B-type supergiants in the Small Magellanic Cloud: rotational velocities and implications for evolutionary models

High-resolution spectra for 24 SMC and Galactic B-type supergiants have been analysed to estimate the contributions of both macroturbulence and rotation to the broadening of their metal lines. Two different methodologies are considered, viz. goodness-of-fit comparisons between observed and theoretical line profiles and identifying zeros in the Fourier transforms of the observed profiles. The advantages and limitations of the two methods are briefly discussed with the latter techniques being adopted for estimating projected rotational velocities ( v sin i) but the former being used to estimate macroturbulent velocities. The projected rotational velocity estimates range from approximately 20 to 60 kms(-1), apart from one SMC supergiant, Sk 191, with a v sin i similar or equal to 90 km s(-1). Apart from Sk 191, the distribution of projected rotational velocities as a function of spectral type are similar in both our Galactic and SMC samples with larger values being found at earlier spectral types. There is marginal evidence for the projected rotational velocities in the SMC being higher than those in the Galactic targets but any differences are only of the order of 5 - 10 km s(-1), whilst evolutionary models predict differences in this effective temperature range of typically 20 to 70 km s(-1). The combined sample is consistent with a linear variation of projected rotational velocity with effective temperature, which would imply rotational velocities for supergiants of 70 kms(-1) at an effective temperature of 28 000 K ( approximately B0 spectral type) decreasing to 32 km s(-1) at 12 000 K (B8 spectral type). For all targets, the macroturbulent broadening would appear to be consistent with a Gaussian distribution ( although other distributions cannot be discounted) with an 1/e half-width varying from approximately 20 km s(-1) at B8 to 60 km s(-1) at B0 spectral types.

Nature of quantum measurement for quantities not represented by Hermitian operators

In the case of a simple quantum system, we investigate the possibility of defining meaningful probabilities for a quantity that cannot be represented by a Hermitian operator. We find that the consistent-histories approach, recently applied to the case of quantum traversal time [N. Yamada, Phys. Rev. Lett. 83, 3350 (1999)], does not provide a suitable criterion and we dispute Yamada's claim of finding a simple solution to the tunneling-time problem. Rather, we define the probabilities for certain types of generally nonorthogonal decomposition of the system's quantum state. These relate to the interaction between the system and its environment, can be observed in a generalized von Neumann measurement, and are consistent with a particular class of positive-operator-valued measures.

Epipolar geometry estimation based on evolutionary agents

This paper presents a novel approach based on the use of evolutionary agents for epipolar geometry estimation. In contrast to conventional nonlinear optimization methods, the proposed technique employs each agent to denote a minimal subset to compute the fundamental matrix, and considers the data set of correspondences as a 1D cellular environment, in which the agents inhabit and evolve. The agents execute some evolutionary behavior, and evolve autonomously in a vast solution space to reach the optimal (or near optima) result. Then three different techniques are proposed in order to improve the searching ability and computational efficiency of the original agents. Subset template enables agents to collaborate more efficiently with each other, and inherit accurate information from the whole agent set. Competitive evolutionary agent (CEA) and finite multiple evolutionary agent (FMEA) apply a better evolutionary strategy or decision rule, and focus on different aspects of the evolutionary process. Experimental results with both synthetic data and real images show that the proposed agent-based approaches perform better than other typical methods in terms of accuracy and speed, and are more robust to noise and outliers.

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Universal elements for non-linear operators and their applications

We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T and M_g is universal, where M_g is multiplication by a generating element of a compact topological group. We use this result to characterize R_+-supercyclic operators and to show that whenever T is a supercyclic operator and z_1,...,z_n are pairwise different non-zero complex numbers, then the operator z_1T\oplus ... \oplus z_n T is cyclic. The latter answers affirmatively a question of Bayart and Matheron.

Non-weakly supercyclic operators

Several methods based on an easy geometric argument are provided to prove that a given operator is not weakly supercyclic. The methods apply to different kinds of operators like composition operators or bilateral weighted shifts. In particular, it is shown that the classical Volterra operator is not weakly supercyclic on any of the LP [0, 1] spaces, 1

Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.