9,889 research outputs found
Approximate closed-form formulas for the zeros of the Bessel Polynomials
We find approximate expressions x(k,n) and y(k,n) for the real and imaginary
parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain
these closed-form formulas we use the fact that the points of well-defined
curves in the complex plane are limit points of the zeros of the normalized
Bessel polynomials. Thus, these zeros are first computed numerically through an
implementation of the electrostatic interpretation formulas and then, a fit to
the real and imaginary parts as functions of k and n is obtained. It is shown
that the resulting complex number x(k,n)+i y(k,n) is O(1/n^2)-convergent to z_k
for fixed kComment: 9 pages, 2 figure
On the logarithmic comparison theorem for integrable logarithmic connections
Let be a complex analytic manifold, a free divisor with
jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor),
the corresponding open inclusion, an integrable
logarithmic connection with respect to and the local system of the
horizontal sections of on . In this paper we prove that the canonical
morphisms between the logarithmic de Rham complex of and
(resp. the logarithmic de Rham complex of and ) are isomorphisms
in the derived category of sheaves of complex vector spaces for
(locally on )Comment: Terminology has changed: "linear jacobian type" instead of
"commutative differential type"); no Koszul hypothesis is needed in theorem
(2.1.1); minor changes. To appear in Proc. London Math. So
Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics
A variety of researchers have successfully obtained the parameters of low
dimensional diffusion models using the data that comes out of atomistic
simulations. This naturally raises a variety of questions about efficient
estimation, goodness-of-fit tests, and confidence interval estimation. The
first part of this article uses maximum likelihood estimation to obtain the
parameters of a diffusion model from a scalar time series. I address numerical
issues associated with attempting to realize asymptotic statistics results with
moderate sample sizes in the presence of exact and approximated transition
densities. Approximate transition densities are used because the analytic
solution of a transition density associated with a parametric diffusion model
is often unknown.I am primarily interested in how well the deterministic
transition density expansions of Ait-Sahalia capture the curvature of the
transition density in (idealized) situations that occur when one carries out
simulations in the presence of a "glassy" interaction potential. Accurate
approximation of the curvature of the transition density is desirable because
it can be used to quantify the goodness-of-fit of the model and to calculate
asymptotic confidence intervals of the estimated parameters. The second part of
this paper contributes a heuristic estimation technique for approximating a
nonlinear diffusion model. A "global" nonlinear model is obtained by taking a
batch of time series and applying simple local models to portions of the data.
I demonstrate the technique on a diffusion model with a known transition
density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly
shortened
Survival and Nonescape Probabilities for Resonant and Nonresonant Decay
In this paper we study the time evolution of the decay process for a particle
confined initially in a finite region of space, extending our analysis given
recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly
the time-dependent Schroedinger equation for a finite-range potential. We
calculate and compare two quantities: (i) the survival probability S(t), i.e.,
the probability that the particle is in the initial state after a time t; and
(ii) the nonescape probability P(t), i.e., the probability that the particle
remains confined inside the potential region after a time t. We analyze in
detail the resonant and nonresonant decay. In the former case, after a very
short time, S(t) and P(t) decay exponentially, but for very long times they
decay as a power law, albeit with different exponents. For the nonresonant case
we obtain that both quantities differ initially. However, independently of the
resonant and nonresonant character of the initial state we always find a
transition to the ground state of the system which indicates a process of
``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from
[email protected] (To be published in Annals of Physics
Evaluating The Effect Of Water Supplementation On Ring-Necked Pheasant And Mesocarnivore Occupancy In Western Kansas
A âguzzlerâ is any structure that stores and supplements water for wildlife populations. They are often used to target economically influential game species where water is thought to be potentially limiting. Upland game, like the ring-necked pheasant (Phasianus colchicus) in the semi-arid landscape of western Kansas, represent such populations as guzzlers have become common practice in wildlife management applications across the region, especially on lands enrolled in the Conservation Reserve Program (CRP). However, little is known about the spatial response, if any, of wildlife populations to guzzlers or the potential increased risk they pose for predation. From June to August of 2011 and 2012 my project used occupancy modeling techniques to identify if guzzlers potentially influenced occupancy by Phasianus colchicus and their potential predators (i.e., mesocarnivores) on CRP lands in western Kansas. Phasianus colchicus detection was most explained by month of survey (highest in June; P \u3c 0.001), with occupancy being most influenced by distance from edge and percent forb cover at cameras, and land cover type at sites (camera data aggregated). For mesocarnivores, guzzler was the top performing habitat feature for explaining detection at cameras, but only raccoon (Procyon lotor) had guzzler best explain detection across sites as well. This suggested that increased predation near guzzlers, especially from an efficient nest predator like P. lotor, might be possible. While controlling for differences in detection, however, guzzlers did not perform well for explaining any target species occupancy. However, future studies are needed to truly evaluate this potential, as well as to assess the capacity for guzzlers to augment local population abundance, even if only during times of drought
SPITZER observations of the λ Orionis cluster. II. Disks around solar-type and low-mass stars
We present IRAC/MIPS Spitzer Space Telescope observations of the solar-type and the low-mass stellar population
of the young (~5Myr) λ Orionis cluster. Combining optical and Two Micron All Sky Survey photometry, we identify
436 stars as probable members of the cluster. Given the distance (450 pc) and the age of the cluster, our sample
ranges in mass from 2 M_â to objects below the substellar limit. With the addition of the Spitzer mid-infrared data,
we have identified 49 stars bearing disks in the stellar cluster. Using spectral energy distribution slopes, we place
objects in several classes: non-excess stars (diskless), stars with optically thick disks, stars with âevolved disksâ
(with smaller excesses than optically thick disk systems), and âtransitional diskâ candidates (in which the inner
disk is partially or fully cleared). The disk fraction depends on the stellar mass, ranging from ~6% for K-type stars (R_C â J 4). We confirm the dependence of disk
fraction on stellar mass in this age range found in other studies. Regarding clustering levels, the overall fraction of disks in the λ Orionis cluster is similar to those reported in other stellar groups with ages normally quoted as ~5Myr
Searching for star-forming dwarf galaxies in the Antlia cluster
The formation and evolution of dwarf galaxies in clusters need to be
understood, and this requires large aperture telescopes. In this sense, we
selected the Antlia cluster to continue our previous work in the Virgo, Fornax,
and Hydra clusters and in the Local Volume (LV). Because of the scarce
available literature data, we selected a small sample of five blue compact
dwarf (BCD) candidates in Antlia for observation. Using the Gemini South and
GMOS camera, we acquired the Halpha imaging needed to detect star-forming
regions in this sample. With the long-slit spectroscopic data of the brightest
seven knots detected in three BCD candidates, we derived their basic chemical
properties. Using archival VISTA VHS survey images, we derived K_S magnitudes
and surface brightness profile fits for the whole sample to assess basic
physical properties. FS90-98, FS90-106, and FS90-147 are confirmed as BCDs and
cluster members, based on their morphology, K_S surface photometry, oxygen
abundance, and velocity redshift. FS90-155 and FS90-319 did not show any
H{\alpha} emission, and they could not be confirmed as dwarf cluster
star-forming galaxies. Based on our data, we studied some fundamental relations
to compare star forming dwarfs (BCDs and dIs) in the LV and in the Virgo,
Fornax, Hydra, and Antlia clusters. Star-forming dwarfs in nearby clusters
appear to follow same fundamental relations in the near infrared with similar
objects in the LV, specifically the size-luminosity and the
metallicity-luminosity, while other more fundamental relations could not be
checked in Antlia due to lack of data.Comment: Accepted for publication in A&A (early 2014
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