D-harmonic distributions and global hypoellipticity on nilmanifolds

Let M = Γ\N be a compact nilmanifold. A system of differential operators D1, …, Dk on M is globally hypoelliptic (GH) if when D1f = g1,…, Dkf=gk with f ∈ D’ (M), g1, …, gk ∈ C∞ (M) then f ∈ C∞ (M). Let X1, …, Xk be real vector fields on M induced by the Lie algebra N of N. We study the relationships between (GH) of the system X1, …, Xk on M, (GH) of the operator D = X12 + … + Xk2, the constancy of D-harmonic distributions on M, and related algebraic conditions on X1, …, Xk ∈ N. © 1991 by Pacific Journal of Mathematics

Voyager 2 Observations Near the Heliopause

This paper discusses plasma characteristics in the heliosheath region before the heliopause (HP), at the HP, and in the very local interstellar medium (VLISM). The Voyager 2 (V2) HP was a sharp boundary where the radial plasma currents went to background levels. The radial flow speeds derived from 53-85 keV (V1) and 28-43 keV (V2) ion data decreased about 2 years (8 AU) before the HP at V1 and V2. A speed decrease was not observed by the V2 plasma instrument until 160 days (1.5 AU) before the HP crossing when V2 entered the plasma boundary layer where the plasma density and 28-43 keV ion intensity increased. We determine the HP orientation based on the plasma flow and magnetic field data and show these observations are consistent with models predicting a blunt HP. Variations are observed in the currents observed in the VLISM; roll data from this region clearly show the plasma instrument observes the interstellar plasma and may be consistent with larger than expected VLISM temperatures near the HP

Voyager 2 Observations Near the Heliopause

This paper discusses plasma characteristics in the heliosheath region before the heliopause (HP), at the HP, and in the very local interstellar medium (VLISM). The Voyager 2 (V2) HP was a sharp boundary where the radial plasma currents went to background levels. The radial flow speeds derived from 53-85 keV (V1) and 28-43 keV (V2) ion data decreased about 2 years (8 AU) before the HP at V1 and V2. A speed decrease was not observed by the V2 plasma instrument until 160 days (1.5 AU) before the HP crossing when V2 entered the plasma boundary layer where the plasma density and 28-43 keV ion intensity increased. We determine the HP orientation based on the plasma flow and magnetic field data and show these observations are consistent with models predicting a blunt HP. Variations are observed in the currents observed in the VLISM; roll data from this region clearly show the plasma instrument observes the interstellar plasma and may be consistent with larger than expected VLISM temperatures near the HP

Observations of Energetic Ions and Electrons in the Distant Heliosphere: 2001 – 2005.0

As Voyager 1 (V1) moves closer to the heliospheric termination shock (TS), a new energetic particle population is observed: Termination Shock Particle events (TSP). Interplanetary disturbances in the form of merged interaction regions (MIRs) — identified using Voyager 2 (V2) data — have a major effect on the V1 TSP events from their onset to termination along with triggering episodic increases in higher energy ions (35 MeV H) and MeV electrons. The nature of these interactions appear to evolve as V1 moves closer to the TS

Sequenceserver: A Modern Graphical User Interface for Custom BLAST Databases

Comparing newly obtained and previously known nucleotide and amino-acid sequences underpins modern biological research. BLAST is a well-established tool for such comparisons but is challenging to use on new data sets. We combined a user-centric design philosophy with sustainable software development approaches to create Sequenceserver, a tool for running BLAST and visually inspecting BLAST results for biological interpretation. Sequenceserver uses simple algorithms to prevent potential analysis errors and provides flexible text-based and visual outputs to support researcher productivity. Our software can be rapidly installed for use by individuals or on shared servers

Low Luminosity Type II Supernovae: Spectroscopic and Photometric Evolution

In this paper we present spectroscopic and photometric observations for four core collapse supernovae (SNe), namely SNe 1994N, 1999br, 1999eu and 2001dc. Together with SN 1997D, we show that they form a group of exceptionally low-luminosity events. These SNe have narrow spectral lines (indicating low expansion velocities) and low luminosities at every phase (significantly lower than those of typical core-collapse supernovae). The very low luminosity during the ^{56}Co radioactive decay tail indicates that the mass of ^{56}Ni ejected during the explosion is much smaller (M(Ni) ~ 2-8 x 10^{-3} Mo) than the average (M(Ni) ~ 6-10 x 10^{-2} Mo). Two supernovae of this group (SN 1999br and SN 2001dc) were discovered very close to the explosion epoch, allowing us to determine the lengths of their plateaux (~ 100 days) as well as establishiing the explosion epochs of the other, less-completely observed SNe. It is likely that this group of SNe represent the extreme low-luminosity tail of a single continuous distribution of SN II-P events. Their kinetic energy is also exceptionally low. Although an origin from low mass progenitors has also been proposed for low-luminosity core-collapse SNe, recent work provides evidence in favour of the high mass progenitor scenario. The incidence of these low--luminosity SNe could be as high as 4-5$$ of all type II SNe.Comment: 23 pages, 26 figures, accepted for publication in MNRA