Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Fos and Jun bend the AP-1 site: effects of probe geometry on the detection of protein-induced DNA bending.

The effect of Fos and Jun binding on the structure of the AP-1 recognition site is controversial. Results from phasing analysis and phase-sensitive detection studies of DNA bending by Fos and Jun have led to opposite conclusions. The differences between these assays, the length of the spacer between two bends and the length of the sequences flanking the bends, are investigated here using intrinsic DNA bend standards. Both an increase in the spacer length as well as a decrease in the length of flanking sequences resulted in a reduction in the phase-dependent variation in electrophoretic mobilities. Probes with a wide separation between the bends and short flanking sequences, such as those used in the phase-sensitive detection studies, displayed no phase-dependent mobility variation. This shape-dependent variation in electrophoretic mobilities was reproduced by complexes formed by truncated Fos and Jun. Results from ligase-catalyzed cyclization experiments have been interpreted to indicate the absence of DNA bending in the Fos-Jun-AP-1 complex. However, truncated Fos and Jun can alter the relative rates of inter- and intramolecular ligation through mechanisms unrelated to DNA bending, confounding the interpretation of cyclization data. The analogous phase- and shape-dependence of the electrophoretic mobilities of the Fos-Jun-AP-1 complex and an intrinsic DNA bend confirm that Fos and Jun bend DNA, which may contribute to their functions in transcription regulation.

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.

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.

Activation of a spherical carbon for toluene adsorption at low concentration

This paper complements a previous one [1] about toluene adsorption on a commercial spherical activated carbon and on samples obtained from it by CO2 or steam activation. The present paper deals with the activation of a commercial spherical carbon (SC) having low porosity and high bed density (0.85 g/cm3) using the same procedure. Our results show that SC can be well activated with CO2 or steam. The increase in the burn-off percentage leads to an increase in the gravimetric adsorption capacity (more intensively for CO2) and a decrease in bed density (more intensively for CO2). However, for similar porosity developments similar bed densities are achieved for CO2 and steam. Especial attention is paid to differences between both activating agents, comparing samples having similar or different activation rates, showing that CO2 generates more narrow porosity and penetrates more inside the spherical particles than steam. Steam activates more from the outside to the interior of the spheres and hence produces larger spheres size reductions. With both activation agents and with a suitable combination of porosity development and bed density, quite high volumetric adsorption values of toluene (up to 236 g toluene/L) can be obtained even using a low toluene concentration (200 ppmv).

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.

Spherical activated carbon as an enhanced support for TiO2/AC photocatalysts

Titanium dioxide nanoparticles prepared in situ by sol–gel method were supported on a spherical activated carbon to prepare TiO2/AC hybrid photocatalysts for the oxidation of gaseous organic compounds. Additionally, a granular activated carbon was studied for comparison purposes. In both types of TiO2/AC composites the effect of different variables (i.e., the thermal treatment conditions used during the preparation of these materials) and the UV-light wavelength used during photocatalytic oxidation were analyzed. The prepared materials were deeply characterized (by gas adsorption, TGA, XRD, SEM and photocatalytic propene oxidation). The obtained results show that the carbon support has an important effect on the properties of the deposited TiO2 and, therefore, on the photocatalytic activity of the resulting TiO2/AC composites. Thus, the hybrid materials prepared over the spherical activated carbon show better results than those prepared over the granular one; a good TiO2 coverage with a high crystallinity of the deposited titanium dioxide, which just needs an air oxidation treatment at low-moderate temperature (350–375 °C) to present high photoactivity, without the need of additional inert atmosphere treatments. Additionally, these materials are more active at 365 nm than at 257.7 nm UV radiation, opening the possibility of using solar light for this application.

Spherical carbons: Synthesis, characterization and activation processes

Spherical carbons have been prepared through hydrothermal treatment of three carbohydrates (glucose, saccharose and cellulose). Preparation variables such as treatment time, treatment temperature and concentration of carbohydrate have been analyzed to obtain spherical carbons. These spherical carbons can be prepared with particle sizes larger than 10 μm, especially from saccharose, and have subsequently been activated using different activation processes (H3PO4, NaOH, KOH or physical activation with CO2) to develop their textural properties. All these spherical carbons maintained their spherical morphology after the activation process, except when KOH/carbon ratios higher than 4/1 were used, which caused partial destruction of the spheres. The spherical activated carbons develop interesting textural properties with the four activating agents employed, reaching surface areas up to 3100 m2/g. Comparison of spherical activated carbons obtained with the different activating agents, taking into account the yields obtained after the activation process, shows that phosphoric acid activation produces spherical activated carbons with higher developed surface areas. Also, the spherical activated carbons present different oxygen groups’ content depending on the activating agent employed (higher surface oxygen groups content for chemical activation than for physical activation).

Factors governing the adsorption of ethanol on spherical activated carbons

Ethanol adsorption on different activated carbons (mostly spherical ones) was investigated covering the relative pressure range from 0.001 to 1. Oxygen surface contents of the ACs were modified by oxidation (in HNO3 solution or air) and/or by thermal treatment in N2. To differentiate the concomitant effects of porosity and oxygen surface chemistry on ethanol adsorption, different sets of samples were used to analyze different relative pressure ranges (below 1000 ppmv concentration and close to unity). To see the effect of oxygen surface chemistry, selected samples having similar porosity but different oxygen contents were studied in the low relative pressure range. At low ethanol concentration (225 ppmv) adsorption is favored in oxidized samples, remarking the effect of the oxidizing treatment used (HNO3 is more effective than air) and the type of oxygen functionalities created (carboxyl and anhydride groups are more effective than phenolic, carbonyl and derivatives). To analyze the high relative pressure range, spherical and additional ACs were used. As the relative pressure of ethanol increases, the effect of oxygen-containing surface groups decreases and microporosity becomes the most important variable affecting the adsorption of ethanol.

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.

Cabecera cuadrada renacentista con bóveda pseudo-esférica cruzada en la iglesia Santiago de Orihuela (Alicante)

Jerónimo Quijano fue uno de los ilustres arquitectos destacados del Renacimiento pleno en España. Su obra, la iglesia de Santiago en Orihuela -Alicante- posee una Capilla Mayor renacentista, de carácter funerario, de planta central y adosada a una nave gótica. Destaca su bóveda superior de 4 pares de arcos entrecruzados y revirados. Al ser dobles se reduce la superficie central de plementería y se gana en resistencia. Es de complicada geometría esférica y cuadrada a la vez: bóveda pseudo-vaída (esférica solo hasta los arcos exteriores) y plementería lateral adaptándose a la planta cuadrada. Supone la fusión de la antigüedad clásica con la tradición hispanomusulmana. Como referencia, se estudia sucintamente la Capilla Benavides en Baeza - Jaén-, obra de Andrés de Vandelvira e incluida en el tratado de arquitectura de su hijo Alonso, la cual plantea un gran espacio cuadrado cubierto por una bóveda vaída y reforzada por 4 arcos entrecruzados.