817,520 research outputs found
DOMAIN THEORY AND INTEGRATION
We present a domain-theoretic framework for measure theory and integration of bounded real-valued functions with respect to bounded Borel measures on compact metric spaces. The set of normalised Borel measures of the metric space can be embedded into the maximal elements of the normalised probabilistic power domain of its upper space. Any bounded Borel measure on the compact metric space can then be obtained as the least upper bound of an !-chain of linear combinations of point valuations (simple valuations) on the upper space, thus providing a constructive setup for these measures. We use this setting to define a new notion of integral of a bounded real-valued function with respect to a bounded Borel measure on a compact metric space. By using an !-chain of simple valuations, whose lub is the given Borel measure, we can then obtain increasingly better approximations to the value of the integral, similar to the way the Riemann integral is obtained in calculus by using step functions. ..
Distributions and Integration in superspace
Distributions in superspace constitute a very useful tool for establishing an
integration theory. In particular, distributions have been used to obtain a
suitable extension of the Cauchy formula to superspace and to define
integration over the superball and the supersphere through the Heaviside and
Dirac distributions, respectively.
In this paper, we extend the distributional approach to integration over more
general domains and surfaces in superspace. The notions of domain and surface
in superspace are defined by smooth bosonic phase functions . This allows to
define domain integrals and oriented (as well as non-oriented) surface
integrals in terms of the Heaviside and Dirac distributions of the
superfunction . It will be shown that the presented definition for the
integrals does not depend on the choice of the phase function defining the
corresponding domain or surface. In addition, some examples of integration over
a super-paraboloid and a super-hyperboloid will be presented. Finally, a new
distributional Cauchy-Pompeiu formula will be obtained, which generalizes and
unifies the previously known approaches.Comment: 25 page
Domain decomposition and multilevel integration for fermions
The numerical computation of many hadronic correlation functions is
exceedingly difficult due to the exponentially decreasing signal-to-noise ratio
with the distance between source and sink. Multilevel integration methods,
using independent updates of separate regions in space-time, are known to be
able to solve such problems but have so far been available only for pure gauge
theory. We present first steps into the direction of making such integration
schemes amenable to theories with fermions, by factorizing a given observable
via an approximated domain decomposition of the quark propagator. This allows
for multilevel integration of the (large) factorized contribution to the
observable, while its (small) correction can be computed in the standard way.Comment: 14 pages, 6 figures, v2: published version, talk presented at the
34th annual International Symposium on Lattice Field Theory, 24-30 July 2016,
University of Southampton, U
Evolution of electromagnetic and Dirac perturbations around a black hole in Horava gravity
The evolution of electromagnetic and Dirac perturbations in the spacetime
geometry of Kehagias-Sfetsos(KS) black hole in the deformed Horava-Lifshitz(HL)
gravity is investigated and the associated quasinormal modes are evaluated
using time domain integration and WKB methods. We find a considerable deviation
in the nature of field evolution in HL theory from that in the Schwarzschild
spacetime and QNMs region extends over a longer time in HL theory before the
power-law tail decay begins. The dependence of the field evolution on the HL
parameter are studied. In the time domain picture we find that the
length of QNM region increases with . But the late time decay of field
follows the same power-law tail behavior as in the case of Schwarzschild black
hole.Comment: The article was fully rewritten, references added, to appear in MPL
Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case
Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of the data generating mechanism in the frequency domain. The modified local Whittle estimator is shown to be consistent for 0Discrete Fourier transform, fractional Brownian motion, fractional integration, long memory, nonstationarity, semiparametric estimation, Whittle likelihood
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