8,406 research outputs found
Equivalence of quotient Hilbert modules
Let \cl{M} be a Hilbert module of holomorphic functions over a natural
function algebra , where \Omega \subseteq \bb{C}^m is a
bounded domain. Let \cl{M}_0\subseteq \cl{M} be the submodule of functions
vanishing to order on a hypersurface \cl{Z} \subseteq \Omega. We describe
a method, which in principle may be used, to construct a set of complete
unitary invariants for quotient modules \cl{Q}=\cl{M} \ominus \cl{M}_0. The
invariants are given explicitly in the particular case of .Comment: 11 page
Quasi-free resolutions of Hilbert modules
The notion of a quasi-free Hilbert module over a function algebra
consisting of holomorphic functions on a bounded domain
in complex space is introduced. It is shown that quasi-free Hilbert modules
correspond to the completion of the direct sum of a certain number of copies of
the algebra . A Hilbert module is said to be weakly regular
(respectively, regular) if there exists a module map from a quasi-free module
with dense range (respectively, onto). A Hilbert module is said
to be compactly supported if there exists a constant satisfying for some compact subset of and
in , in . It is shown that if a Hilbert
module is compactly supported then it is weakly regular. The paper identifies
several other classes of Hilbert modules which are weakly regular. In addition,
this result is extended to yield topologically exact resolutions of such
modules by quasi-free ones
Modulational instability of ion-acoustic wave packets in quantum pair-ion plasmas
Amplitude modulation of quantum ion-acoustic waves (QIAWs) in a quantum
electron-pair-ion plasma is studied. It is shown that the quantum coupling
parameter (being the ratio of the plasmonic energy density to the Fermi
energy) is ultimate responsible for the modulational stability of QIAW packets,
without which the wave becomes modulational unstable. New regimes for the
modulational stability (MS) and instability (MI) are obtained in terms of
and the positive to negative ion density ratio . The growth rate of MI
is obtained, the maximum value of which increases with and decreases
with . The results could be important for understanding the origin of
modulated QIAW packets in the environments of dense astrophysical objects,
laboratory negative ion plasmas as well as for the next generation laser solid
density plasma experiments.Comment: 4 pages, 2 figures (to appear in Astrophysics and Space Science
Fluctuation Cumulant Behavior for the Field-Pulse Induced Magnetisation-Reversal Transition in Ising Models
The universality class of the dynamic magnetisation-reversal transition,
induced by a competing field pulse, in an Ising model on a square lattice,
below its static ordering temperature, is studied here using Monte Carlo
simulations. Fourth order cumulant of the order parameter distribution is
studied for different system sizes around the phase boundary region. The
crossing point of the cumulant (for different system sizes) gives the
transition point and the value of the cumulant at the transition point
indicates the universality class of the transition. The cumulant value at the
crossing point for low temperature and pulse width range is observed to be
significantly less than that for the static transition in the same
two-dimensional Ising model. The finite size scaling behaviour in this range
also indicates a higher correlation length exponent value. For higher
temperature and pulse width range, the transition seems to fall in a mean-field
like universality class.Comment: 5 pages, 8 eps figures, thoroughly revised manuscript with new
figures, accepted in Phys. Rev. E (2003
Fractal Measures and Nonlinear Dynamics of Overcontact Binaries
Overcontact binary stars are systems of two stars where the component stars
are in contact with each other. This implies that they share a common envelope
of gas. In this work we seek signatures of nonlinearity and chaos in these
stars by using time series analysis techniques. We use three main techniques,
namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The
former two are calculated from the reconstructed dynamics, while the latter is
calculated from the Fourier transforms of the time series of intensity
variations(light curves) of these stars. Our dataset consists of data from 463
overcontact binary stars in the Kepler field of view [1]. Our analysis
indicates nonlinearity and signatures of chaos in almost all the light curves.
We also explore whether the underlying nonlinear properties of the stars are
related to their physical properties like fill-out-factor, a measure of the
extend of contact between the components of an overcontact binary system . We
observe that significant correlations exist between the fill out factor and the
nonlinear quantifiers. This correlation is more pronounced in specific
subcategories constructed based on the mass ratios and effective temperatures
of the binaries. The correlations observed can be indicative of variations in
the nonlinear properties of the star as it ages. We believe that this study
relating nonlinear and astrophysical properties of binary stars is the first of
its kind and is an important starting point for such studies in other
astrophysical objects displaying nonlinear dynamical behaviour.Comment: 17 pages, 12 figures, submitted to Communications in Nonlinear
Science and Numerical Simulatio
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