9,315 research outputs found
Carath\'{e}odory interpolation on the non-commutative polydisk
The Carath\'{e}odory problem in the -variable non-commutative
Herglotz--Agler class and the Carath\'{e}odory--Fej\'{e}r problem in the
-variable non-commutative Schur--Agler class are posed. It is shown that the
Carath\'{e}odory (resp., Carath\'{e}odory--Fej\'{e}r) problem has a solution if
and only if the non-commutative polynomial with given operator coefficients
(the data of the problem indexed by an admissible set ) takes operator
values with positive semidefinite real part (resp., contractive operator
values) on -tuples of -jointly nilpotent contractive
matrices, for all .Comment: to appear in J. Funct. Ana
Stable p-wave resonant two-dimensional Fermi-Bose dimers
We consider two-dimensional weakly-bound heterospecies molecules formed in a
Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose
interactions. Bosonic exchanges lead to an intermolecular attraction, which can
be controlled and tuned to a p-wave resonance. Such attractive fermionic
molecules can be realized in quasi-two-dimensional ultracold isotopic or
heteronuclear mixtures. We show that they are stable with respect to the
recombination to deeply-bound molecular states and with respect to the
formation of higher-order clusters (trimers, tetramers, etc.
Metastable states and macroscopic quantum tunneling in a cold atom Josephson ring
We study macroscopic properties of a system of weakly interacting neutral
bosons confined in a ring-shaped potential with a Josephson junction. We derive
an effective low energy action for this system and evaluate its properties. In
particular we find that the system possesses a set of metastable
current-carrying states and evaluate the rates of transitions between these
states due to macroscopic quantum tunneling. Finally we discuss signatures of
different metastable states in the time-of-flight images and argue that the
effect is observable within currently available experimental technique.Comment: 4 pages, 2 figure
Sensitivity analysis of utility-based prices and risk-tolerance wealth processes
In the general framework of a semimartingale financial model and a utility
function defined on the positive real line, we compute the first-order
expansion of marginal utility-based prices with respect to a ``small'' number
of random endowments. We show that this linear approximation has some important
qualitative properties if and only if there is a risk-tolerance wealth process.
In particular, they hold true in the following polar cases:
\begin{tabular}@p97mm@ for any utility function , if and only if the set of
state price densities has a greatest element from the point of view of
second-order stochastic dominance;for any financial model, if and only if
is a power utility function ( is an exponential utility function if it is
defined on the whole real line). \end{tabular}Comment: Published at http://dx.doi.org/10.1214/105051606000000529 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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