On the Gibson Bounds over Finite Fields

2010 Mathematics Subject Classification: 15A15, 15A04.We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of the upper Gibson barrier for the conversion and establish the lower convertibility barrier.* The work on this project is partially supported by the grants MD-2502.2012.1 and RFBR 12-01-00140

Lengths of quasi-commutative pairs of matrices

In this paper we discuss some partial solutions of the length conjecture which describes the length of a generating system for matrix algebras. We consider mainly the algebras generated by two matrices which are quasi-commuting. It is shown that in this case the length function is linearly bounded. We also analyze which particular natural numbers can be realized as the lengths of certain special generating sets and prove that for commuting or product-nilpotent pairs all possible numbers are realizable, however there are non-realizable values between lower and upper bounds for the other quasi-commuting pairs. In conclusion we also present several related open problems

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first Super-Earth with measured radius

We report the discovery of very shallow (DF/F = 3.4 10-4), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as due to the presence of a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We use CoRoT color information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy and preliminary results from Radial Velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star are derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. We examine carefully all conceivable cases of false positives, and all tests performed support the planetary hypothesis. Blends with separation larger than 0.40 arcsec or triple systems are almost excluded with a 8 10-4 risk left. We conclude that, as far as we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 10-5 day and a radius of Rp = 1.68 +/- 0.09 REarth. Analysis of preliminary radial velocity data yields an upper limit of 21 MEarth for the companion mass, supporting the finding. CoRoT-7b is very likely the first Super-Earth with a measured radius.Comment: Accepted in Astronomy and Astrophysics; typos and language corrections; version sent to the printer w few upgrade

Aftercare service development for children in residential treatment

Increasingly, aftercare services for children returning home from residential treatment are recognized as vital to maintain a child's gains. However, to date, specific knowledge about effective aftercare services, as well as the actual delivery of such services continue to require development. This paper describes an empirically-based, concrete aftercare program that addresses these concerns.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44267/1/10566_2005_Article_BF01184759.pd

The places parents go: understanding the breadth, scope, and experiences of activity spaces for parents

The final publication is available at Springer via https://doi.org/10.1007/s10708-015-9690-yNeighborhood environments are related to parenting behaviors, which in turn have a life-long effect on children’s health and well-being. Activity spaces, which measure individual routine patterns of movement, may be helpful in assessing how physical and social environments shape parenting. In this study we use qualitative data and GIS mapping from four California cities to examine parental activity spaces. Parents described a number of factors that shape their activity spaces including caregiving status, the age of their children, and income. Parental activity spaces also varied between times (weekends vs. weekdays) and places (adult-only vs. child-specific places). Knowing how to best capture and study parental activity spaces could identify mechanisms by which environmental factors influence parenting behaviors and child health

The geometric albedo of the hot Jupiter HD 189733b measured with CHEOPS

Context. Measurements of the occultation of an exoplanet at visible wavelengths allow us to determine the reflective properties of a planetary atmosphere. The observed occultation depth can be translated into a geometric albedo. This in turn aids in characterising the structure and composition of an atmosphere by providing additional information on the wavelength-dependent reflective qualities of the aerosols in the atmosphere. Aims. Our aim is to provide a precise measurement of the geometric albedo of the gas giant HD 189733b by measuring the occultation depth in the broad optical bandpass of CHEOPS (350 - 1100 nm). Methods. We analysed 13 observations of the occultation of HD 189733b performed by CHEOPS utilising the Python package PyCHEOPS. The resulting occultation depth is then used to infer the geometric albedo accounting for the contribution of thermal emission from the planet. We also aid the analysis by refining the transit parameters combining observations made by the TESS and CHEOPS space telescopes. Results. We report the detection of an $24.7 \pm 4.5$ ppm occultation in the CHEOPS observations. This occultation depth corresponds to a geometric albedo of $0.076 \pm 0.016$. Our measurement is consistent with models assuming the atmosphere of the planet to be cloud-free at the scattering level and absorption in the CHEOPS band to be dominated by the resonant Na doublet. Taking into account previous optical-light occultation observations obtained with the Hubble Space Telescope, both measurements combined are consistent with a super-stellar Na elemental abundance in the dayside atmosphere of HD 189733b. We further constrain the planetary Bond albedo to between 0.013 and 0.42 at 3$\sigma$ confidence.Comment: 17 pages, 10 figures, accepted for publication in A&

CHEOPS geometric albedo of the hot Jupiter HD 209458 b

Funding: P.F.L.M. acknowledges support from STFC research grant number ST/M001040/1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project Four Aces. grant agreement No 724427).We report the detection of the secondary eclipse of the hot Jupiter HD 209458 b in optical/visible light using the CHEOPS space telescope. Our measurement of 20.4-3.3+3.2 parts per million translates into a geometric albedo of Ag = 0.096 ± 0.016. The previously estimated dayside temperature of about 1500 K implies that our geometric albedo measurement consists predominantly of reflected starlight and is largely uncontaminated by thermal emission. This makes the present result one of the most robust measurements of Ag for any exoplanet. Our calculations of the bandpassintegrated geometric albedo demonstrate that the measured value of Ag is consistent with a cloud-free atmosphere, where starlight is reflected via Rayleigh scattering by hydrogen molecules, and the water and sodium abundances are consistent with stellar metallicity. We predict that the bandpass-integrated TESS geometric albedo is too faint to detect and that a phase curve of HD 209458 b observed by CHEOPS would have a distinct shape associated with Rayleigh scattering if the atmosphere is indeed cloud free.Publisher PDFPeer reviewe