1,125 research outputs found
Karhunen-Lo\`{e}ve expansions of mean-centered Wiener processes
For , we provide the Karhunen-Lo\`{e}ve expansion of the
weighted mean-centered Wiener process, defined by for . We show that the
orthogonal functions in these expansions have simple expressions in term of
Bessel functions. Moreover, we obtain that the norm of
is identical in distribution with the norm of the weighted Brownian
bridge .Comment: Published at http://dx.doi.org/10.1214/074921706000000761 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A new test procedure of independence in copula models via chi-square-divergence
We introduce a new test procedure of independence in the framework of
parametric copulas with unknown marginals. The method is based essentially on
the dual representation of -divergence on signed finite measures. The
asymptotic properties of the proposed estimate and the test statistic are
studied under the null and alternative hypotheses, with simple and standard
limit distributions both when the parameter is an interior point or not.Comment: 23 pages (2 figures). Submitted to publicatio
Constraints on the core mu-gradient of the solar-like star HD 49385 via low-degree mixed modes
The existence of an l=1 avoided crossing in the spectrum of the solar-like
pulsator CoRoT-target HD 49385 was established by Deheuvels & Michel (2009). It
is the first confirmed detection of such a phenomenon. The authors showed in a
preliminary modeling of the star that it was in a post main sequence status.
Being a 1.3 Msun-star, HD 49385 has had a convective core during its main
sequence phase. The mu-gradient left by the withdrawal of this core bears
information about the processes of transport at the boundary of the core. We
here investigate the constraints that the observed avoided crossing brings on
the mu-gradient in the core of the star.Comment: 5 pages, 5 figures, accepted in Astron. Nach. This work was presented
at the HELAS Conference in Lanzarote in February 201
Mapping plant diversity in cocoa-based agroforestry systems to improve overall productivity
In cocoa-based agroforestry systems (CAFS), the cocoa trees are associated with other cultivated plant species at variable densities. There, the spatial distribution of the cultivated plants can be regular, random or aggregated, and their age may vary even in the same species. Variables of (i) density, (ii) spatial distribution and (iii) age can thus influence the overall productivity of CAFS and its distribution in space. We studied the relationships between these 3 variables and CAFS productivity based on data collected in 34 experimental yield tracking plots placed in agroforestry fields of producers in the Dominican Republic. A mapping of the cultivated plants was carried out on each plot at their installation and harvests of the ripe products of each individual plant were carried out every two weeks over a period of one year. The first results of this study indicate that optimal CAFS productivity can be maintained along a decreasing density gradient of crops, associated with cocoa tree ageing. In addition, regular and random spatial distribution of all plant species may increase overall productivity. The analysis of the variability of cocoa, fruit, tuber and timber yields allows us to provide recommendations on the most suitable species and the optimal distance between plants to improve overall productivity and therefore the producer's income
Sobolev extension property for tree-shaped domains with self-contacting fractal boundary
International audienceIn this paper, we investigate the existence of extension operators fromW1,p( ) toW1,p(R2) (1 < p < 1) for a class of tree-shaped domains with a self-similar fractal boundary pre- viously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the results of Jones imply that there exist such extension operators for all p 2 [1,1]. In the case when the fractal boundary self-intersects, this result does not hold. Here, we prove however that extension operators exist for p < p? where p? depends only on the dimension of the self-intersection of the boundary. The construction of these operators mainly relies on the self-similar properties of the domains
Angular momentum transport efficiency in post-main sequence low-mass stars
Context. Using asteroseismic techniques, it has recently become possible to
probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and
red giant stars. Under the assumption of local angular momentum conservation,
the core contraction and envelope expansion occurring at the end of the main
sequence would result in a much larger internal differential rotation than
observed. This suggests that angular momentum redistribution must be taking
place in the interior of these stars. Aims. We investigate the physical nature
of the angular momentum redistribution mechanisms operating in stellar
interiors by constraining the efficiency of post-main sequence rotational
coupling. Methods. We model the rotational evolution of a 1.25 Msun star using
the Yale Rotational stellar Evolution Code. Our models take into account the
magnetic wind braking occurring at the surface of the star and the angular
momentum transport in the interior, with an efficiency dependent on the degree
of internal differential rotation. Results. We find that models including a
dependence of the angular momentum transport efficiency on the radial
rotational shear reproduce very well the observations. The best fit of the data
is obtained with an angular momentum transport coefficient scaling with the
ratio of the rotation rate of the radiative interior over that of the
convective envelope of the star as a power law of exponent ~3. This scaling is
consistent with the predictions of recent numerical simulations of the
Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular
momentum transport process whose efficiency varies during the stellar evolution
through a dependence on the level of internal differential rotation is required
to explain the observed post-main sequence rotational evolution of low-mass
stars.Comment: 8 pages, 6 figures; accepted for publication in Astronomy &
Astrophysic
Probing core overshooting using asteroseismology
Modeling properly the interface between convective cores and radiative
interiors is one the most challenging and important open questions in modern
stellar physics. The rapid development of asteroseismology, with the advent of
space missions partly dedicated to this discipline, has provided new
constraints to progress on this issue. We here give an overview of the
information that can be obtained from pressure modes, gravity modes and mixed
modes. We also review some of the most recent constraints obtained from
space-based asteroseismology on the nature and the amount of mixing beyond
convective cores.Comment: To appear in the proceedings of the workshop "How Much do we Trust
Stellar Models?" held in Li\`ege in September 201
Period spacings in red giants I. Disentangling rotation and revealing core structure discontinuities
Asteroseismology allows us to probe the physical conditions inside the core
of red giant stars. This relies on the properties of the global oscillations
with a mixed character that are highly sensitive to the physical properties of
the core. However, overlapping rotational splittings and mixed-mode spacings
result in complex structures in the mixed-mode pattern, which severely
complicates its identification and the measurement of the asymptotic period
spacing. This work aims at disentangling the rotational splittings from the
mixed-mode spacings, in order to open the way to a fully automated analysis of
large data sets. An analytical development of the mixed-mode asymptotic
expansion is used to derive the period spacing between two consecutive mixed
modes. The \'echelle diagrams constructed with the appropriately stretched
periods are used to exhibit the structure of the gravity modes and of the
rotational splittings. We propose a new view on the mixed-mode oscillation
pattern based on corrected periods, called stretched periods, that mimic the
evenly spaced gravity-mode pattern. This provides a direct understanding of all
oscillation components, even in the case of rapid rotation. The measurement of
the asymptotic period spacing and the signature of the structural glitches on
mixed modes are then made easy. This work opens the possibility to derive all
seismic global parameters in an automated way, including the identification of
the different rotational multiplets and the measurement of the rotational
splitting, even when this splitting is significantly larger than the period
spacing. Revealing buoyancy glitches provides a detailed view on the radiative
core.Comment: Accepted in A&
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