7,468 research outputs found
Operator pencils on the algebra of densities
In this paper we continue to study equivariant pencil liftings and
differential operators on the algebra of densities. We emphasize the role that
the geometry of the extended manifold plays. Firstly we consider basic
examples. We give a projective line of diff()-equivariant pencil liftings
for first order operators, and the canonical second order self-adjoint lifting.
Secondly we study pencil liftings equivariant with respect to volume preserving
transformations. This helps to understand the role of self-adjointness for the
canonical pencils. Then we introduce the Duval-Lecomte-Ovsienko (DLO)-pencil
lifting which is derived from the full symbol calculus of projective
quantisation. We use the DLO-pencil lifting to describe all regular
proj-equivariant pencil liftings. In particular the comparison of these pencils
with the canonical pencil for second order operators leads to objects related
to the Schwarzian. Within this paper the question of whether the pencil lifting
factors through a full symbol map naturally arises.Comment: 23 pages, LaTeX file Small corrections are mad
Vegetation-soil relations in a highly sodic landscape, Yelarbon, southern Queensland
Soil and vegetation data were collected from a sodic-scald near Yelarbon in southern Queensland. The surface of the landscape includes relatively light textured pedestals of the A-horizon with slightly alkaline pH and slopes leading down to scalded basement representing the surface of the strongly alkaline B-horizon. The strongest gradient within the floristic patterns was associated with wetland vegetation in drainage lines, but a secondary and orthogonal gradient was related to soil pH, which was probably a function of lower alkalinity on the more stable and weathered A-horizons. There were few significant differences between soil or vegetation characteristics from plot data comparing parts of the landscape with differing historical grazing regimes. Sites included stock routes heavily grazed between the 1920s and 1970s, and subsequently almost ungrazed; and grazed paddocks that have had moderate use throughout this period. There is clear evidence that the area is naturally active in terms of erosion and deposition during flooding regardless of grazing
Unevenly-sampled signals: a general formalism of the Lomb-Scargle periodogram
The periodogram is a popular tool that tests whether a signal consists only
of noise or if it also includes other components. The main issue of this method
is to define a critical detection threshold that allows identification of a
component other than noise, when a peak in the periodogram exceeds it. In the
case of signals sampled on a regular time grid, determination of such a
threshold is relatively simple. When the sampling is uneven, however, things
are more complicated. The most popular solution in this case is to use the
"Lomb-Scargle" periodogram, but this method can be used only when the noise is
the realization of a zero-mean, white (i.e. flat-spectrum) random process. In
this paper, we present a general formalism based on matrix algebra, which
permits analysis of the statistical properties of a periodogram independently
of the characteristics of noise (e.g. colored and/or non-stationary), as well
as the characteristics of sampling.Comment: 10 pages, 11 figures, Astronomy and Astrophysics, in pres
Assessing the importance of a self-generated detachment process in river biofilm models
1. Epilithic biofilm biomass was measured for 14 months in two sites, located up- and downstream of the city of Toulouse in the Garonne River (south-west France). Periodical sampling provided a biomass data set to compare with simulations from the model of Uehlinger, Bürher and Reichert (1996: Freshwater Biology, 36, 249–263.), in order to evaluate the impact of hydraulic disturbance.
2. Despite differences in application conditions (e.g. river size, discharge, frequency of disturbance), the base equation satisfactorily predicted biomass between low and high water periods of the year, suggesting that the flood disturbance regime may be considered a universal mechanism controlling periphyton biomass.
3. However modelling gave no agreement with biomass dynamics during the 7-month long low water period that the river experienced. The influence of other biomass-regulating factors (temperature, light and soluble reactive phosphorus) on temporal biomass dynamics was weak.
4. Implementing a supplementary mechanism corresponding to a temperature-dependent self-generated loss because of heterotrophic processes allowed us to accurately reproduce the observed pattern: a succession of two peaks. This case study suggests that during typical summer low water periods (flow stability and favourable temperature) river biofilm modelling requires self-generated detachment to be considered
Operator pencil passing through a given operator
Let be a linear differential operator acting on the space of
densities of a given weight \lo on a manifold . One can consider a pencil
of operators \hPi(\Delta)=\{\Delta_\l\} passing through the operator
such that any \Delta_\l is a linear differential operator acting on densities
of weight \l. This pencil can be identified with a linear differential
operator \hD acting on the algebra of densities of all weights. The existence
of an invariant scalar product in the algebra of densities implies a natural
decomposition of operators, i.e. pencils of self-adjoint and anti-self-adjoint
operators. We study lifting maps that are on one hand equivariant with respect
to divergenceless vector fields, and, on the other hand, with values in
self-adjoint or anti-self-adjoint operators. In particular we analyze the
relation between these two concepts, and apply it to the study of
\diff(M)-equivariant liftings. Finally we briefly consider the case of
liftings equivariant with respect to the algebra of projective transformations
and describe all regular self-adjoint and anti-self-adjoint liftings.Comment: 32 pages, LaTeX fil
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