31,844 research outputs found
Some Results On Normal Homogeneous Ideals
In this article we investigate when a homogeneous ideal in a graded ring is
normal, that is, when all positive powers of the ideal are integrally closed.
We are particularly interested in homogeneous ideals in an N-graded ring
generated by all homogeneous elements of degree at least m and monomial ideals
in a polynomial ring over a field. For ideals of the first trype we generalize
a recent result of S. Faridi. We prove that a monomial ideal in a polynomial
ring in n indeterminates over a field is normal if and only if the first n-1
positive powers of the ideal are integrally closed. We then specialize to the
case of ideals obtained by taking integral closures of m-primary ideals
generated by powers of the variables. We obtain classes of normal monomial
ideals and arithmetic critera for deciding when the monomial ideal is not
normal.Comment: 19 page
Criteria for generalized macroscopic and mesoscopic quantum coherence
We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of
eigenstates of an observable, and develop some signatures for their existence.
We define the extent, or size of a superposition, with respect to an
observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that
superposition. Such superpositions are referred to as generalized -scopic
superpositions to distinguish them from the extreme superpositions that
superpose only the two states that have a difference in their prediction
for the observable. We also consider generalized -scopic superpositions of
coherent states. We explore the constraints that are placed on the statistics
if we suppose a system to be described by mixtures of superpositions that are
restricted in size. In this way we arrive at experimental criteria that are
sufficient to deduce the existence of a generalized -scopic superposition.
The signatures developed are useful where one is able to demonstrate a degree
of squeezing. We also discuss how the signatures enable a new type of
Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.
On the Computation of Power in Volume Integral Equation Formulations
We present simple and stable formulas for computing power (including
absorbed/radiated, scattered and extinction power) in current-based volume
integral equation formulations. The proposed formulas are given in terms of
vector-matrix-vector products of quantities found solely in the associated
linear system. In addition to their efficiency, the derived expressions can
guarantee the positivity of the computed power. We also discuss the application
of Poynting's theorem for the case of sources immersed in dissipative
materials. The formulas are validated against results obtained both with
analytical and numerical methods for scattering and radiation benchmark cases
Letter from A. G. Reid
Letter concerning a position as football coach at Utah Agricultural College
Broadband phase coherence between an ultrafast laser and an OPO using lock-to-zero CEO stabilization
Chromospheric Inversions of a Micro-flaring Region
We use spectropolarimetric observations of the Ca II 8542~\AA\ line, taken
from the Swedish 1-m Solar Telescope (SST), in an attempt to recover dynamic
activity in a micro-flaring region near a sunspot via inversions. These
inversions show localized mean temperature enhancements of 1000~K in the
chromosphere and upper photosphere, along with co-spatial bi-directional
Doppler shifting of 5 - 10 km s. This heating also extends along a
nearby chromospheric fibril, co-spatial to 10 - 15 km s down-flows.
Strong magnetic flux cancellation is also apparent in one of the footpoints,
concentrated in the chromosphere. This event more closely resembles that of an
Ellerman Bomb (EB), though placed slightly higher in the atmosphere than is
typically observed.Comment: 9 pages, 9 figures, accepted in ApJ. Movies are stored here:
https://star.pst.qub.ac.uk/webdav/public/areid/Microflare
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