1,579 research outputs found
Horrocks Correspondence on a Quadric Surface
We extend the Horrocks correspondence between vector bundles and cohomology
modules on the projective plane to the product of two projective lines. We
introduce a set of invariants for a vector bundle on the product of two
projective lines, which includes the first cohomology module of the bundle, and
prove that there is a one to one correspondence between these sets of
invariants and isomorphism classes of vector bundles without line bundle
summands.Comment: 19 page
Horrocks Correspondence on ACM Varieties
We describe a vector bundle \sE on a smooth -dimensional ACM variety in
terms of its cohomological invariants H^i_*(\sE), , and
certain graded modules of "socle elements" built from \sE. In this way we
give a generalization of the Horrocks correspondence. We prove existence
theorems where we construct vector bundles from these invariants and uniqueness
theorems where we show that these data determine a bundle up to isomorphisms.
The cases of the quadric hypersurface in and the Veronese
surface in are considered in more detail.Comment: 18 pages, not figure
The Bis(ferrocenyl)phosphenium Ion Revisited
The bis(ferrocenyl)phosphenium ion, [Fc2P]+, reported by Cowley et al. (J. Am. Chem. Soc. 1981, 103, 714–715), was the only claimed donor‐free divalent phosphenium ion. Our examination of the molecular and electronic structure reveals that [Fc2P]+ possesses significant intramolecular Fe⋅⋅⋅P contacts, which are predominantly electrostatic and moderate the Lewis acidity. Nonetheless, [Fc2P]+ undergoes complex formation with the Lewis bases PPh3 and IPr to give the donor–acceptor complexes [Fc2P(PPh3)]+ and [Fc2P(IPr)]+ (IPr=1,3‐bis(2,6‐diisopropylphenyl)imidazole‐2‐ylidene)
Rank two bundles on P^n with isolated cohomology
The purpose of this paper is to study minimal monads associated to a rank two
vector bundle on . In particular, we study situations
where has for , except for one
pair of values . We show that on if , then must be decomposable. More
generally, we show that for , there is no indecomposable bundle
for which all intermediate cohomology modules except for are zero.Comment: 14 pages, no figure
On the traction problem for steady elastic oscillations equations: the double layer potential ansatz
The three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means of a double layer potential is considered instead of the more usual simple layer potential
On the double layer potential ansatz for the n-dimensional helmholtz equation with Neumann condition
In the present paper we consider the Neumann problem for the ndimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials
The water supercooled regime as described by four common water models
The temperature scale of simple water models in general does not coincide
with the natural one. Therefore, in order to make a meaningful evaluation of
different water models a temperature rescaling is necessary. In this paper we
introduce a rescaling using the melting temperature and the temperature
corresponding to the maximum of the heat capacity to evaluate four common water
models (TIP4P-Ew, TIP4P-2005, TIP5P-Ew and Six-Sites) in the supercooled
regime. Although all the models show the same general qualitative behavior, the
TIP5P-Ew appears as the best representation of the supercooled regime when the
rescaled temperature is used. We also analyze, using thermodynamic arguments,
the critical nucleus size for ice growth. Finally, we speculate on the possible
reasons why atomistic models do not usually crystalize while the coarse grained
mW model do crystallize.Comment: 8 pages, 8 figure
- …