfitting value of 1.57 µm (5 mm pupil). The contact lens wearing was referred as comfortable, with no anterior segment alterations. Conclusion: The SynergEyes Clearkone contact lens seems to be another potentially useful option for the visual rehabilitation after PKP, especially in cases of donor-host misalignment.

Evaluating Taphonomic Bias in a Storm-Disturbed Carbonate Platform: Effects of Compositional and Environmental Factors in Lower Jurassic Brachiopod Accumulations (Eastern Subbetic Basin, Spain)

In order to evaluate taxonomic and environmental control on the preservation pattern of brachiopod accumulations, sedimentologic and taphonomic data have been integrated with those inferred from the structure of brachiopod accumulations from the easternmost Lower Jurassic Subbetic deposits in Spain. Two brachiopod communities (Praesphaeroidothyris and Securina communities) were distinguished showing a mainly free-lying way of life in soft-bottom habitats. Three taphofacies are discriminated based on proportion of disarticulation, fragmentation, packing, and shell filling. Taphofacies 1 is represented by thinly fragmented, dispersed brachiopod shells in wackestone beds. Taphofacies 2 is spatially restricted to small lenses where shells are poorly fragmented, rarely disarticulated, usually void filled, and highly packed. Taphofacies 3 is represented by mud or cement filled, loosely packed, articulated brachiopods forming large pocket-like structures. Temporal and spatial averaging were minimally involved in taphofacies 2 and 3. It is interpreted that patchy preservation implies preservation of primary original patchiness of brachiopod communities on the seafloor. The origin of shell-rich taphofacies (2 and 3) is related to rapid burial due to episodic storm activity, while shell-poor taphofacies 1 records background conditions. The nature and comparative diversity of these taphofacies underscores the importance of rapid burial for shell beds preservation. Differences in preservation between taphofacies 2 and 3 are mainly related to environmental criteria, most importantly storm energy and water depth. In contrast, the taxonomic-specific pattern of the communities is a subordinate element of control, controlling only minor within-taphofacies differences in preservation.

3D geometry of growth strata in a fault-propagation fold: insights into space–time evolution of the Crevillente Fault (Abanilla-Alicante sector), Betic Cordillera, Spain

This work presents a 3D geometric model of growth strata cropping out in a fault-propagation fold associated with the Crevillente Fault (Abanilla-Alicante sector) from the Bajo Segura Basin (eastern Betic Cordillera, southern Spain). The analysis of this 3D model enables us to unravel the along-strike and along-section variations of the growth strata, providing constraints to assess the fold development, and hence, the fault kinematic evolution in space and time. We postulate that the observed along-strike dip variations are related to lateral variation in fault displacement. Along-section variations of the progressive unconformity opening angles indicate greater fault slip in the upper Tortonian–Messinian time span; from the Messinian on, quantitative analysis of the unconformity indicate a constant or lower tectonic activity of the Crevillente Fault (Abanilla-Alicante sector); the minor abundance of striated pebbles in the Pliocene-Quaternary units could be interpreted as a decrease in the stress magnitude and consequently in the tectonic activity of the fault. At a regional scale, comparison of the growth successions cropping out in the northern and southern limits of the Bajo Segura Basin points to a southward migration of deformation in the basin. This means that the Bajo Segura Fault became active after the Crevillente Fault (Abanilla-Alicante sector), for which activity on the latter was probably decreasing according to our data. Consequently, we propose that the seismic hazard at the northern limit of the Bajo Segura Basin should be lower than at the southern limit.

Compositional signatures of the Cenozoic sedimentary succesions of the Malaguide Complex (Betic Cordillera, Spain)

The studied Cenozoic sedimentary successions consist of deposits from continental/shallow-water to deep-marine environments of the Malaguide Complex (Betic Cordillera) outcropping in the Sierra Espuña area (SE Spain). The aim of this study is to characterize the composition, source area(s) provenance and weathering processes of these sedimentary successions from the pre-orogenic (Paleocene-Early Oligocene) to the syn-orogenic (Late Oligocene-Early Miocene) stage using petrological and geochemical methodologies. The studied sandstones are mainly quartzolithic with abundant metamorphic and sedimentary lithic fragments. In particular, the composition of samples from the pre-orogenic cycle is mainly carbonate with important siliciclastic components that occur within the medium to fine grained arenites. The composition of samples from the syn-orogenic cycle is characterized by a sharp change from carbonate to siliciclastic terms. Thus, the composition of the overall sandstone samples is very heterogeneous and suggests a source area mainly characterized by the Malaguide basement and lower units of the Internal Betic Zone, that partially compose the Mesomediterranean Microplate. The geochemical proxies suggest a provenance mainly from felsic source area with a minor supply from mafic rocks in some samples of the syn-orogenic stage. Furthermore, palaeoweathering indices indicate low to moderate weathering conditions for the sources. The Cenozoic sedimentary successions of the Malaguide Complex played an important role in the geodynamic evolution of the Betic Cordillera that represents the key tectonic element of the western domains of the Mesomediterranean Microplate.

Notebook on geometry, geography, astronomy, and navigation, ca. 1714-1718

This heavily illustrated notebook contains entries on the following topics: geometrical definitions and axioms, geographical and astronomical definitions, compasses, plain sailing, parallel sailing, and Mercator's sailing. It also contains pages designated for notes on "Currents, Lee Way, & Variation," but these pages have been left blank. The back cover contains calculations which appear to relate to charting a course from Jamaica to "Lizzard."

Elements of geometry : manuscript, 1798

Contains work on geometry, trigonometry, surveying, mensuration of heights and distances, and navigation. The graphs and diagrams illustate story problems and navigational examples.

Geometry of Dirac Operators

Thesis (Master, Mathematics & Statistics) -- Queen's University, 2016-07-04 20:27:20.386

Greenland and Antarctic ice sheet topography, cavity geometry, and global bathymetry (RTopo-2), links to NetCDF files

The ocean plays an important role in modulating the mass balance of the polar ice sheets by interacting with the ice shelves in Antarctica and with the marine-terminating outlet glaciers in Greenland. Given that the flux of warm water onto the continental shelf and into the sub-ice cavities is steered by complex bathymetry, a detailed topography data set is an essential ingredient for models that address ice-ocean interaction. We followed the spirit of the global RTopo-1 data set and compiled consistent maps of global ocean bathymetry, upper and lower ice surface topographies and global surface height on a spherical grid with now 30-arc seconds resolution. We used the General Bathymetric Chart of the Oceans (GEBCO, 2014) as the backbone and added the International Bathymetric Chart of the Arctic Ocean version 3 (IBCAOv3) and the Interna- tional Bathymetric Chart of the Southern Ocean (IBCSO) version 1. While RTopo-1 primarily aimed at a good and consistent representation of the Antarctic ice sheet, ice shelves and sub-ice cavities, RTopo-2 now also contains ice topographies of the Greenland ice sheet and outlet glaciers. In particular, we aimed at a good representation of the fjord and shelf bathymetry sur- rounding the Greenland continent. We corrected data from earlier gridded products in the areas of Petermann Glacier, Hagen Bræ and Sermilik Fjord assuming that sub-ice and fjord bathymetries roughly follow plausible Last Glacial Maximum ice flow patterns. For the continental shelf off northeast Greenland and the floating ice tongue of Nioghalvfjerdsfjorden Glacier at about 79°N, we incorporated a high-resolution digital bathymetry model considering original multibeam survey data for the region. Radar data for surface topographies of the floating ice tongues of Nioghalvfjerdsfjorden Glacier and Zachariæ Isstrøm have been obtained from the data centers of Technical University of Denmark (DTU), Operation Icebridge (NASA/NSF) and Alfred Wegener Institute (AWI). For the Antarctic ice sheet/ice shelves, RTopo-2 largely relies on the Bedmap-2 product but applies corrections for the geometry of Getz, Abbot and Fimbul ice shelf cavities.