8,248 research outputs found
CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary
The purpose of this paper is to describe certain CR-covariant differential
operators on a strictly pseudoconvex CR manifold as residues of the
scattering operator for the Laplacian on an ambient complex K\"{a}hler manifold
having as a `CR-infinity.' We also characterize the CR -curvature in
terms of the scattering operator. Our results parallel earlier results of
Graham and Zworski \cite{GZ:2003}, who showed that if is an asymptotically
hyperbolic manifold carrying a Poincar\'{e}-Einstein metric, the -curvature
and certain conformally covariant differential operators on the `conformal
infinity' of can be recovered from the scattering operator on . The
results in this paper were announced in \cite{HPT:2006}.Comment: 32 page
Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
The FEAST method for solving large sparse eigenproblems is equivalent to
subspace iteration with an approximate spectral projector and implicit
orthogonalization. This relation allows to characterize the convergence of this
method in terms of the error of a certain rational approximant to an indicator
function. We propose improved rational approximants leading to FEAST variants
with faster convergence, in particular, when using rational approximants based
on the work of Zolotarev. Numerical experiments demonstrate the possible
computational savings especially for pencils whose eigenvalues are not well
separated and when the dimension of the search space is only slightly larger
than the number of wanted eigenvalues. The new approach improves both
convergence robustness and load balancing when FEAST runs on multiple search
intervals in parallel.Comment: 22 pages, 8 figure
Solid state NMR and X-ray diffraction studies of α-d-galacturonic acid monohydrate
Crystalline a-d-galacturonic acid monohydrate has been studied by 13C CPMAS NMR and X-ray crystallography. The molecular dynamics were investigated by evaluating 13C spin-lattice relaxation in the rotating frame (T1?) and chemical-shift-anisotropy properties of each carbon. Only limited molecular motions can be detected in the low frequency
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