1,095 research outputs found

    Determinantal representations of hyperbolic plane curves: An elementary approach

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    If a real symmetric matrix of linear forms is positive definite at some point, then its determinant is a hyperbolic hypersurface. In 2007, Helton and Vinnikov proved a converse in three variables, namely that every hyperbolic plane curve has a definite real symmetric determinantal representation. The goal of this paper is to give a more concrete proof of a slightly weaker statement. Here we show that every hyperbolic plane curve has a definite determinantal representation with Hermitian matrices. We do this by relating the definiteness of a matrix to the real topology of its minors and extending a construction of Dixon from 1902. Like Helton and Vinnikov's theorem, this implies that every hyperbolic region in the plane is defined by a linear matrix inequality.Comment: 15 pages, 4 figures, minor revision

    Constraints on the Atmospheric Circulation and Variability of the Eccentric Hot Jupiter XO-3b

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    We report secondary eclipse photometry of the hot Jupiter XO-3b in the 4.5~μ\mum band taken with the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses. We fit these data simultaneously with two transits observed in the same band in order to obtain a global best-fit secondary eclipse depth of 0.1580±0.0036%0.1580\pm 0.0036\% and a center of eclipse phase of 0.67004±0.000130.67004\pm 0.00013 . We assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05%\%. The new secondary eclipse observations extend the total baseline from one and a half years to nearly three years, allowing us to place an upper limit on the periastron precession rate of 2.9×10−32.9\times 10^{-3} degrees/day the tightest constraint to date on the periastron precession rate of a hot Jupiter. We use the new transit observations to calculate improved estimates for the system properties, including an updated orbital ephemeris. We also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit-to-orbit variability of an eccentric hot Jupiter and demonstrate the consistency of multiple-epoch Spitzer observations.Comment: 14 pages, 11 figures, published by Ap

    Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models

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    We show that every rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration. The fibers of these Landau-Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau-Ginzburg model coming from a toric degeneration.Comment: v3: minor corrections for final versio

    Perception of academic learning environments and perceived impact on articulation of employability; a mixed methods study

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    This study reports on the findings of a mixed methods study that was undertaken to establish student perceptions of academic learning environments and the perceived impact of these on their articulation of employability skills. This was so student perspectives on employability could be used to inform reflection on pedagogic practices for their educators in higher education. Using a purposive sample of 250 students based in a recently modernised Sciences Complex Building in a Higher Education Institution (HEI), the study was cross sectional and descriptive by design. The social learning spaces researched were perceived by participants to provide optimal academic learning environments for their development of knowledge, skills and professionalism through certain signature pedagogies as they progressed through their programmes of study. Students also expressed the view that their acquisition of functional skills were significantly more important than any personal attributes/characteristics that they brought to programmes. What also mattered was whether the importance of certain graduate skills to the workplace had been made explicit to them so that they could see the relevance of their studies to practice. In defining ‘graduateness’, in employability terms the research Hayes et al. Perception of academic learning environments and perceived impact on articulation of employability skills Journal of Learning Development in Higher Education, Issue 10: November 2016 2 concluded that it was necessary to consider how it was shaped by the context of delivery of subject disciplines, stages of academic progression, and the use of social learning spaces, as they all had a significant impact on the perceptions students held about their potential employability upon completion of their academic programmes. Keywords: learning environments; employability; signature pedagogies; situated cognition; problem based learning

    3.6 and 4.5 μ\mum Spitzer{\it Spitzer} Phase Curves of the Highly-Irradiated Hot Jupiters WASP-19b and HAT-P-7b

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    We analyze full-orbit phase curve observations of the transiting hot Jupiters WASP-19b and HAT-P-7b at 3.6 and 4.5 μ\mum obtained using the Spitzer Space Telescope. For WASP-19b, we measure secondary eclipse depths of 0.485%±0.024%0.485\%\pm 0.024\% and 0.584%±0.029%0.584\%\pm 0.029\% at 3.6 and 4.5 μ\mum, which are consistent with a single blackbody with effective temperature 2372±602372 \pm 60 K. The measured 3.6 and 4.5 μ\mum secondary eclipse depths for HAT-P-7b are 0.156%±0.009%0.156\%\pm 0.009\% and 0.190%±0.006%0.190\%\pm 0.006\%, which are well-described by a single blackbody with effective temperature 2667±572667\pm 57 K. Comparing the phase curves to the predictions of one-dimensional and three-dimensional atmospheric models, we find that WASP-19b's dayside emission is consistent with a model atmosphere with no dayside thermal inversion and moderately efficient day-night circulation. We also detect an eastward-shifted hotspot, suggesting the presence of a superrotating equatorial jet. In contrast, HAT-P-7b's dayside emission suggests a dayside thermal inversion and relatively inefficient day-night circulation; no hotspot shift is detected. For both planets, these same models do not agree with the measured nightside emission. The discrepancies in the model-data comparisons for WASP-19b might be explained by high-altitude silicate clouds on the nightside and/or high atmospheric metallicity, while the very low 3.6 μ\mum nightside planetary brightness for HAT-P-7b may be indicative of an enhanced global C/O ratio. We compute Bond albedos of 0 (<0.08<0.08 at 1σ1\sigma) and 0.38±0.060.38\pm 0.06 for WASP-19b and HAT-P-7b, respectively. In the context of other planets with thermal phase curve measurements, we show that WASP-19b and HAT-P-7b fit the general trend of decreasing day-night heat recirculation with increasing irradiation.Comment: 22 pages, 29 figures, accepted by Ap

    Climate and transportation policy sequencing in California and Quebec

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    We compare flexible low-carbon regulations in the transportation sector and their interaction and sequencing with greenhouse gas emissions trading systems in California and Quebec. As momentum builds for greater climate action, it is necessary to better understand how carbon markets and other low-carbon transportation policies influence one another. First, we demonstrate that emissions trading between California and Quebec has been asymmetric, with linking having little influence on carbon prices from California\u27s perspective but leading to a considerable cost reduction from the point of view of Quebec. Second, we present evidence that Quebec has replicated many of California\u27s low-carbon transportation policies that promote increased electric vehicle use, where Quebec has an advantage, while deferring to the Canadian federal government with regard to policies that incentivize the production of other low-carbon transportation fuels. Third, we demonstrate that while the stringency of the policy mix of carbon pricing and flexible transportation regulations has increased over time in both jurisdictions, the stringency of flexible regulations has been more aggressively ratcheted up and is expected to continue to dominate. Overall, our findings suggest that the policy sequence observed in California and Quebec can be attributed to the political economy benefits that the selected instruments confer to governments seeking to move from the middle towards the bottom of the clean technology experience curve. We discuss a number of important research questions and associated hypotheses emanating from our findings, which provide the basis for more in-depth studies involving a larger universe of cases and economic sectors

    Spitzer Secondary Eclipse Observations of Five Cool Gas Giant Planets and Empirical Trends in Cool Planet Emission Spectra

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    In this work we present Spitzer 3.6 and 4.5 micron secondary eclipse observations of five new cool (<1200 K) transiting gas giant planets: HAT-P-19b, WASP-6b, WASP-10b, WASP-39b, and WASP-67b. We compare our measured eclipse depths to the predictions of a suite of atmosphere models and to eclipse depths for planets with previously published observations in order to constrain the temperature- and mass-dependent properties of gas giant planet atmospheres. We find that the dayside emission spectra of planets less massive than Jupiter require models with efficient circulation of energy to the night side and/or increased albedos, while those with masses greater than that of Jupiter are consistently best-matched by models with inefficient circulation and low albedos. At these relatively low temperatures we expect the atmospheric methane to CO ratio to vary as a function of metallicity, and we therefore use our observations of these planets to constrain their atmospheric metallicities. We find that the most massive planets have dayside emission spectra that are best-matched by solar metallicity atmosphere models, but we are not able to place strong constraints on metallicities of the smaller planets in our sample. Interestingly, we find that the ratio of the 3.6 and 4.5 micron brightness temperatures for these cool transiting planets is independent of planet temperature, and instead exhibits a tentative correlation with planet mass. If this trend can be confirmed, it would suggest that the shape of these planets' emission spectra depends primarily on their masses, consistent with the hypothesis that lower-mass planets are more likely to have metal-rich atmospheres.Comment: 16 pages, 14 figures, accepted for publication in Ap
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