16,613 research outputs found
Degree of the generalized Pl\"ucker embedding of a Quot scheme and Quantum cohomology
We compute the degree of the generalized Pl\"ucker embedding of a
Quot scheme over \PP^1. The space can also be considered as a
compactification of the space of algebraic maps of a fixed degree from \PP^1
to the Grassmanian . Then the degree of the embedded variety
can be interpreted as an intersection product of pullbacks of
cohomology classes from through the map that evaluates
a map from \PP^1 at a point x\in \PP^1. We show that our formula for the
degree verifies the formula for these intersection products predicted by
physicists through Quantum cohomology~\cite{va92}~\cite{in91}~\cite{wi94}. We
arrive at the degree by proving a version of the classical Pieri's formula on
the variety , using a cell decomposition of a space that lies in between
and .Comment: 18 pages, Latex documen
Displacement Data Assimilation
We show that modifying a Bayesian data assimilation scheme by incorporating
kinematically-consistent displacement corrections produces a scheme that is
demonstrably better at estimating partially observed state vectors in a setting
where feature information important. While the displacement transformation is
not tied to any particular assimilation scheme, here we implement it within an
ensemble Kalman Filter and demonstrate its effectiveness in tracking
stochastically perturbed vortices.Comment: 26 Pages, 9 figures, 5 table
A selected history of expectation bias in physics
The beliefs of physicists can bias their results towards their expectations
in a number of ways. We survey a variety of historical cases of expectation
bias in observations, experiments, and calculations.Comment: 6 pages, 2 figure
Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations
I present a matched-wave asymptotic analysis of the driving of solar
oscillations by a general localised source. The analysis provides a simple
mathematical description of the asymmetric peaks in the power spectrum in terms
of the relative locations of eigenmodes and troughs in the spectral response.
It is suggested that the difference in measured phase function between the
modes and the troughs in the spectrum will provide a key diagnostic of the
source of the oscillations. I also suggest a form for the asymmetric line
profiles to be used in the fitting of solar power spectra.
Finally I present a comparison between the numerical and asymptotic
descriptions of the oscillations. The numerical results bear out the
qualitative features suggested by the asymptotic analysis but suggest that
numerical calculations of the locations of the troughs will be necessary for a
quantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap
Microwave remote sensing of soil moisture, volume 1
Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone
Multifrequency remote sensing of soil moisture
Multifrequency sensor data collected at Guymon, Oklahoma and Dalhart, Texas using NASA's C-130 aircraft were used to determine which of the all-weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. In comparison to other active and passive microwave sensors the L-band radiometer (1) was influenced least by ranges in surface roughness; (2) demonstrated the most sensitivity to soil moisture differences in terms of the range of return from the full range of soil moisture; and (3) was less sensitive to errors in measurement in relation to the range of sensor response. L-band emissivity related more strongly to soil moisture when moisture was expressed as percent of field capacity. The perpendicular vegetation index as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture
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