Dihedral Quintic Fields with a Power Basis

It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p

The use of real time digital simulation and hardware in the loop to de-risk novel control algorithms

Low power demonstrators are commonly used to validate novel control algorithms. However, the response of the demonstrator to network transients and faults is often unexplored. The importance of this work has, in the past, justified facilities such as the T45 Shore Integration Test Facility (SITF) at the Electric Ship Technology Demonstrator (ESTD). This paper presents the use of real time digital simulation and hardware in the loop to de-risk a innovative control algorithm with respect to network transients and faults. A novel feature of the study is the modelling of events at the power electronics level (time steps of circa 2 μs) and the system level (time steps of circa 50 μs)

The Prime Ideal Factorization of 2 in Pure Quartic Fields with Index 2

The prime ideal decomposition of 2 in a pure quartic field with field index 2 is determined explicitly.</p

3-quasi-Sasakian manifolds

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update

The Distance to the Cygnus Loop from Hubble Space Telescope Imaging of the Primary Shock Front

We present a Hubble Space Telescope/WFPC2 narrow-band H-alpha image of a region on the northeastern limb of the Cygnus Loop supernova remnant. This location provides a detailed example of where the primary blast wave first encounters the surrounding interstellar medium. The filament structure is seen in exquisite detail in this image, which was obtained primarily as an EARLY ACQuisition image for a follow-up spectroscopic program. We compare the HST image to a digitized version of the POSS-I red plate to measure the proper motion of this filament. By combining this value for the proper motion with previous measurements of the shock velocity at this position we find that the distance to the Cygnus Loop is 440 (+130, -100) pc, considerably smaller than the canonical value of 770 pc. We briefly discuss the ramifications of this new distance estimate for our understanding of this prototypical supernova remnant.Comment: 18 pages, 3 Figures (2 JPEG and one Postscript