26,761 research outputs found
Constructing Involutive Tableaux with Guillemin Normal Form
Involutivity is the algebraic property that guarantees solutions to an
analytic and torsion-free exterior differential system or partial differential
equation via the Cartan-K\"ahler theorem. Guillemin normal form establishes
that the prolonged symbol of an involutive system admits a commutativity
property on certain subspaces of the prolonged tableau. This article examines
Guillemin normal form in detail, aiming at a more systematic approach to
classifying involutive systems. The main result is an explicit quadratic
condition for involutivity of the type suggested but not completed in Chapter
IV, \S 5 of the book Exterior Differential Systems by Bryant, Chern, Gardner,
Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and
characterizes involutive tableaux.Comment: This article co-evolved with "Degeneracy of the Characteristic
Variety," arXiv:1410.6947 and most notation is shared. However, be aware that
the meaning of the indices i,j,k,l and the space Y is not the same between
these article
The Presidency, War, and Foreign Affairs: Practice Under the Framers
Varje år träder ca 50 000 människor ur Svenska kyrkan och avsäger sig därmed rätten att begravas i Svenska kyrkans ceremoniella ordning och lokaler. Man träder ut ur kyrkans ordning, och ut ur kyrkans rum, men man träder inte in i något annat. Mitt kandidatarbete är ett försök att visa på en annan ordning och andra rum. Every year some 50 000 people exits the Swedish Church and disclaims thus the right to be buried in the Swedish Church ceremonial order and premises. They leave behind the order of the Church, and exits the church room, but they do not enter anything else. My graduate work is an attempt to present an alternative order and alternative rooms
Wind-wind collision in the eta Carinae binary system - III. The HeII 4686 line profile
We modeled the HeII 4686 line profiles observed in the eta Carinae binary
system close to the 2003.5 spectroscopic event, assuming that they were formed
in the shocked gas that flows at both sides of the contact surface formed by
wind-wind collision. We used a constant flow velocity and added turbulence in
the form of a gaussian velocity distribution. We allowed emission from both the
primary and secondary shocks but introduced infinite opacity at the contact
surface, implying that only the side of the contact cone visible to the
observer contributed to the line profile. Using the orbital parameters of the
binary system derived from the 7 mm light curve during the last spectroscopic
event (Paper II) we were able to reproduce the line profiles obtained with the
HST at different epochs, as well as the line mean velocities obtained with
ground based telescopes. A very important feature of our model is that the line
profile depends on the inclination of the orbital plane; we found that to
explain the latitude dependent mean velocity of the line, scattered into the
line of sight by the Homunculus, the orbit inclination should be close to 90
degrees, meaning that it does not lie in the Homunculus equatorial plane, as
usually assumed. This inclination, together with the relative position of the
stars during the spectroscopic events, allowed us to explain most of the
observational features, like the variation of the Purple Haze with the orbital
phase, and to conciliate the X-ray absorption with the postulated shell effect
used to explain the optical and UV light curves.Comment: to appear in the MNRA
Recommended from our members
Tubule density at different sample sites around the stratum medium of horse hoof horn
Microscopic analysis shows that equine hoof wall is composed of distinct phases of tubular and intertubular horn. The tubule density (TD) of hoof horn is found by ascertaining the number of tubules per unit area and is believed to relate to mechanical properties, resistance to wear, “quality”, hardness and moisture content. The straight grid previously used to ascertain the TD of hoof horn may omit certain tubules on both the inner and outer hoof wall as the wall itself is curved. This present study examined whether there was a significant difference in results for TD between using the conventional straight grid method and a novel method using a curved grid. TD was also compared across three sample sites. An analysis of TD from four equal sections (zones) across the hoof wall was also carried out
The Pierre Auger Observatory: Results on Ultra-High Energy Cosmic Rays
The focus of this article is on recent results on ultra-high energy cosmic
rays obtained with the Pierre Auger Observatory. The world's largest instrument
of this type and its performance are described. The observations presented here
include the energy spectrum, the primary particle composition, limits on the
fluxes of photons and neutrinos and a discussion of the anisotropic
distribution of the arrival directions of the most energetic particles.
Finally, plans for the construction of a Northern Auger Observatory in
Colorado, USA, are discussed.Comment: Proceedings of the International Workshop on Advances in Cosmic Ray
Science, Waseda University, Shinjuku, Tokyo, Japan, March 2008; to be
published in the Journal of the Physical Society of Japan (JPSJ) supplemen
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