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An intractability result for multiple integration
Our aim is to show that in the worst case setting the integration problem is intractable. The implications of the intractability result for lattice methods are considered briefly in Section 3
Generalized Geologic Map for Land-Use Planning: Lincoln County, Kentucky
This map is not intended to be used for selecting individual sites. Its purpose is to inform land-use planners, government officials, and the public in a general way about geologic bedrock conditions that affect the selection of sites for various purposes. The properties of thick soils may supercede those of the underlying bedrock and should be considered on a site-to-site basis. At any site, it is important to understand the characteristics of both the soils and the underlying rock
Modelling the alumina abundance of oxygen-rich evolved stars in the Large Magellanic Cloud
In order to determine the composition of the dust in the circumstellar
envelopes of oxygen-rich asymptotic giant branch (AGB) stars we have computed a
grid of modust radiative-transfer models for a range of dust compositions,
mass-loss rates, dust shell inner radii and stellar parameters. We compare the
resulting colours with the observed oxygen-rich AGB stars from the SAGE-Spec
Large Magellanic Cloud (LMC) sample, finding good overall agreement for stars
with a mid-infrared excess. We use these models to fit a sample of 37 O-rich
AGB stars in the LMC with optically thin circumstellar envelopes, for which
535-m Spitzer infrared spectrograph (IRS) spectra and broadband
photometry from the optical to the mid-infrared are available. From the
modelling, we find mass-loss rates in the range to
M, and we show that a grain
mixture consisting primarily of amorphous silicates, with contributions from
amorphous alumina and metallic iron provides a good fit to the observed
spectra. Furthermore, we show from dust models that the AKARI [11][15]
versus [3.2][7] colour-colour diagram, is able to determine the fractional
abundance of alumina in O-rich AGB stars.Comment: 22 pages, 17 figures, accepted MNRA
Generalized Geologic Map for Land-Use Planning: Breathitt County, Kentucky
This map is not intended to be used for selecting individual sites. Its purpose is to inform land-use planners, government officials, and the public in a general way about geologic bedrock conditions that affect the selection of sites for various purposes. The properties of thick soils may supercede those of the underlying bedrock and should be considered on a site-to-site basis. At any site, it is important to understand the characteristics of both the soils and the underlying rock
CORRECTION TO "QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND”
ISSN:1446-1811ISSN:1446-873
Quasi-Monte Carlo methods for high-dimensional integration: the standard (weighted Hilbert space) setting and beyond
This paper is a contemporary review of quasi-Monte Carlo (QMC) methods, that is, equal-weight rules for the approximate evaluation of high-dimensional integrals over the unit cube . It first introduces the by-now standard setting of weighted Hilbert spaces of functions with square-integrable mixed first derivatives, and then indicates alternative settings, such as non-Hilbert spaces, that can sometimes be more suitable. Original contributions include the extension of the fast component-by-component (CBC) construction of lattice rules that achieve the optimal convergence order (a rate of almost , where is the number of points, independently of dimension) to so-called “product and order dependent†(POD) weights, as seen in some recent applications. Although the paper has a strong focus on lattice rules, the function space settings are applicable to all QMC methods. Furthermore, the error analysis and construction of lattice rules can be adapted to polynomial lattice rules from the family of digital nets.
doi:10.1017/S144618111200007
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