Connection between type B (or C) and F factorizations and construction of algebras

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.Comment: minor changes, 1 additional reference, final form to be published in JP

High-contrast imaging of Sirius~A with VLT/SPHERE: Looking for giant planets down to one astronomical unit

Sirius has always attracted a lot of scientific interest, especially after the discovery of a companion white dwarf at the end of the 19th century. Very early on, the existence of a potential third body was put forward to explain some of the observed properties of the system. We present new coronagraphic observations obtained with VLT/SPHERE that explore, for the very first time, the innermost regions of the system down to 0.2" (0.5 AU) from Sirius A. Our observations cover the near-infrared from 0.95 to 2.3 $\mu$m and they offer the best on-sky contrast ever reached at these angular separations. After detailing the steps of our SPHERE/IRDIFS data analysis, we present a robust method to derive detection limits for multi-spectral data from high-contrast imagers and spectrographs. In terms of raw performance, we report contrasts of 14.3 mag at 0.2", ~16.3 mag in the 0.4-1.0" range and down to 19 mag at 3.7". In physical units, our observations are sensitive to giant planets down to 11 $M_{Jup}$ at 0.5 AU, 6-7 $M_{Jup}$ in the 1-2 AU range and ~4 $M_{Jup}$ at 10 AU. Despite the exceptional sensitivity of our observations, we do not report the detection of additional companions around Sirius A. Using a Monte Carlo orbital analysis, we show that we can reject, with about 50% probability, the existence of an 8 $M_{Jup}$ planet orbiting at 1 AU. In addition to the results presented in the paper, we provide our SPHERE/IFS data reduction pipeline at http://people.lam.fr/vigan.arthur/ under the MIT license.Comment: 16 pages, 10 figures, accepted for publication in MNRA

UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schr\"odinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) L^p-boundedness properties for the square functions to our Banach valued setting by using \gamma-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property

To What Extent Does Land Use Catchment Lead to the Design of Junction along EDSA?

The coordination of transport and land use have proven to be difficult in the developing world. Three junctions along EDSA (Epifanio de Los Santos Avenue) were analysed and investigated upon how land use affects the behaviour of traffic on a theoretical basis of trip generation. Each junction was modelled on VISSIM, and this paper uses average speed, queue length and average delay as assessment indicators to conduct the comparison. The relationship between the land use pattern and traffic activity was evident in each case study with regard to the occupancy of land. Thus, stronger implementation of policies and better governance is required to alleviate the issues found and raised from each of the case studies and literature