6,852 research outputs found
Approximation of fuzzy numbers by convolution method
In this paper we consider how to use the convolution method to construct
approximations, which consist of fuzzy numbers sequences with good properties,
for a general fuzzy number. It shows that this convolution method can generate
differentiable approximations in finite steps for fuzzy numbers which have
finite non-differentiable points. In the previous work, this convolution method
only can be used to construct differentiable approximations for continuous
fuzzy numbers whose possible non-differentiable points are the two endpoints of
1-cut. The constructing of smoothers is a key step in the construction process
of approximations. It further points out that, if appropriately choose the
smoothers, then one can use the convolution method to provide approximations
which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201
Near-threshold Z-pair production in the semi-phenomenological model of unstable particles
Near-threshold production of neutral boson pairs is considered within the
framework of the model of unstable particles with smeared mass. The results of
calculations are in good agreement with LEP II data and Monte-Carlo
simulations.Comment: 7 pages, 2 figure
Confidence limits of evolutionary synthesis models. IV Moving forward to a probabilistic formulation
Synthesis models predict the integrated properties of stellar populations.
Several problems exist in this field, mostly related to the fact that
integrated properties are distributed. To date, this aspect has been either
ignored (as in standard synthesis models, which are inherently deterministic)
or interpreted phenomenologically (as in Monte Carlo simulations, which
describe distributed properties rather than explain them). We approach
population synthesis as a problem in probability theory, in which stellar
luminosities are random variables extracted from the stellar luminosity
distribution function (sLDF). We derive the population LDF (pLDF) for clusters
of any size from the sLDF, obtaining the scale relations that link the sLDF to
the pLDF. We recover the predictions of standard synthesis models, which are
shown to compute the mean of the sLDF. We provide diagnostic diagrams and a
simplified recipe for testing the statistical richness of observed clusters,
thereby assessing whether standard synthesis models can be safely used or a
statistical treatment is mandatory. We also recover the predictions of Monte
Carlo simulations, with the additional bonus of being able to interpret them in
mathematical and physical terms. We give examples of problems that can be
addressed through our probabilistic formalism. Though still under development,
ours is a powerful approach to population synthesis. In an era of resolved
observations and pipelined analyses of large surveys, this paper is offered as
a signpost in the field of stellar populations.Comment: Accepted by A&A. Substantially modified with respect to the 1st
draft. 26 pages, 14 fig
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