Extremal problems for matrix-valued polynomials on the unit circle and applications to multivariate stationary sequences

AbstractThe paper is devoted to a matrix generalization of a problem studied by Grenander and Rosenblatt (Trans. Amer. Math. Soc. 76 (1954) 112–126) and deals with the computation of the infimum Δ of ∫TQ∗(z)M(dz)Q(z), where M is a non-negative Hermitian matrix-valued Borel measure on the unit circle T and Q runs through the set of matrix-valued polynomials with prescribed values of some of their derivatives at a finite set J of complex numbers. Under some additional assumptions on M and J, the value of Δ is computed and the results are applied to linear prediction problems of multivariate weakly stationary random sequences. A related truncated problem is studied and further extremal problems are briefly discussed

Hands-On TAROT: Intercontinental use of the TAROT for Education and Public Outreach

The TAROT telescope has for primary goal the search for the prompt optical counterpart of Cosmic Gamma-Ray Bursts. It is a completely autonomous 25cm telescope installed near Nice (France), able to point any location of the sky within 1-2 seconds. The control, scheduling, and data processing activities are completely automated, so the instrument is completely autonomous. In addition to its un-manned modes, we added recently the possibility to remotely control the telescope, as a request of the "Hands-On Universe" (HOU) program for exchange of time within automatic telescopes for the education and public outreach. To this purpose we developed a simple control interface. A webcam was installed to visualize the telescope. Access to the data is possible through a web interface. The images can be processed by the HOU software, a program specially suited for use within the classroom. We experienced these feature during the open days of the University of California Berkeley and the Astronomy Festival of Fleurance (France). We plan a regular use for an astronomy course of the Museum of Tokyo, as well as for French schools. Not only does Hands-On TAROT gives the general public an access to professional astronomy, but it is also a more general tool to demonstrate the use of a complex automated system, the techniques of data processing and automation. Last but not least, through the use of telescopes located in many countries over the globe, a form of powerful and genuine cooperation between teachers and children from various countries is promoted, with a clear educational goal.Comment: 4 pages, Based on a demonstration presented at the ADASS X Conference, Boston, MA, USA, October 2000, to appear in ASP Conf. Serie

A study of the effectiveness of a direct instruction program in mathematics

The purpose of this project was to determine if participation in a year long mathematics direct instructional program would accelerate the rate of mathematical achievement in a group of learning disabled children. The subjects of this study were comprised of five eleven-year-old fifth grade students who were classified as Learning Disabled. Outcome measures utilized included teacher assigned report card grades, a basic skills test, a two-step word problem assessment and the Key Math Diagnostic Arithmetic Test-Revised as a functional measure. The results of this study indicate that, when utilizing formal and functional measures, students make greater progress acquiring facts and problem solving skills in a direct instruction program as implemented in Connecting Math Concepts than in a traditional basal mathematics curriculum

GDPR and E-Commerce

Creative sector companies are likely to be significantly impacted by data protection laws particularly given the fact that they are likely to store, analyse and transfer personal data as part of their day to day operations. This review looks at two general areas that will impact companies i) The new General Data Protection Regulation (‘GDPR’) – the largest overall change in data protection laws in 20 years. This is on most international companies’ agenda’s particularly given the large fines that will accompany it; and ii) Data transfers – the restrictions regarding data transfers inside and outside the EU – which may particularly be complicated post - Brexit. This specific restriction (which applied under previous laws as well as GDPR) creates complexities to global companies and could potentially be further complicated as a result of Brexit

A modern study of HD166734: a massive supergiant system

Aims. HD166734 is an eccentric eclipsing binary system composed of two supergiant O-type stars, orbiting with a 34.5-day period. In this rare configuration for such stars, the two objects mainly evolve independently, following single-star evolution so far. This system provides a chance to study the individual parameters of two supergiant massive stars and to derive their real masses. Methods. An intensive monitoring was dedicated to HD166734.We analyzed mid- and high-resolution optical spectra to constrain the orbital parameters of this system. We also studied its light curve for the first time, obtained in the VRI filters. Finally, we disentangled the spectra of the two stars and modeled them with the CMFGEN atmosphere code in order to determine the individual physical parameters. Results. HD166734 is a O7.5If+O9I(f) binary. We confirm its orbital period but we revise the other orbital parameters. In comparison to what we found in the literature, the system is more eccentric and, now, the hottest and the most luminous component is also the most massive one. The light curve exhibits only one eclipse and its analysis indicates an inclination of 63.0{\deg} $\pm$ 2.7{\deg}. The photometric analysis provides us with a good estimation of the luminosities of the stars, and therefore their exact positions in the Hertzsprung-Russell diagram. The evolutionary and the spectroscopic masses show good agreement with the dynamical masses of 39.5 Msun for the primary and 33.5 Msun for the secondary, within the uncertainties. The two components are both enriched in helium and in nitrogen and depleted in carbon. In addition, the primary also shows a depletion in oxygen. Their surface abundances are however not different from those derived from single supergiant stars, yielding, for both components, an evolution similar to that of single stars.Comment: 13 pages, 13 figures, A&A accepte