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