9,946 research outputs found
A comparison of the finite element method on Shishkin and Gartland-type meshes for convection-diffusion problems
Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+
The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in
43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+
ion. We determine the hyperfine structure constants of the metastable level as
A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with
respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the
existence of transitions that become independent of the first-order Zeeman
shift at non-zero low magnetic fields. These transitions might be better suited
for building a frequency standard than the well-known 'clock transitions'
between m=0 levels at zero magnetic field.Comment: corrected for sign errors in the hyperfine constants. No corrections
to were made to the data analysi
Resonant ion-pair formation in electron recombination with HF^+
The cross section for resonant ion-pair formation in the collision of
low-energy electrons with HF^+ is calculated by the solution of the
time-dependent Schrodinger equation with multiple coupled states using a wave
packet method. A diabatization procedure is proposed to obtain the electronic
couplings between quasidiabatic potentials of ^1Sigma^+ symmetry for HF. By
including these couplings between the neutral states, the cross section for
ion-pair formation increases with about two orders of magnitude compared with
the cross section for direct dissociation. Qualitative agreement with the
measured cross section is obtained. The oscillations in the calculated cross
section are analyzed. The cross section for ion-pair formation in electron
recombination with DF^+ is calculated to determine the effect of isotopic
substitution.Comment: 12 pages, 12 figure
Ellipticity Conditions for the Lax Operator of the KP Equations
The Lax pseudo-differential operator plays a key role in studying the general
set of KP equations, although it is normally treated in a formal way, without
worrying about a complete characterization of its mathematical properties. The
aim of the present paper is therefore to investigate the ellipticity condition.
For this purpose, after a careful evaluation of the kernel with the associated
symbol, the majorization ensuring ellipticity is studied in detail. This leads
to non-trivial restrictions on the admissible set of potentials in the Lax
operator. When their time evolution is also considered, the ellipticity
conditions turn out to involve derivatives of the logarithm of the
tau-function.Comment: 21 pages, plain Te
Balanced metrics on Cartan and Cartan-Hartogs domains
This paper consists of two results dealing with balanced metrics (in S.
Donaldson terminology) on nonconpact complex manifolds. In the first one we
describe all balanced metrics on Cartan domains. In the second one we show that
the only Cartan-Hartogs domain which admits a balanced metric is the complex
hyperbolic space. By combining these results with those obtained in [13]
(Kaehler-Einstein submanifolds of the infinite dimensional projective space, to
appear in Mathematische Annalen) we also provide the first example of complete,
Kaehler-Einstein and projectively induced metric g such that is not
balanced for all .Comment: 11 page
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