8,324 research outputs found
Counting fixed points and rooted closed walks of the singular map modulo powers of a prime
The "self-power" map modulo and its generalized form modulo are of considerable interest for both theoretical
reasons and for potential applications to cryptography. In this paper, we use
-adic methods, primarily -adic interpolation, Hensel's lemma, and lifting
singular points modulo , to count fixed points and rooted closed walks of
equations related to these maps when is a prime power. In particular, we
introduce a new technique for lifting singular solutions of several congruences
in several unknowns using the left kernel of the Jacobian matrix.Comment: 18 pages. Version 2 shortens proofs, reduces redundancy, and
introduces new technique for counting rooted closed walks. Version 3 updates
title to agree with journal publicatio
Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example
We have studied properties of nonlinear waves in a mathematical model of a
predator-prey system with pursuit and evasion. We demonstrate a new type of
propagating wave in this system. The mechanism of propagation of these waves
essentially depends on the ``taxis'', represented by nonlinear
``cross-diffusion'' terms in the mathematical formulation. We have shown that
the dependence of the velocity of wave propagation on the taxis has two
distinct forms, ``parabolic'' and ``linear''. Transition from one form to the
other correlates with changes in the shape of the wave profile. Dependence of
the propagation velocity on diffusion in this system differs from the
square-root dependence typical of reaction-diffusion waves. We demonstrate also
that, for systems with negative and positive taxis, for example, pursuit and
evasion, there typically exists a large region in the parameter space, where
the waves demonstrate quasisoliton interaction: colliding waves can penetrate
through each other, and waves can also reflect from impermeable boundaries.Comment: 15 pages, 18 figures, submitted to Physica
Pursuit-evasion predator-prey waves in two spatial dimensions
We consider a spatially distributed population dynamics model with excitable
predator-prey dynamics, where species propagate in space due to their taxis
with respect to each other's gradient in addition to, or instead of, their
diffusive spread. Earlier, we have described new phenomena in this model in one
spatial dimension, not found in analogous systems without taxis: reflecting and
self-splitting waves. Here we identify new phenomena in two spatial dimensions:
unusual patterns of meander of spirals, partial reflection of waves, swelling
wavetips, attachment of free wave ends to wave backs, and as a result, a novel
mechanism of self-supporting complicated spatio-temporal activity, unknown in
reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao
X-ray Observations of Distant Optically Selected Cluster
We have measured fluxes or flux limits for 31 of the 79 cluster candidates in
the Palomar Distant Cluster Survey (PDCS) using archival ROSAT/PSPC pointed
observations. Our X-ray survey reaches a flux limit of erg s cm (0.4 - 2.0 keV), which corresponds to
luminosities of erg s ( = 50 km
s Mpc, = ), if we assume the PDCS estimated
redshifts. Of the 31 cluster candidates, we detect six at a signal-to-noise
greater than three. We estimate that (90% confidence
limits) of these six detections are a result of X-ray emission from objects
unrelated to the PDCS cluster candidates. The net surface density of X-ray
emitting cluster candidates in our survey, clusters
deg, agrees with that of other, X-ray selected, surveys. It is possible,
given the large error on our contamination rate, that we have not detected
X-ray emission from any of our observed PDCS cluster candidates. We find no
statistically significant difference between the X-ray luminosities of PDCS
cluster candidates and those of Abell clusters of similar optical richness.
This suggests that the PDCS contains objects at high redshift similar to the
low redshift clusters in the Abell catalogs. We show that the PDCS cluster
candidates are not bright X-ray sources, the average luminosity of the six
detected candidates is only erg s (0.4-2.0
keV). This finding is in agreement with previous X-ray studies of high
redshift, optically selected, rich clusters of galaxies.Comment: 19 pages, LaTeX with AAS Preprint Macros (v. 4), 3 embedded
postscript figures, 3 Seperate Tables using aj_pt4.sty, Accepted by the
Astronomical Journal for November 199
Genetic diversity at the FMR1 locus in the Indonesian population
We report an analysis of allelic diversity at short tandem repeat polymorphisms within the fragile XA locus in 1069 male volunteers from twelve Indonesian sub-populations. An odd numbered allele of DXS548 was found at high frequency in all Indonesian populations. Greater allelic diversity was identified at the loci under study than has been previously reported for an Asian population. These differences distinguish the Indonesian population from all previously reported Asian, European and African populations. A high frequency of small premutation alleles, 4/120 (3.3%, 95% CI 0.9–8.3%), was identified in the Moluccan population of Hiri Island
Irish Dairy Farming: Effects of Introducing a Maize Component on Grassland Management Over the Next 50 Years
Typical management of Irish dairy units is based on a low-cost spring-calving strategy with 90% of annual feed derived from grass grown on the farm. Almost 70% of feed is from grazed grass managed by rotational grazing, the remainder is conserved forage and concentrates. The objectives of the work were to examine how the management system has to be modified when part of the dairy unit land is allocated to maize silage instead of grass silage production, and to examine how climate change over the next 50 years will impact on grass and maize management within the production system
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Controls on the spatial distribution of oceanic <i>δ</i><sup>13</sup>C<sub>DIC</sub>
We describe the design and evaluation of a large ensemble of coupled climate–carbon cycle simulations with the Earth system model of intermediate complexity GENIE. This ensemble has been designed for application to a range of carbon cycle questions, including the causes of late- Quaternary fluctuations in atmospheric CO2. Here we evaluate the ensemble by applying it to a transient experiment over the recent industrial era (1858 to 2008 AD). We employ singular vector decomposition and principal component emulation to investigate the spatial modes of ensemble variability of oceanic dissolved inorganic carbon (DIC) δ13C, considering both the spun-up pre-industrial state and the transient change. These analyses allow us to separate the natural (preindustrial) and anthropogenic controls on the δ13CDIC distribution. We apply the same dimensionally reduced emulation techniques to consider the drivers of the spatial uncertainty in anthropogenic DIC. We show that the sources of uncertainty related to the uptake of anthropogenic δ13CDIC and DIC are quite distinct. Uncertainty in anthropogenic δ13C uptake is controlled by air–sea gas exchange, which explains 63% of modelled variance. This mode of variability is largely absent from the ensemble variability in CO2 uptake, which is rather driven by uncertainties in thermocline ventilation rates. Although the need to account for air–sea gas exchange is well known, these results suggest that, to leading order, uncertainties in the ocean uptake of anthropogenic 13C and CO2 are governed by very different processes. This illustrates the difficulties in reconstructing one from the other, and furthermore highlights the need for careful targeting of both δ13CDIC and DIC observations to better constrain the ocean sink of anthropogenic CO2
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