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 the variable AGB star π1\pi^1 Gruis

Observations of the $^{12}$CO(3-2) emission of the circumstellar envelope (CSE) of the variable star $\pi^1$ 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 $^{12}$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

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

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 $\sim$100 and $\sim$350 au from the stars using ALMA observations of the SiO ($\nu$=0, $J$=5-4) and CO ($\nu$=0, $J$=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 $\sim$5 to 10 au away from Mira A.Comment: 20 pages, 17 figures, accepted for publication in MNRA