7,307 research outputs found
On conjectures and problems of Ruzsa concerning difference graphs of S-units
Given a finite nonempty set of primes S, we build a graph with
vertex set by connecting x and y if the prime divisors of both the
numerator and denominator of x-y are from S. In this paper we resolve two
conjectures posed by Ruzsa concerning the possible sizes of induced
nondegenerate cycles of , and also a problem of Ruzsa concerning
the existence of subgraphs of which are not induced subgraphs.Comment: 15 page
New RR Lyrae variables in binary systems
Despite their importance, very few RR Lyrae (RRL) stars have been known to
reside in binary systems. We report on a search for binary RRL in the OGLE-III
Galactic bulge data. Our approach consists in the search for evidence of the
light-travel time effect in so-called observed minus calculated ()
diagrams. Analysis of 1952 well-observed fundamental-mode RRL in the OGLE-III
data revealed an initial sample of 29 candidates. We used the recently released
OGLE-IV data to extend the baselines up to 17 years, leading to a final sample
of 12 firm binary candidates. We provide diagrams and binary parameters
for this final sample, and also discuss the properties of 8 additional
candidate binaries whose parameters cannot be firmly determined at present. We
also estimate that per cent of the RRL reside in binary systems.Comment: MNRAS Letters, in pres
Stratigraphy of a Middle Jurassic — Lower Cretaceous sequence N of Zobákpuszta, Mecsek Mts., Hungary
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