1,147 research outputs found
Coding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding
theory and algebraic combinatorics, with most of the focus on the interaction
of codes with combinatorial designs, finite geometries, simple groups, sphere
packings, kissing numbers, lattices, and association schemes. In particular,
special interest is devoted to the relationship between codes and combinatorial
designs. We describe and recapitulate important results in the development of
the state of the art. In addition, we give illustrative examples and
constructions, and highlight recent advances. Finally, we provide a collection
of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in
Information and Coding Theory", ed. by I. Woungang et al., World Scientific,
Singapore, 201
Dynamics on flag manifolds: domains of proper discontinuity and cocompactness
For noncompact semisimple Lie groups we study the dynamics of the actions
of their discrete subgroups on the associated partial flag manifolds
. Our study is based on the observation that they exhibit also in higher
rank a certain form of convergence type dynamics. We identify geometrically
domains of proper discontinuity in all partial flag manifolds. Under certain
dynamical assumptions equivalent to the Anosov subgroup condition, we establish
the cocompactness of the -action on various domains of proper
discontinuity, in particular on domains in the full flag manifold . We
show in the regular case (of -Anosov subgroups) that the latter domains are
always nonempty if if has (locally) at least one noncompact simple factor
not of the type or .Comment: 65 page
A model metal potential exhibiting polytetrahedral clusters
Putative global minima have been located for clusters interacting with an
aluminium glue potential for N<190. Virtually all the clusters have
polytetrahedral structures, which for larger sizes involve an ordered array of
disclinations that are similar to those in the Z, H and sigma Frank-Kasper
phases. Comparisons of sequences of larger clusters suggest that the majority
of the global minima will adopt the bulk face-centred-cubic structure beyond
N=500.Comment: 14 pages, 7 figure
The distribution of forces affects vibrational properties in hard sphere glasses
We study theoretically and numerically the elastic properties of hard sphere
glasses, and provide a real-space description of their mechanical stability. In
contrast to repulsive particles at zero-temperature, we argue that the presence
of certain pairs of particles interacting with a small force soften elastic
properties. This softening affects the exponents characterizing elasticity at
high pressure, leading to experimentally testable predictions. Denoting
the force distribution of such pairs and the
packing fraction at which pressure diverges, we predict that (i) the density of
states has a low-frequency peak at a scale , rising up to it as
, and decaying above as where and is the frequency,
(ii) shear modulus and mean-squared displacement are inversely proportional
with where
, and (iii) continuum elasticity breaks down on a
scale where
and , where is the
coordination and the spatial dimension. We numerically test (i) and provide
data supporting that in our bi-disperse system,
independently of system preparation in two and three dimensions, leading to
, , and . Our results for the
mean-square displacement are consistent with a recent exact replica computation
for , whereas some observations differ, as rationalized by the
present approach.Comment: 5 pages + 4 pages supplementary informatio
Explicit birational geometry of 3-folds of general type, I
Let be a complex nonsingular projective 3-fold of general type. We prove
and for some positive
integer . A direct consequence is the birationality of the
pluricanonical map for all . Besides, the canonical
volume has a universal lower bound .Comment: 29 pages, Ann Sci Ecole Norm Sup (to appear
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