620 research outputs found
On the trapping of stars by a newborn stellar supercluster
Numerical experiments conducted by Fellhauer et al. (MNRAS, 372, 338, 2006)
suggest that a supercluster may capture up to about 40 per cent of its mass
from the galaxy where it belongs. Nevertheless, in those experiments the
cluster was created making appear its mass out of nothing, rather than from
mass already present in the galaxy. Here we use a thought experiment, plus a
few simple computations, to show that the difference between the dynamical
effects of these two scenarios (i.e., mass creation vs. mass concentration) is
actually very important. We also present the results of new numerical
experiments, simulating the formation of the cluster through mass
concentration, that show that trapping depends critically on the process of
cluster formation and that the amounts of gained mass are substantially smaller
than those obtained from mass creation.Comment: 6 pages, 3 figures. Submitted to MNRA
Models of cuspy triaxial stellar systems. III: The effect of velocity anisotropy on chaoticity
In several previous investigations we presented models of triaxial stellar
systems, both cuspy and non cuspy, that were highly stable and harboured large
fractions of chaotic orbits. All our models had been obtained through cold
collapses of initially spherical --body systems, a method that necessarily
results in models with strongly radial velocity distributions. Here we
investigate a different method that was reported to yield cuspy triaxial models
with virtually no chaos. We show that such result was probably due to the use
of an inadequate chaos detection technique and that, in fact, models with
significant fractions of chaotic orbits result also from that method. Besides,
starting with one of the models from the first paper in this series, we
obtained three different models by rendering its velocity distribution much
less radially biased (i.e., more isotropic) and by modifying its axial ratios
through adiabatic compression. All three models yielded much higher fractions
of regular orbits than most of those from our previous work. We conclude that
it is possible to obtain stable cuspy triaxial models of stellar systems whose
velocity distribution is more isotropic than that of the models obtained from
cold collapses. Those models still harbour large fractions of chaotic orbits
and, although it is difficult to compare the results from different models, we
can tentatively conclude that chaoticity is reduced by velocity isotropy.Comment: 11 pages, 14 figures. Accepted for publication in MNRA
Upper and lower nearly (i, j)-continuous multifunctions
In this paper the authors introduce and study upper and lower nearly
(I,J)-continuous multifunctions. Some characterizations and several properties concerning upper (lower) nearly (I,J)-continuous multifunctions are obtained. The results
improves many results in Literature
On the correct computation of all Lyapunov exponents in Hamiltonian dynamical systems
The Lyapunov Characteristic Exponents are a useful indicator of chaos in
astronomical dynamical systems. They are usually computed through a standard,
very efficient and neat algorithm published in 1980. However, for Hamiltonian
systems the expected result of pairs of opposite exponents is not always
obtained with enough precision. We find here why in these cases the initial
order of the deviation vectors matters, and how to sort them in order to obtain
a correct result.Comment: 8 pages, 3 figure
A note on preservation of generalized fredholm spectra in berkani’s sense
In this paper, we study the relationships between the spectra derived from B-Fredholm theory
corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient
conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators
are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an
operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral
properties corresponding to two given operators are the same. As application of our results, we obtain
conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm
theory are the same
Weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions
The purpose of the present paper is to introduce, study
and characterize upper and lower weakly (I, J)-continuous multifunctions and contra (I, J)-continuous multifunctions.
Also, we investigate its relation with another class of continuous multifunctions.
AMS Subject Classification: 54C10, 54C08, 54C05,
54C6
Near ω-continuous multifunctions on bitopological spaces
In this paper, we introduce and study basic characterizations, several properties of upper (lower) nearly (i; j)-!-continuous multifunctions on bitopological space
On the hereditary character of new strong variations of weyl type theorems
Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied
strong variations of Weyl type Theorems. In this paper, we study the behavior of these
strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T
n
(X) ⊆ W for some n ≥ 1, where T ∈ L(X) and
X is an infinite-dimensional complex Banach space. The main purpose of this paper is to
prove that for these subspaces (which generalize the case T
n
(X) closed for some n ≥ 0),
these strong variations of Weyl type theorems are preserved from T to its restriction on W
and vice-versa. As consequence of our results, we give sufficient conditions for which these
strong variations of Weyl type Theorems are equivalent for two given operators. Also, some
applications to multiplication operators acting on the boundary variation space BV [0, 1]
are given
Θ-modifications on weak spaces
In this article, we want to study and investigate if it is
possible to use the notions of weak structures to develop a new theory
of - modi cations in weak spaces and study their properties, nally we
study some forms of weak continuity using this modi cations
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