124 research outputs found
The Extensions of the Generalized Quadrangle of Order (3, 9)
AbstractIt is shown that there is only one extension of GQ(3, 9) namely the one admitting the sporadic simple groupMcLas a flag-transitive automorphism group. The proof depends on a computer calculation
Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory
In this article we obtain a fundamental measure functional for the model of
aligned hard hexagons in the plane. Our aim is not just to provide a functional
for a new, admittedly academic, model, but to investigate the structure of
fundamental measure theory. A model of aligned hard hexagons has similarities
with the hard disk model. Both share "lost cases", i.e. admit configurations of
three particles in which there is pairwise overlap but not triple overlap.
These configurations are known to be problematic for fundamental measure
functionals, which are not able to capture their contribution correctly. This
failure lies in the inability of these functionals to yield a correct low
density limit of the third order direct correlation function. Here we derive
the functional by projecting aligned hard cubes on the plane x+y+z=0. The
correct dimensional crossover behavior of these functionals permits us to
follow this strategy. The functional of aligned hard cubes, however, does not
have lost cases, so neither had the resulting functional for aligned hard
hexagons. The latter exhibits, in fact, a peculiar structure as compared to the
one for hard disks. It depends on a uniparametric family of weighted densities
through a new term not appearing in the functional for hard disks. Apart from
studying the freezing of this system, we discuss the implications of the
functional structure for new developments of fundamental measure theory.Comment: 10 pages, 9 figures, uses RevTeX
Localization of the 17q breakpoint of a constitutional 1;17 translocation in a patient with neuroblastoma within a 25-kb segment located between the ACCN1 and TLK2 genes and near the distal breakpoints of two microdeletions in neurofibromatosis type I patients.
We have constructed a 1.4-Mb P1 artificial chromosome/bacterial artificial chromosome (PAC/BAC) contig spanning the 17q breakpoint of a constitutional translocation t(1;17)(p36.2;q11.2) in a patient with neuroblastoma. Three 17q breakpoint-overlapping cosmids were identified and sequenced. No coding sequences were found in the immediate proximity of the 17q breakpoint. The PAC/BAC contig covers the region between the proximally located ACCN1 gene and the distally located TLK2 gene and SCYA chemokine gene cluster. The observation that the 17q breakpoint region could not be detected in any of the screened yeast artificial chromosome libraries and the localization of the 17q breakpoint in the vicinity of the distal breakpoints of two microdeletions in patients with neurofibromatosis type 1 suggest that this chromosomal region is genetically unstable and prone to rearrangement
Groups of Lie type generated by long root elements in F4(K)
AbstractLet K be a field and G a quasi-simple subgroup of the Chevalley group F4(K). We assume that G is generated by a class Σ of abstract root subgroups such that there are A,C∈Σ with [A,C]∈Σ and any A∈Σ is contained in a long root subgroup of F4(K). We determine the possibilities for G and describe the embedding of G in F4(K)
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