103,216 research outputs found
The existence of k-radius sequences
Let and be positive integers, and let be an alphabet of size .
A sequence over of length is a \emph{-radius sequence} if any two
distinct elements of occur within distance of each other somewhere in
the sequence. These sequences were introduced by Jaromczyk and Lonc in 2004, in
order to produce an efficient caching strategy when computing certain functions
on large data sets such as medical images.
Let be the length of the shortest -ary -radius sequence. The
paper shows, using a probabilistic argument, that whenever is fixed and
The paper observes that the same argument generalises to the situation when
we require the following stronger property for some integer such that
: any distinct elements of must simultaneously occur
within a distance of each other somewhere in the sequence.Comment: 8 pages. More papers cited, and a minor reorganisation of the last
section, since last version. Typo corrected in the statement of Theorem
Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences
A new ordering, extending the notion of universal cycles of Chung {\em et
al.} (1992), is proposed for the blocks of -uniform set systems. Existence
of minimum coverings of pairs by triples that possess such an ordering is
established for all orders. Application to the construction of short 2-radius
sequences is given, with some new 2-radius sequences found through computer
search.Comment: 18 pages, to appear in Mathematics of Computatio
Sequences of globally regular and black hole solutions in SU(4) Einstein-Yang-Mills theory
SU(4) Einstein-Yang-Mills theory possesses sequences of static spherically
symmetric globally regular and black hole solutions. Considering solutions with
a purely magnetic gauge field, based on the 4-dimensional embedding of
in , these solutions are labelled by the node numbers of
the three gauge field functions , and . We classify the various
types of solutions in sequences and determine their limiting solutions. The
limiting solutions of the sequences of neutral solutions carry charge, and the
limiting solutions of the sequences of charged solutions carry higher charge.
For sequences of black hole solutions with node structure and
, several distinct branches of solutions exist up to critical values
of the horizon radius. We determine the critical behaviour for these sequences
of solutions. We also consider SU(4) Einstein-Yang-Mills-dilaton theory and
show that these sequences of solutions are analogous in most respects to the
corresponding SU(4) Einstein-Yang-Mills sequences of solutions.Comment: 40 pages, 5 tables, 19 Postscript figures, use revtex.st
Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds
We study curvature functionals for immersed 2-spheres in non-compact,
three-dimensional Riemannian manifold without boundary. First, under
the assumption that is the euclidean 3-space endowed with a
semi-perturbed metric with perturbation small in norm and of compact
support, we prove that if there is some point with scalar
curvature then there exists a smooth embedding minimizing the Willmore functional , where
is the mean curvature. Second, assuming that is of bounded geometry
(i.e. bounded sectional curvature and strictly positive injectivity radius) and
asymptotically euclidean or hyperbolic we prove that if there is some point
with scalar curvature then there exists a
smooth immersion minimizing the functional , where is the second fundamental form. Finally, adding the
bound to the last assumptions, we obtain a smooth minimizer for the functional . The assumptions of
the last two theorems are satisfied in a large class of 3-manifolds arising as
spacelike timeslices solutions of the Einstein vacuum equation in case of null
or negative cosmological constant.Comment: 19 Page
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