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

The characterization of operators preserving primitivity for matrix k-tuples

AbstractWe obtain a complete characterization of surjective additive operators acting on the Cartesian product of several matrix spaces over an antinegative semiring without zero divisors, which map primitive matrix k-tuples to primitive matrix k-tuples

Paternal Psychosocial Characteristics and Corporal Punishment of their 3-Year Old Children

This study uses data from 2,309 biological fathers who participated in the Fragile Families and Child Wellbeing Study (FFCWS) to examine associations between psychosocial characteristics and levels of corporal punishment (CP) toward their 3-year old children over the past month. Results indicate that 61% of the fathers reported no CP over the past month, 23% reported using CP once or twice, and 16% reported using CP a few times in the past month or more. In multivariate models controlling for important socio-demographic factors as well as characteristics of the child, fathers’ parenting stress, major depression, alcohol use, and drug use were significantly associated with greater use of CP, whereas involvement with the child and generalized anxiety order were not. Girls were less likely to be the recipient of CP than boys, and child externalizing behavior problems but not internalizing behavior problems were associated with more CP.Fragile families, childbearing, nonmarital childbearing, fartherhood, fathers, corporal punishment, behavior problems, stress, depression

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

An Investigation into the Radial Velocity Variations of CoRoT-7

CoRoT-7b, the first transiting ``superearth'' exoplanet, has a radius of 1.7 R_Earth and a mass of 4.8 M_Earth. Ground-based radial velocity measurements also detected an additional companion with a period of 3.7 days (CoRoT-7c) and a mass of 8.4 M_Earth. The mass of CoRoT-7b is a crucial parameter for planet structure models, but is difficult to determine because CoRoT-7 is a modestly active star and there is at least one additional companion. A Fourier analysis was performed on spectral data for CoRoT-7 taken with the HARPS spectrograph. These data include RV measurements, spectral line bisectors, the full width at half maximum of the cross-correlation function, and Ca II emission. The latter 3 quantities vary due to stellar activity and were used to assess the nature of the observed RV variations. An analysis of a sub-set of the RV measurements where multiple observations were made per night was also used to estimate the RV amplitude from CoRoT-7b that was less sensitive to activity variations. Our analysis indicates that the 0.85-d and 3.7-d RV signals of CoRoT-7b and CoRoT-7c are present in the spectral data with a high degree of statistical significance. We also find evidence for another significant RV signal at 9 days. An analysis of the activity indicator data reveals that this 9-d signal most likely does not arise from activity, but possibly from an additional companion. If due to a planetary companion the mass is m = 19.5 M_Earth, assuming co-planarity with CoRoT-7b. A dynamical study of the three planet system shows that it is stable over several hundred millions of years. Our analysis yields a RV amplitude of 5.04 +/- 1.09 m/s for CoRoT-7b which corresponds to a planet mass of m = 6.9 +/- 1.4 M_Earth. This increased mass would make the planet CoRoT-7b more Earth-like in its internal structure.Comment: 20 pages, 20 figure

A phosphorus-rich polymer as a homogeneous catalyst scavenger

© The Royal Society of Chemistry 2017. A soft polymer network prepared through a phosphane-ene reaction successfully sequestered Rh and Ru from hydrogenation and ring closing metathesis reactions, respectively. Scavenging effectively quenches catalytic activity and ultimately removes \u3e98% of the metal