Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory

In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator

Revealing the structure of the outer disks of Be stars

Context. The structure of the inner parts of Be star disks (20 stellar radii) is well explained by the viscous decretion disk (VDD) model, which is able to reproduce the observable properties of most of the objects studied so far. The outer parts, on the ther hand, are not observationally well-explored, as they are observable only at radio wavelengths. A steepening of the spectral slope somewhere between infrared and radio wavelengths was reported for several Be stars that were previously detected in the radio, but a convincing physical explanation for this trend has not yet been provided. Aims. We test the VDD model predictions for the extended parts of a sample of six Be disks that have been observed in the radio to address the question of whether the observed turndown in the spectral energy distribution (SED) can be explained in the framework of the VDD model, including recent theoretical development for truncated Be disks in binary systems. Methods. We combine new multi-wavelength radio observations from the Karl. G. Jansky Very Large Array (JVLA) and Atacama Pathfinder Experiment (APEX) with previously published radio data and archival SED measurements at ultraviolet, visual, and infrared wavelengths. The density structure of the disks, including their outer parts, is constrained by radiative transfer modeling of the observed spectrum using VDD model predictions. In the VDD model we include the presumed effects of possible tidal influence from faint binary companions. Results. For 5 out of 6 studied stars, the observed SED shows strong signs of SED turndown between far-IR and radio wavelengths. A VDD model that extends to large distances closely reproduces the observed SEDs up to far IR wavelengths, but fails to reproduce the radio SED. ... (abstract continues but did not fit here)Comment: 20 pages, 8 figure

Multitechnique testing of the viscous decretion disk model I. The stable and tenuous disk of the late-type Be star β\beta CMi

The viscous decretion disk (VDD) model is able to explain most of the currently observable properties of the circumstellar disks of Be stars. However, more stringent tests, focusing on reproducing multitechnique observations of individual targets via physical modeling, are needed to study the predictions of the VDD model under specific circumstances. In the case of nearby, bright Be star $\beta$ CMi, these circumstances are a very stable low-density disk and a late-type (B8Ve) central star. The aim is to test the VDD model thoroughly, exploiting the full diagnostic potential of individual types of observations, in particular, to constrain the poorly known structure of the outer disk if possible, and to test truncation effects caused by a possible binary companion using radio observations. We use the Monte Carlo radiative transfer code HDUST to produce model observables, which we compare with a very large set of multitechnique and multiwavelength observations that include ultraviolet and optical spectra, photometry covering the interval between optical and radio wavelengths, optical polarimetry, and optical and near-IR (spectro)interferometry. Due to the absence of large scale variability, data from different epochs can be combined into a single dataset. A parametric VDD model with radial density exponent of $n$ = 3.5, which is the canonical value for isothermal flaring disks, is found to explain observables typically formed in the inner disk, while observables originating in the more extended parts favor a shallower, $n$ = 3.0, density falloff. Modeling of radio observations allowed for the first determination of the physical extent of a Be disk (35$^{+10}_{-5}$ stellar radii), which might be caused by a binary companion. Finally, polarization data allowed for an indirect measurement of the rotation rate of the star, which was found to be $W \gtrsim 0.98$, i.e., very close to critical.Comment: 19 pages (35 including online material), 17 figures, 2 online figures, 2 online tables with dat