6,173 research outputs found
Digital Repository of Mathematical Formulae
The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is
to create a digital compendium of mathematical formulae for orthogonal
polynomials and special functions (OPSF) and of associated mathematical data.
The DRMF addresses needs of working mathematicians, physicists and engineers:
providing a platform for publication and interaction with OPSF formulae on the
web. Using MediaWiki extensions and other existing technology (such as software
and macro collections developed for the NIST Digital Library of Mathematical
Functions), the DRMF acts as an interactive web domain for OPSF formulae.
Whereas Wikipedia and other web authoring tools manifest notions or
descriptions as first class objects, the DRMF does that with mathematical
formulae. See http://gw32.iu.xsede.org/index.php/Main_Page
KSZ tomography and the bispectrum
Several statistics have been proposed for measuring the kSZ effect by
combining the small-scale CMB with galaxy surveys. We review five such
statistics, and show that they are all mathematically equivalent to the optimal
bispectrum estimator of type . Reinterpreting these kSZ
statistics as special cases of bispectrum estimation makes many aspects
transparent, for example optimally weighting the estimator, or incorporating
photometric redshift errors. We analyze the information content of the
bispectrum and show that there are two observables: the small-scale
galaxy-electron power spectrum , and the large-scale
galaxy-velocity power spectrum . The cosmological constraining power
of the kSZ arises from its sensitivity to fluctuations on large length scales,
where its effective noise level can be much better than galaxy surveys.Comment: 39 page
Multi-Satellite Observations of Cygnus X-1 to Study the Focused Wind and Absorption Dips
High-mass X-ray binary systems are powered by the stellar wind of their donor
stars. The X-ray state of Cygnus X-1 is correlated with the properties of the
wind which defines the environment of mass accretion. Chandra-HETGS
observations close to orbital phase 0 allow for an analysis of the photoionzed
stellar wind at high resolution, but because of the strong variability due to
soft X-ray absorption dips, simultaneous multi-satellite observations are
required to track and understand the continuum, too. Besides an earlier joint
Chandra and RXTE observation, we present first results from a recent campaign
which represents the best broad-band spectrum of Cyg X-1 ever achieved: On 2008
April 18/19 we observed this source with XMM-Newton, Chandra, Suzaku, RXTE,
INTEGRAL, Swift, and AGILE in X- and gamma-rays, as well as with VLA in the
radio. After superior conjunction of the black hole, we detect soft X-ray
absorption dips likely due to clumps in the focused wind covering >95 % of the
X-ray source, with column densities likely to be of several 10^23 cm^-2, which
also affect photon energies above 20 keV via Compton scattering.Comment: 10 pages, contributed talk at the 7th Microquasar Workshop, Foca,
Turkey, Sept. 1-5, 200
Non-equilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the
quantitative analysis of physical and biological systems, such as the
generation of action potentials by nerve cells, the release and reuptake of
vesicles at a synapse, and the counting of particles by detector devices. Here
we present an extension of renewal theory to describe ensembles of point
processes with time varying input. This is made possible by a representation in
terms of occupation numbers of two states: Active and refractory. The dynamics
of these occupation numbers follows a distributed delay differential equation.
In particular, our theory enables us to uncover the effect of refractoriness on
the time-dependent rate of an ensemble of encoding point processes in response
to modulation of the input. We present exact solutions that demonstrate generic
features, such as stochastic transients and oscillations in the step response
as well as resonances, phase jumps and frequency doubling in the transfer of
periodic signals. We show that a large class of renewal processes can indeed be
regarded as special cases of the model we analyze. Hence our approach
represents a widely applicable framework to define and analyze non-stationary
renewal processes.Comment: 8 pages, 4 figure
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