Enumeration of nilpotent loops up to isotopy

We modify tools introduced by Daniel Daly and Petr Vojtechovsky in order to count, for any odd prime q, the number of nilpotent loops of order 2q up to isotopy, instead of isomorphy.Comment: 20 pages; important typos corrected (section 6

Three notes on Petronius

Autor razmatra, prvo, Petr. 61.7 benemoria (čitanje po opšteprimljenoj konjekturi) u vezi s tekstom jednog mozaičnog natpisa iz Afrike; drugo, donosi novih paralela za Petr. 43.8 olim oliorum "odavno"; treće, razmatra oblik i značenje Petr. 52.4 i .6 nugax.The author discusses, firstly, Petr. 61.7 benemoria (a conjectural reading which has won universal acceptance) in connexion with an African inscription in mosaic; secondly, he adduces new parallels to Petr. 43.8 olim oliorum "for quite a while"; thirdly, he discusses the form and meaning of Petr. 52.4 and .6 nugax

02-26-1974 Preliminary Memorandum

***A response has been filed by the State of Virginia. Petr has been given the opportunity under the USDC order in question here to proceed in state habeas on the claim referred by USDC. Petr refused to proceed, desiring to await this Court\u27s determination in this appeal

A Tale of Three Cities : OmegaCAM discovers multiple sequences in the color-magnitude diagram of the Orion Nebula Cluster

Reproduced with permission from Astronomy & Astrophysics, © 2017 ESO. Published by EDP Sciences.As part of the Accretion Discs in H$\alpha$ with OmegaCAM (ADHOC) survey, we imaged in r, i and H-alpha a region of 12x8 square degrees around the Orion Nebula Cluster. Thanks to the high-quality photometry obtained, we discovered three well-separated pre-main sequences in the color-magnitude diagram. The populations are all concentrated towards the cluster's center. Although several explanations can be invoked to explain these sequences we are left with two competitive, but intriguing, scenarios: a population of unresolved binaries with an exotic mass ratio distribution or three populations with different ages. Independent high-resolution spectroscopy supports the presence of discrete episodes of star formation, each separated by about a million years. The stars from the two putative youngest populations rotate faster than the older ones, in agreement with the evolution of stellar rotation observed in pre-main sequence stars younger than 4 Myr in several star forming regions. Whatever the final explanation, our results prompt for a revised look at the formation mode and early evolution of stars in clusters.Peer reviewedFinal Published versio

Killing spinor-valued forms and the cone construction

On a pseudo-Riemannian manifold $\mathcal{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathcal{M}$ and parallel fields on the metric cone over $\mathcal{M}$ for spinor-valued forms

The mean infrared emission of SagittariusA*

(abridged) The massive black hole at the center of the Milky Way, SagittariusA* is, in relative terms, the weakest accreting black hole accessible to observations. At the moment, the mean SED of SgrA* is only known reliably in the radio to mm regimes. The goal of this paper is to provide constraints on the mean emission from SgrA* in the near-to-mid infrared. Excellent imaging quality was reached in the MIR by using speckle imaging combined with holographic image reconstruction, a novel technique for this kind of data. No counterpart of SgrA* is detected at 8.6 microns. At this wavelength, SgrA* is located atop a dust ridge, which considerably complicates the search for a potential point source. An observed 3 sigma upper limit of ~10 mJy is estimated for the emission of SgrA* at 8.6 microns, a tighter limit at this wavelength than in previous work. The de-reddened 3 sigma upper limit, including the uncertainty of the extinction correction, is ~84 mJy . Based on the available data, it is argued that, with currently available instruments, SgrA* cannot be detected in the MIR, not even during flares. At 4.8 and 3.8 microns, on the other hand, SgrA* is detected at all times, at least when considering timescales of a few up to 13 min. We derive well-defined time-averaged, de-reddened flux densities of 3.8+-1.3 mJy at 4.8 microns and 5.0+-0.6 mJy at 3.8 microns. Observations with NIRC2/Keck and NaCo/VLT from the literature provide good evidence that SgrA* also has a fairly well-defined de-reddened mean flux of 0.5-2.5 mJy at wavelengths of 2.1-2.2 microns. We present well-constrained anchor points for the SED of SgrA* on the high-frequency side of the Terahertz peak. The new data are in general agreement with published theoretical SEDs of the mean emission from SgrA*, but we expect them to have an appreciable impact on the model parameters in future theoretical work.Comment: accepted for publication by Astronomy & Astrophysics on 20 June 201

MBM 12: young protoplanetary discs at high galactic latitude

(abridged) We present Spitzer infrared observations to constrain disc and dust evolution in young T Tauri stars in MBM 12, a star-forming cloud at high latitude with an age of 2 Myr and a distance of 275 pc. The region contains 12 T Tauri systems, with primary spectral types between K3 and M6; 5 are weak-line and the rest classical T Tauri stars. We first use MIPS and literature photometry to compile spectral energy distributions for each of the 12 members in MBM 12, and derive their IR excesses. The IRS spectra are analysed with the newly developed two-layer temperature distribution (TLTD) spectral decomposition method. For the 7 T Tauri stars with a detected IR excess, we analyse their solid-state features to derive dust properties such as mass-averaged grain size, composition and crystallinity. We find a spatial gradient in the forsterite to enstatite range, with more enstatite present in the warmer regions. The fact that we see a radial dependence of the dust properties indicates that radial mixing is not very efficient in the discs of these young T Tauri stars. The SED analysis shows that the discs in MBM 12, in general, undergo rapid inner disc clearing, while the binary sources have faster discevolution. The dust grains seem to evolve independently from the stellar properties, but are mildly related to disc properties such as flaring and accretion rates.Comment: 14 pages, accepted by Astronomy and Astrophysic