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 $N$--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

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

Learning Based on Problems (ABP), Impact of RAEE: A Case Study

Using a case of research as a methodological tool, applied in the research lab with students of the ninth semester of the academic program of chemical engineering (IQ) of the Faculty of chemical sciences and engineering (FCQeI) of the Autonomous University of the State of Morelos (UAEM), analyzed competition to students include scientific concepts acquired, where education is a human process more than verify that cognitive skills according to the approach [1], are developed during the resolution of the case. The results showed that students managed to explain the concepts involved, reflected on his own work and realized what had to be improved. For that, students employed higher order cognitive skills, such as explain, investigate, conclude, argue, make decisions and cognitive skills of low order, such as describing, enunciating, memorize and reproduce