2,155 research outputs found
Isomorphisms between strongly triangular matrix rings
We describe isomorphisms between strongly triangular matrix rings that were
defined earlier in Berkenmeier et al. (2000) as ones having a complete set of
triangulating idempotents, and we show that the so-called triangulating
idempotents behave analogously to idempotents in semiperfect rings. This study
yields also a way to compute theoretically the automorphism groups of such
rings in terms of corresponding automorphism groups of certain subrings and
bimodules involved in their structure
Divisibility Theory of Commutative Rings and Ideal Distributivity
We begin by investigating the class of commutative unital rings in which no
two distinct elements divide the same elements. We prove that this class forms
a finitely axiomatizable, relatively ideal distributive quasivariety, and it
equals the quasivariety generated by the class of integral domains with trivial
unit group. We end the paper by proving a representation theorem that provides
more evidence to the conjecture that B\'ezout monoids describe exactly the
monoids of finitely generated ideals of commutative unital rings with
distributive ideal lattice
Idempotents and structures of rings
We study a ring containing a complete set of orthogonal idempotents as a
generalized matrix ring via its Peirce decomposition. We focus on the case
where some of the underlying bimodule homomorphisms are zero. Upper and lower
triangular generalized matrix rings are pertinent examples of the class of
rings which we study. The triviality of the particular bimodule homomorphisms
motivates the introduction of three new types of idempotents, namely inner
Peirce trivial idempotents, outer Peirce trivial idempotents and Peirce trivial
idempotents. These idempotents provide the main tools in our investigations.Comment: The version, which has been accepted for publication in Linear and
Multilinear Algebra, replaces the previous version. The only difference from
the previous version is an added referenc
Space reconstruction of the morphology and kinematics of axisymmetric radio sources
The unprecedented quality of the observations available from the Atacama
Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making
the best of them. Reconstructing in space the morphology and kinematics of
radio sources is an underdetermined problem that requires imposing additional
constraints for its solution. The hypothesis of rotational invariance about a
well-defined star axis, which is a good approximation to the description of the
gas envelopes of many evolved stars and protostars, is particularly efficient
in this role. In the first part of the article, a systematic use of simulated
observations allows for identifying the main problems and for constructing
quantities aimed at solving them. In particular the evaluation of the
orientation of the star axis in space and the differentiation between expansion
along the star axis and rotation about it are given special attention. The use
of polar rather than Cartesian sky coordinates is shown to better match the
morphology and kinematics of actual stars. The radial dependence of the gas
density and temperature and the possible presence of velocity gradients are
briefly considered. In the second part, the results obtained in the first part
are applied to a few stars taken as examples with the aim of evaluating their
usefulness when applied to concrete cases. A third part takes stock of what
precedes and formulates some guidelines for modelling the radio emission of
axisymmetric radio sources, limited however to the mathematics and geometry of
the problem, physics considerations being ignored.Comment: 21 pages, 19 figures, published MNRAS 461, 4276 (2016
Correlated oscillations due to similar multi-path effects seen in two widely separated radio telescopes
A multipath mechanism similar to that used in Australia sixty years ago by
the Sea-cliff Interferometer is shown to generate correlations between the
periods of oscillations observed by two distant radio telescopes pointed to the
Sun. The oscillations are the result of interferences between the direct wave
detected in the main antenna lobe and its reflection on ground detected in a
side lobe. A model is made of such oscillations in the case of two
observatories located at equal longitudes and opposite tropical latitudes,
respectively in Ha Noi (Viet Nam) and Learmonth (Australia), where similar
radio telescopes are operated at 1.4 GHz. Simple specular reflection from
ground is found to give a good description of the observed oscillations and to
explain correlations that had been previously observed and for which no
satisfactory interpretation, instrumental or other, had been found.Comment: 7 pages, 8 figures, accepted for publication in PAS
Morphology and kinematics of the gas envelope of the Mira binary W Aquilae
We analyse ALMA observations of the 12CO(3-2) emission of the circumstellar
envelope (CSE) of the Mira variable binary star W Aql. These provide, for the
first time, spatially resolved Doppler velocity spectra of the CSE up to
angular distances to the central star of ~ 5" (meaning some 2000 AU). The
exploratory nature of the observations (only five minutes in each of two
different configurations) does not allow for a detailed modelling of the
properties of the CSE but provides important qualitative information on its
morphology and kinematics. Emission is found to be enhanced along an axis
moving from east/west to north-east/south-west when the angular distance from
the central star projected on the plane of the sky increases from zero to four
arcseconds. In parallel, the Doppler velocity distribution displays asymmetry
along an axis moving from east/west to north-west/south-east. The results are
discussed in the context of earlier observations, in particular of the dust
morphology.Comment: 11 pages, 12 figure
Morphology and kinematics of the gas envelope of Mira Ceti
Observations of 12CO(3-2) emission of the circumbinary envelope of Mira Ceti,
made by ALMA are analysed. The observed Doppler velocity distribution is made
of three components: a blue-shifted south-eastern arc, which can be described
as a ring in slow radial expansion, ~1.7 km/s, making an angle of ~50 deg with
the plane of the sky and born some 2000 years ago; a few arcs, probably born at
the same epoch as the blue-shifted arc, all sharing Doppler velocities
red-shifted by approximately 3 +/- 2 km/s with respect to the main star; the
third, central region dominated by the circumbinary envelope, displaying two
outflows in the south-western and north-eastern hemispheres. At short distances
from the star, up to ~1.5", these hemispheres display very different
morphologies: the south-western outflow covers a broad solid angle, expands
radially at a rate between 5 and 10 km/s and is slightly red shifted; the
north-eastern outflow consists of two arms, both blue-shifted, bracketing a
broad dark region where emission is suppressed. At distances between ~1.5" and
~2.5" the asymmetry between the two hemispheres is significantly smaller and
detached arcs, particularly spectacular in the north-eastern hemisphere are
present. Close to the stars, we observe a mass of gas surrounding Mira B, with
a size of a few tens of AU, and having Doppler velocities with respect to Mira
B reaching +/-1.5 km/s, which we interpret as gas flowing from Mira A toward
Mira B.Comment: 16 pages, 21 figure
Morphology and kinematics of the gas envelope of the variable AGB star Gruis
Observations of the CO(3-2) emission of the circumstellar envelope
(CSE) of the variable star Gru using the compact array (ACA) of the
ALMA observatory have been recently made accessible to the public. An analysis
of the morphology and kinematics of the CSE is presented with a result very
similar to that obtained earlier for CO(2-1) emission by Chiu et al.
(2006) using the Sub-Millimeter Array. A quantitative comparison is made using
their flared disk model. A new model is presented that provides a significantly
better description of the data, using radial winds and smooth evolutions of the
radio emission and wind velocity from the stellar equator to the poles.Comment: accepted for publication in Research in Astronomy and Astrophysics
(RAA
The protoplanetary disc of HD 163296 as observed by ALMA
HD 163296 is one of the few protoplanetary discs displaying rings in the dust
component. The present work uses ALMA observations of the 0.9 mm continuum
emission having significantly better spatial resolution (~8 au) than previously
available, providing new insight on the morphology of the dust disc and its
double ring structure. The disc is shown to be thin and its position angle and
inclination with respect to the sky plane are accurately measured as are the
locations and shapes that characterize the observed ring/gap structure.
Significant modulation of the intensity of the outer ring emission have been
revealed and discussed. In addition, earlier ALMA observations of the emission
of three molecular lines, CO(2-1), C18O(2-1), and DCO+(3-2), having a
resolution of ~70 au, are used to demonstrate the Keplerian motion of the gas,
found consistent with a central mass of 2.3 solar masses. An upper limit of ~9%
of the rotation velocity is placed on the in-fall velocity. The beam size is
shown to give the dominant contribution to the line widths, accounting for both
their absolute values and their dependence on the distance to the central star.Comment: 17 pages, 21 figures, published in Vietnam Journal of Science,
Technology and Engineerin
Revealing new features of the millimetre emission of the circumbinary envelope of Mira Ceti
We study the morpho-kinematics of the circumbinary envelope of Mira Ceti
between 100 and 350 au from the stars using ALMA observations of
the SiO (=0, =5-4) and CO (=0, =3-2) emissions with the aim of
presenting an accurate and reliable picture of what cannot be ignored when
modelling the dynamics at stake. A critical study of the uncertainties attached
to imaging is presented. The line emissions are shown to be composed of a few
separated fragments. They are described in detail and plausible interpretations
of their genesis are discussed. Evidence for a focusing effect of the Mira A
wind by Mira B over the past century is presented; it accounts for only a small
fraction of the overall observed emission but its accumulation over several
orbital periods may have produced an enhancement of CO emission in the orbital
plane of Mira B. We identify a South-western outflow and give arguments for the
anti-correlation observed between CO and SiO emissions being the result of a
recent mass ejection accompanied by a shock wave. We discuss the failure of
simple scenarios that have been proposed earlier to explain some of the
observed features and comment on the apparent lack of continuity between the
present observations and those obtained in the close environment of the stars.
Evidence is obtained for the presence of large Doppler velocity components near
the line of sight aiming to the star, possibly revealing the presence of
important turbulence at 5 to 10 au away from Mira A.Comment: 20 pages, 17 figures, accepted for publication in MNRA
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