1,948 research outputs found
Level crossings and other level functionals of stationary Gaussian processes
This paper presents a synthesis on the mathematical work done on level
crossings of stationary Gaussian processes, with some extensions. The main
results [(factorial) moments, representation into the Wiener Chaos, asymptotic
results, rate of convergence, local time and number of crossings] are
described, as well as the different approaches [normal comparison method, Rice
method, Stein-Chen method, a general -dependent method] used to obtain them;
these methods are also very useful in the general context of Gaussian fields.
Finally some extensions [time occupation functionals, number of maxima in an
interval, process indexed by a bidimensional set] are proposed, illustrating
the generality of the methods. A large inventory of papers and books on the
subject ends the survey.Comment: Published at http://dx.doi.org/10.1214/154957806000000087 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the second moment of the number of crossings by a stationary Gaussian process
Cram\'{e}r and Leadbetter introduced in 1967 the sufficient condition
to have a
finite variance of the number of zeros of a centered stationary Gaussian
process with twice differentiable covariance function . This condition is
known as the Geman condition, since Geman proved in 1972 that it was also a
necessary condition. Up to now no such criterion was known for counts of
crossings of a level other than the mean. This paper shows that the Geman
condition is still sufficient and necessary to have a finite variance of the
number of any fixed level crossings. For the generalization to the number of a
curve crossings, a condition on the curve has to be added to the Geman
condition.Comment: Published at http://dx.doi.org/10.1214/009117906000000142 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nuclear Structure Studies at ISOLDE and their Impact on the Astrophysical r-Process
The focus of the present review is the production of the heaviest elements in
nature via the r-process. A correct understanding and modeling requires the
knowledge of nuclear properties far from stability and a detailed prescription
of the astrophysical environment. Experiments at CERN/ISOLDE have played a
pioneering role in exploring the characteristics of nuclear structure in terms
of masses and beta-decay properties. Initial examinations paid attention to far
unstable nuclei with magic neutron numbers related to r-process peaks, while
present activities are centered on the evolution of shell effects with the
distance from the valley of stability. We first show in site-independent
applications the effect of both types of nuclear properties on r-process
abundances. Then, we explore the results of calculations related to two
different `realistic' astrophysical sites, (i) the supernova neutrino wind and
(ii) neutron star mergers. We close with a list of remaining theoretical and
experimental challenges needed to overcome for a full understanding of the
nature of the r-process, and the role CERN/ISOLDE can play in this process.Comment: LATEX, 38 pages, 16 figures, submitted to Hyperfine Interaction
Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
AbstractWe propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process
Charged-Particle and Neutron-Capture Processes in the High-Entropy Wind of Core-Collapse Supernovae
The astrophysical site of the r-process is still uncertain, and a full
exploration of the systematics of this process in terms of its dependence on
nuclear properties from stability to the neutron drip-line within realistic
stellar environments has still to be undertaken. Sufficiently high neutron to
seed ratios can only be obtained either in very neutron-rich low-entropy
environments or moderately neutron-rich high-entropy environments, related to
neutron star mergers (or jets of neutron star matter) and the high-entropy wind
of core-collapse supernova explosions. As chemical evolution models seem to
disfavor neutron star mergers, we focus here on high-entropy environments
characterized by entropy , electron abundance and expansion velocity
. We investigate the termination point of charged-particle reactions,
and we define a maximum entropy for a given and ,
beyond which the seed production of heavy elements fails due to the very small
matter density. We then investigate whether an r-process subsequent to the
charged-particle freeze-out can in principle be understood on the basis of the
classical approach, which assumes a chemical equilibrium between neutron
captures and photodisintegrations, possibly followed by a -flow
equilibrium. In particular, we illustrate how long such a chemical equilibrium
approximation holds, how the freeze-out from such conditions affects the
abundance pattern, and which role the late capture of neutrons originating from
-delayed neutron emission can play.Comment: 52 pages, 31 figure
Nucleosynthesis Basics and Applications to Supernovae
This review concentrates on nucleosynthesis processes in general and their
applications to massive stars and supernovae. A brief initial introduction is
given to the physics in astrophysical plasmas which governs composition
changes. We present the basic equations for thermonuclear reaction rates and
nuclear reaction networks. The required nuclear physics input for reaction
rates is discussed, i.e. cross sections for nuclear reactions,
photodisintegrations, electron and positron captures, neutrino captures,
inelastic neutrino scattering, and beta-decay half-lives. We examine especially
the present state of uncertainties in predicting thermonuclear reaction rates,
while the status of experiments is discussed by others in this volume (see M.
Wiescher). It follows a brief review of hydrostatic burning stages in stellar
evolution before discussing the fate of massive stars, i.e. the nucleosynthesis
in type II supernova explosions (SNe II). Except for SNe Ia, which are
explained by exploding white dwarfs in binary stellar systems (which will not
be discussed here), all other supernova types seem to be linked to the
gravitational collapse of massive stars (M8M) at the end of their
hydrostatic evolution. SN1987A, the first type II supernova for which the
progenitor star was known, is used as an example for nucleosynthesis
calculations. Finally, we discuss the production of heavy elements in the
r-process up to Th and U and its possible connection to supernovae.Comment: 52 pages, 20 figures, uses cupconf.sty (included); to appear in
"Nuclear and Particle Astrophysics", eds. J. Hirsch., D. Page, Cambridge
University Pres
Development of Acid-Sensitive Platinum(II) Complexes With Protein-Binding Properties
Four new protein-binding platinum(II) complexes, 10, 11, 21, 22, in which the dichloroplatinum moiety is coordinated either to a carbon-substituted or a nitrogen-substituted ethylene diamino ligand, were prepared in ten-step syntheses. According to pH-dependent stability studies with strictly related compounds, 11 and 22 exhibit acid-sensitive properties
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