Open cluster survival within the solar circle: Teutsch 145 and Teutsch 146 star

Teutsch 145 and Teutsch 146 are shown to be open clusters (OCs) orbiting well inside the solar circle, a region where several dynamical processes combine to disrupt most OCs on a time-scale of a few 108 yr. BVI photometry from the GALILEO telescope is used to investigate the nature and derive the fundamental and structural parameters of the optically faint and poorly known OCs Teutsch 145 and 146. These parameters are computed by means of field-star-decontaminated colour-magnitude diagrams and stellar radial density profiles (RDPs). Cluster mass estimates are made based on the intrinsic mass functions (MFs). We derive the ages 200+100(-50) and 400 +/- 100 Myr, and the distances from the Sun d(circle dot) = 2.7 +/- 0.3 and 3.8 +/- 0.2 kpc, respectively, for Teutsch 145 and 146. Their integrated apparent and absolute magnitudes are m(V) approximate to 12.4 and 13.3 and M(V) approximate to -5.6 and -5.3. The MFs (detected for stars with m greater than or similar to 1 M(circle dot)) have slopes similar to Salpeter`s initial mass function. Extrapolated to the H-burning limit, the MFs would produce total stellar masses of similar to 1400 M(circle dot), typical of relatively massive OCs. Both OCs are located deep into the inner Galaxy and close to the Crux-Scutum arm. Since cluster-disruption processes are important, their primordial masses must have been higher than the present-day values. The conspicuous stellar density excess observed in the innermost bin of both RDPs might reflect the dynamical effects induced by a few 108 yr of external tidal stress.

TRANSITIVE CIRCLE EXCHANGE TRANSFORMATIONS WITH FLIPS

We study the existence of transit we exchange transformations with flips defined on the unit circle S(1). We provide a complete answer to the question of whether there exists a transitive exchange transformation of S(1) defined on a subintervals and having f flips.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function phi : S(1) -> R and an endomorphism f : S(1)-> S(1), whose f-invariant probability measures maximize integral phi d mu. We prove that the set of endomorphisms having a f maximizing invariant measure supported on a periodic orbit is C(0) dense.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Evaluation of three indices for biofilm accumulation on complete dentures

Objectives: The objective of this study was to evaluate the accuracy and reproducibility of three complete denture biofilm indices (Prosthesis Hygiene Index; Jeganathan et al. Index; Budtz-J circle divide rgensen Index) by means of a computerised comparison method. Background: Clinical studies into denture hygiene have employed a large number of biofilm indices among their outcome variables. However, the knowledge about the validity of these indices is still scarce. Materials and methods: Sixty-two complete denture wearers were selected. The internal surfaces of the upper complete dentures were stained (5% erythrosine) and photographed. The slides were projected on paper, and the biofilm indices were applied over the photos by means of a scoring method. For the computerised method, the areas (total and biofilm-covered) were measured by dedicated software (Image Tool). In addition, to compare the results of the computerised method and Prosthetic Hygiene Index, a new scoring scale (including four and five graded) was introduced. For the Jeganathan et al. and Budtz-J circle divide rgensen indices, the original scales were used. Values for each index were compared with the computerised method by the Friedman test. Their reproducibility was measured by means of weighed kappa. Significance for both tests was set at 0.05. Results: The indices tested provided similar mean measures but they tended to overestimate biofilm coverage when compared with the computerised method (p < 0.001). Agreement between the Prosthesis Hygiene Index and the computerised method was not significant, regardless of the scale used. Jeghanathan et al. Index showed weak agreement, and consistent results were found for Budtz-Jorgensen Index (kappa = 0.19 and 0.39 respectively). Conclusion: Assessment of accuracy for the biofilm indices showed instrument bias that was similar among the tested methods. Weak inter-instrument reproducibility was found for the indices, except for the Budtz-J circle divide rgensen Index. This should be the method of choice for clinical studies when more sophisticated approaches are not possible.

The old metal-poor open cluster ESO 92-SC05: accreted from a dwarf galaxy ?

The study of old open clusters outside the solar circle can bring constraints on formation scenarios of the outer disc. In particular, accretion of dwarf galaxies has been proposed as a likely mechanism in the area. We use BVI photometry for determining fundamental parameters of the faint open cluster ESO 92-SC05. Colour-magnitude diagrams are compared with Padova isochrones, in order to derive age, reddening and distance. We derive a reddening E(B - V) = 0.17, and an old age of similar to 6.0 Gyr. It is one of the rare open clusters known to be older than 5 Gyr. A metallicity of Z similar to 0.004 or [M/H] similar to -0.7 is found. The rather low metallicity suggests that this cluster might be the result of an accretion episode of a dwarf galaxy.

On the mass distribution of neutron stars

The distribution of masses for neutron stars is analysed using the Bayesian statistical inference, evaluating the likelihood of the proposed Gaussian peaks by using 54 measured points obtained in a variety of systems. The results strongly suggest the existence of a bimodal distribution of the masses, with the first peak around 1.37 M(circle dot) and a much wider second peak at 1.73 M(circle dot). The results support earlier views related to the different evolutionary histories of the members for the first two peaks, which produces a natural separation (even if no attempt to `label` the systems has been made here). They also accommodate the recent findings of similar to M(circle dot) masses quite naturally. Finally, we explore the existence of a subgroup around 1.25 M(circle dot), finding weak, if any, evidence for it. This recently claimed low-mass subgroup, possibly related to the O-Mg-Ne core collapse events, has a monotonically decreasing likelihood and does not stand out clearly from the rest of the sample.

Gas streaming motions towards the nucleus of M81

We present two-dimensional stellar and gaseous kinematics of the inner 120 x 250 pc2 of the LINER/Seyfert 1 galaxy M81, from optical spectra obtained with the Gemini Multi-Object Spectrograph (GMOS) integral field spectrograph on the Gemini-North telescope at a spatial resolution of approximate to 10 pc. The stellar velocity field shows circular rotation and, overall, is very similar to the published large-scale velocity field, but deviations are observed close to the minor axis which can be attributed to stellar motions possibly associated with a nuclear bar. The stellar velocity dispersion of the bulge is 162 +/- 15 km s-1, in good agreement with previous measurements and leading to a black hole mass of M(BH) = 5.5+3.6(-2.0) x 107 M(circle dot) based on the M(BH)-Sigma relationship. The gas kinematics is dominated by non-circular motions and the subtraction of the stellar velocity field reveals blueshifts of approximate to-100 km s-1 on the far side of the galaxy and a few redshifts on the near side. These characteristics can be interpreted in terms of streaming towards the centre if the gas is in the plane. On the basis of the observed velocities and geometry of the flow, we estimate a mass inflow rate in ionized gas of approximate to 4.0 x 10-3 M(circle dot) yr-1, which is of the order of the accretion rate necessary to power the LINER nucleus of M81. We have also applied the technique of principal component analysis (PCA) to our data, which reveals the presence of a rotating nuclear gas disc within approximate to 50 pc from the nucleus and a compact outflow, approximately perpendicular to the disc. The PCA combined with the observed gas velocity field shows that the nuclear disc is being fed by gas circulating in the galaxy plane. The presence of the outflow is supported by a compact jet seen in radio observations at a similar orientation, as well as by an enhancement of the [O i]/H alpha line ratio, probably resulting from shock excitation of the circumnuclear gas by the radio jet. With these observations we are thus resolving both the feeding - via the nuclear disc and observed gas inflow, and the feedback - via the outflow, around the low-luminosity active nucleus of M81.