13,561 research outputs found
Embeddings of rearrangement invariant spaces that are not strictly singular
We give partial answers to the following conjecture: the natural embedding of
a rearrangement invariant space E into L_1([0,1]) is strictly singular if and
only if G does not embed into E continuously, where G is the closure of the
simple functions in the Orlicz space L_Phi with Phi(x) = exp(x^2)-1.Comment: Also available at http://www.math.missouri.edu/~stephen/preprint
Reduction, Symmetry and Phases in Mechanics
Various holonomy phenomena are shown to be instances of the reconstruction procedure
for mechanical systems with symmetry. We systematically exploit this point of view for fixed
systems (for example with controls on the internal, or reduced, variables) and for slowly moving
systems in an adiabatic context. For the latter, we obtain the phases as the holonomy for a
connection which synthesizes the Cartan connection for moving mechanical systems with the
Hannay-Berry connection for integrable systems. This synthesis allows one to treat in a natural
way examples like the ball in the slowly rotating hoop and also non-integrable mechanical systems
Constraining the Surface Inhomogeneity and Settling Times of Metals on Accreting White Dwarfs
Due to the short settling times of metals in DA white dwarf atmospheres, any
white dwarfs with photospheric metals must be actively accreting. It is
therefore natural to expect that the metals may not be deposited uniformly on
the surface of the star. We present calculations showing how the temperature
variations associated with white dwarf pulsations lead to an observable
diagnostic of the surface metal distribution, and we show what constraints
current data sets are able to provide. We also investigate the effect that
time-variable accretion has on the metal abundances of different species, and
we show how this can lead to constraints on the gravitational settling times.Comment: 4 pages, 5 figures, accepted for publication in the Astrophysical
Journal Letters, updated reference
Zero gravity tissue-culture laboratory
Hardware was developed for performing experiments to detect the effects that zero gravity may have on living human cells. The hardware is composed of a timelapse camera that photographs the activity of cell specimens and an experiment module in which a variety of living-cell experiments can be performed using interchangeable modules. The experiment is scheduled for the first manned Skylab mission
Driving in ZZ Ceti stars - Problem solved?
There is a fairly tight correlation between the pulsation periods and
effective temperatures of ZZ Ceti stars (cooler stars have longer periods).
This seems to fit the theoretical picture, where driving occurs in the partial
ionization zone, which lies deeper and deeper within the star as it cools. It
is reasonable to assume that the pulsation periods should be related to the
thermal timescale in the region where driving occurs. As that region sinks
further down below the surface, that thermal timescale increases. Assuming this
connection, the pulsation periods could provide an additional way to determine
effective temperatures, independent of spectroscopy. We explore this idea and
find that in practice, things are not so simple.Comment: 4 pages, 3 figure
White Dwarfs In Ngc6397 And M4: Constraints On The Physics Of Crystallization
We explore the physics of crystallization in the dense Coulomb plasma of the deep interiors of white dwarf stars using the color-magnitude diagram and luminosity function constructed from Hubble Space Telescope photometry of the globular cluster M 4 and compare it with our results for proper motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397. We demonstrate that the data are consistent with a binary mixture of carbon and oxygen crystallizing at a value of Gamma higher than the theoretical value for a One Component Plasma (OCP). We show that this result is in line with the latest Molecular Dynamics simulations for binary mixtures of C/O. We discuss implications for future work.Astronom
Chow's theorem and universal holonomic quantum computation
A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
- …