12,986 research outputs found
Taut distance-regular graphs and the subconstituent algebra
We consider a bipartite distance-regular graph with diameter at least
4 and valency at least 3. We obtain upper and lower bounds for the local
eigenvalues of in terms of the intersection numbers of and the
eigenvalues of . Fix a vertex of and let denote the corresponding
subconstituent algebra. We give a detailed description of those thin
irreducible -modules that have endpoint 2 and dimension . In an earlier
paper the first author defined what it means for to be taut. We obtain
three characterizations of the taut condition, each of which involves the local
eigenvalues or the thin irreducible -modules mentioned above.Comment: 29 page
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Amenable hyperbolic groups
We give a complete characterization of the locally compact groups that are
non-elementary Gromov-hyperbolic and amenable. They coincide with the class of
mapping tori of discrete or continuous one-parameter groups of compacting
automorphisms. We moreover give a description of all Gromov-hyperbolic locally
compact groups with a cocompact amenable subgroup: modulo a compact normal
subgroup, these turn out to be either rank one simple Lie groups, or
automorphism groups of semi-regular trees acting doubly transitively on the set
of ends. As an application, we show that the class of hyperbolic locally
compact groups with a cusp-uniform non-uniform lattice, is very restricted.Comment: 41 pages, no figure. v2: revised version (minor changes
A New Type of Exact Arbitrarily Inhomogeneous Cosmology: Evolution of Deceleration in the Flat Homogeneous-On-Average Case
A new method for constructing exact inhomogeneous universes is presented,
that allows variation in 3 dimensions. The resulting spacetime may be
statistically uniform on average, or have random, non-repeating variation. The
construction utilises the Darmois junction conditions to join many different
component spacetime regions. In the initial simple example given, the component
parts are spatially flat and uniform, but much more general combinations should
be possible. Further inhomogeneity may be added via swiss cheese vacuoles and
inhomogeneous metrics. This model is used to explore the proposal, that
observers are located in bound, non-expanding regions, while the universe is
actually in the process of becoming void dominated, and thus its average
expansion rate is increasing. The model confirms qualitatively that the faster
expanding components come to dominate the average, and that inhomogeneity
results in average parameters which evolve differently from those of any one
component, but more realistic modelling of the effect will need this
construction to be generalised.Comment: JCAP Latex, 14pp, 2 figures(2nd with 5 plots), 4 table
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