On Cantor sets and doubling measures

For a large class of Cantor sets on the real-line, we find sufficient and necessary conditions implying that a set has positive (resp. null) measure for all doubling measures of the real-line. We also discuss same type of questions for atomic doubling measures defined on certain midpoint Cantor sets.Comment: to apper in J. Math. Anal. App

AU Pegasi revisited: period evolution and orbital elements of a peculiar Type II Cepheid

New analysis on the period changes of Type II Cepheid AU Peg is presented. The available recent photometric measurements were collected and analysed with various methods. The period has been found to be constant for certain time intervals, although increasing in overall, in contrast with the previous expectations, which suggested the period change to reverse. Superimposed on overall period change, a formerly unknown periodic behaviour has been found in the $O-C$ diagram of AU Peg, which cannot be matched to the radial velocity variations. Since the Cepheid is a member of a binary system, it is probable that the unusual period change is in connection with the companion's tidal force. The orbital elements of the binary system involving AU Peg have been also revised.Comment: 8 pages, 8 figures, accepted for publication in Astrophysics and Space Scienc

Objects and polymorphism in system programming languages: a new approach

A low-level data structure always has a predefined representation which does not fit into an object of traditional object-oriented languages, where explicit type tag denotes its dynamic type. This is the main reason why the advanced features of object-oriented programming cannot be fully used at the lowest level. On the other hand, the hierarchy of low-level data structures is very similar to class-trees, but instead of an explicit tag-field the value of the object determines its dynamic type. Another peculiar requirement in system programming is that some classes have to be polymorphic by-value with their ancestor: objects must fit into the space of a superclass instance. In our paper we show language constructs which enable the system programmer to handle all data structures as objects, and exploit the advantages of object-oriented programming even at the lowest level. Our solution is based on Predicate Dispatching, but adopted to the special needs of system programming. The techniques we show also allow fo r some classes to be polymorphic by-value with their super. We also describe how to implement these features without losing modularity

The effect of emission lines on the performance of photometric redshift estimation algorithms

We investigate the effect of strong emission line galaxies on the performance of empirical photometric redshift estimation methods. In order to artificially control the contribution of photometric error and emission lines to total flux, we develop a PCA-based stochastic mock catalogue generation technique that allows for generating infinite signal-to-noise ratio model spectra with realistic emission lines on top of theoretical stellar continua. Instead of running the computationally expensive stellar population synthesis and nebular emission codes, our algorithm generates realistic spectra with a statistical approach, and - as an alternative to attempting to constrain the priors on input model parameters - works by matching output observational parameters. Hence, it can be used to match the luminosity, colour, emission line and photometric error distribution of any photometric sample with sufficient flux-calibrated spectroscopic follow-up. We test three simple empirical photometric estimation methods and compare the results with and without photometric noise and strong emission lines. While photometric noise clearly dominates the uncertainty of photometric redshift estimates, the key findings are that emission lines play a significant role in resolving colour space degeneracies and good spectroscopic coverage of the entire colour space is necessary to achieve good results with empirical photo-z methods. Template fitting methods, on the other hand, must use a template set with sufficient variation in emission line strengths and ratios, or even better, first estimate the redshift empirically and fit the colours with templates at the best-fit redshift to calculate the K-correction and various physical parameters.Comment: 18 pages, 19 figures, Accepted for publication in MNRA

Closed sets with the Kakeya property

We say that a planar set $A$ has the Kakeya property if there exist two different positions of $A$ such that $A$ can be continuously moved from the first position to the second within a set of arbitrarily small area. We prove that if $A$ is closed and has the Kakeya property, then the union of the nontrivial connected components of $A$ can be covered by a null set which is either the union of parallel lines or the union of concentric circles. In particular, if $A$ is closed, connected and has the Kakeya property, then $A$ can be covered by a line or a circle