48,796 research outputs found
On generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the
chromatic numbers of hypergraphs \KG{r}{\pmb s}{\calS}, "generalized
-uniform Kneser hypergraphs with intersection multiplicities ." It
generalized previous lower bounds by Kriz (1992/2000) for the case without intersection multiplicities, and by Sarkaria (1990) for
\calS=\tbinom{[n]}k. Here we discuss subtleties and difficulties that arise
for intersection multiplicities :
1. In the presence of intersection multiplicities, there are two different
versions of a "Kneser hypergraph," depending on whether one admits hypergraph
edges that are multisets rather than sets. We show that the chromatic numbers
are substantially different for the two concepts of hypergraphs. The lower
bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset
version.
2. The reductions to the case of prime in the proofs Sarkaria and by
Ziegler work only if the intersection multiplicities are strictly smaller than
the largest prime factor of . Currently we have no valid proof for the lower
bound result in the other cases.
We also show that all uniform hypergraphs without multiset edges can be
represented as generalized Kneser hypergraphs.Comment: 9 pages; added examples in Section 2; added reference ([11]),
corrected minor typos; to appear in J. Combinatorial Theory, Series
The Role of Family-Based Designs in Genome-Wide Association Studies
Genome-Wide Association Studies (GWAS) offer an exciting and promising new
research avenue for finding genes for complex diseases. Traditional
case-control and cohort studies offer many advantages for such designs.
Family-based association designs have long been attractive for their robustness
properties, but robustness can mean a loss of power. In this paper we discuss
some of the special features of family designs and their relevance in the era
of GWAS.Comment: Published in at http://dx.doi.org/10.1214/08-STS280 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
First-principles calculations of the vibrational properties of bulk CdSe and CdSe nanowires
We present first-principles calculations on bulk CdSe and CdSe nanowires with
diameters of up to 22 \AA. Density functional linear combination of atomic
orbitals and plane wave calculations of the electronic and structural
properties are presented and discussed. We use an iterative, symmetry-based
method to relax the structures into the ground state. We find that the band gap
depends on surface termination. Vibrational properties in the whole Brillouin
zone of bulk CdSe and the zone-center vibrations of nanowires are calculated
and analyzed. We find strongly size-dependent and nearly constant modes,
depending on the displacement directions. A comparison with available
experimental Raman data is be given
Charmed Hadrons from Fragmentation and B Decays
The fragmentation functions of , , , ,
and at 10.6 GeV are measured
with a data set of 102.7 fb. Fragmentation model parametrizations
(Peterson, Kartvelishvili, Collins-Spiller, Lund, and Bowler models) are
compared to the data. The data at high 1 indicate a contribution of
non-perturbative QCD processes.Comment: presented at CHARM2006, International Workshop on Tau-Charm Physics,
Beijing, June 5-7, 200
Explicit correlation and intermolecular interactions: Investigating carbon dioxide complexes with the CCSD(T)-F12 method
We have optimized the lowest energy structures and calculated interaction energies for the CO₂–Ar, CO₂–N₂, CO₂–CO, CO₂–H₂O, and CO₂–NH₃ dimers with the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)]-F12 methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. For a given cardinal number, we find that results obtained with the CCSD(T)-F12 methods are much closer to the CCSD(T) complete basis set limit than the conventional CCSD(T) results. The relatively modest increase in the computational cost between explicit and conventional CCSD(T) is more than compensated for by the impressive accuracy of the CCSD(T)-F12 method. We recommend use of the CCSD(T)-F12 methods in combination with the VXZ-F12 basis sets for the accurate determination of equilibrium geometries and interaction energies of weakly bound electron donor acceptor complexes
The development of a treadle pump: Lessons from the South African experience
Manual pumps / Design / South Africa
Time domain simulations of dynamic river networks
The problem of simulating a river network is considered. A river network is considered to comprise of rivers, dams/lakes as well as weirs. We suggest a numerical approach with specific features that enable the correct representation of these assets. For each river the flow of water is described by the shallow water equations which is a system of hyperbolic partial differential equations and at the junctions of the rivers, suitable coupling conditions, viewed as interior boundary conditions are used to couple the dynamics. A different model for the dams is also presented. Numerical test cases are presented which show that the model is able to reproduce the expected dynamics of the system.
Other aspects of the modelling such as rainfall, run-off, overflow/flooding, evaporation, absorption/seepage, bed-slopes, bed friction have not been incorporated in the model due to their specific nature
Quantifying cooperative intermolecular interactions for improved carbon dioxide capture materials
We have optimized the geometry and calculated interaction energies for over 100 different complexes of CO₂ with various combinations of electron accepting (Lewis acid) and electron donating (Lewis base) molecules. We have used the recently developed explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)-F12] methods and the associated VXZ-F12 (where X = D,T,Q) basis sets. We observe only modest changes in the geometric parameters of CO₂ upon complexation, which suggests that the geometry of CO₂ adsorbed in a nanoporous material should be similar to that of CO₂ in gas phase. When CO₂ forms a complex with two Lewis acids via the two electron rich terminal oxygen atoms, the interaction energy is less than twice what would be expected for the same complex involving a single Lewis acid. We consider a series of complexes that exhibit simultaneous CO₂-Lewis acid and CO₂-Lewis base intermolecular interactions, with total interaction energies spanning 14.1–105.9 kJ mol⁻¹. For these cooperative complexes, we find that the total interaction energy is greater than the sum of the interaction energies of the constituent complexes. Furthermore, the intermolecular distances of the cooperative complexes are contracted as compared to the constituent complexes. We suggest that metal-organic-framework or similar nanoporous materials could be designed with adsorption sites specifically tailored for CO₂ to allow cooperative intermolecular interactions, facilitating enhanced CO₂ adsorption
A family of Prym-Tyurin varieties of exponent 3
We investigate a family of correspondences associated to \'etale coverings of
degree 3 of hyperelliptic curves. They lead to Prym-Tyurin varieties of
exponent 3. We identify these varieties and derive some consequences.Comment: names of authors correcte
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