Nonparametric estimation of a conditional distribution from length-biased data

In this paper we consider the problem of estimating a conditional distribution function in a nonparametric way, when the response variable is nonnegative, and the observational procedure is length-biased. We propose a proper adaptation of the estimate to right-censoring provoked by limitation in following-up. Large sample analysis of the introduced estimator is given, including rates of convergence, limiting distribution, and efficiency results. We show that the length-bias model results in less variance in estimation, when compared to methods based on observed truncation times. Practical performance of the proposed estimator is explored through simulations. Application to unemployment data analysis is provided.     

Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions

This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill‐posed problem, we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1799–1822, 2017     

Bifurcation of homoclinics

We show that homoclinic trajectories of nonautonomous vector fields parametrized by a circle bifurcate from the stationary solution when the asymptotic stable bundles of the linearization at plus and minus infinity are ``twisted' in different ways.

     

Nonparametric estimation under length-biased sampling and Type I censoring: A moment based approach

Observation of lifetimes by means of cross-sectional surveys typically results in left-truncated, right-censored data. In some applications, it may be assumed that the truncation variable is uniformly distributed on some time interval, leading to the so-called length-biased sampling. This information is relevant, since it allows for more efficient estimation of survival and related parameters. In this work we introduce and analyze new empirical methods in the referred scenario, when the sampled lifetimes are at risk of Type I censoring from the right. We illustrate the method with real economic data. Work supported by the Grants PGIDIT02PXIA30003PR and BFM2002-03213.     

Globalizations of partial actions on nonunital rings

In this note we prove a criteria for the existence of a globalization for a given partial action of a group on an -unital ring. If the globalization exists, it is unique in a natural sense. This extends the globalization theorem from Dokuchaev and Exel, 2005, obtained in the context of rings with

     

CFD analysis of a TG–DSC apparatus

A ThermoGravimetric analyser with differential scanning calorimetry (TG–DSC) has been studied during the fusion of an indium sample using both an experimental procedure and a CFD simulation. To do so, a CAD model of the real device was built and meshed in detail, in order to take into account the small scale processes which occur inside the crucibles. Several theoretical models, some previously existing in the CFD software used and others developed ad hoc, were applied to simulate the whole facility. Therefore, realistic boundary conditions and a PID-based control system already developed for previous studies had to be used. The validation of the CFD model was done by comparing the outcome of the resulting simulation to the results obtained by experimental procedure in a case where natural convection is the main heat and mass transfer mechanism. This comparison was made for two different heating rates inside the furnace. Typical characteristics of phase change process inside a TG-DSC as thermal lag, onset temperature or heat flow exchange during the fusion could be analysed. As well, a more detailed approach to physical phenomena taking place inside the furnace could be done, since CFD simulations allow to obtain data which is not achievable experimentally. Besides, a valid CFD model for a TG-DSC could be later used in further CFD simulations.     

Isobaric thermal expansivity behaviour against temperature and pressure of associating fluids

In order to study the influence of association on the isobaric thermal expansivity, this magnitude has been experimentally determined for a set of associating fluids within the temperature and pressure intervals (278.15 to 348.15) K and (5 to 55) MPa by means of calorimetric measurements. The 1-alcohol series, from methanol to 1-decanol, 2-pentanol, 3-pentanol, and 1-pentylamine were selected. With a view on checking the quality of the experimental data, they are compared with available literature values; good coherence was obtained for most of the studied liquids. The analysis of the experimental results reveals that the association capability presents a strong influence not only on the value of the isobaric thermal expansivity itself, but also on its behaviour against temperature and pressure.     

Information sets in abelian codes: defining sets and Groebner basis

In Bernal and Simón (IEEE Trans Inf Theory 57(12):7990–7999, 2011) we introduced a technique to construct information sets for every semisimple abelian code by means of its defining set. This construction is a non trivial generalization of that given by Imai (Inf Control 34:1–21, 1977) in the case of binary two-dimensional cyclic (TDC) codes. On the other hand, Sakata (IEEE Trans Inf Theory IT-27(5):556–565, 1981) showed a method for constructing information sets for binary TDC codes based on the computation of Groebner basis which agrees with the information set obtained by Imai. Later, Chabanne (IEEE Trans Inf Theory 38(6):1826–1829, 1992) presents a generalization of the permutation decoding algorithm for binary abelian codes by using Groebner basis, and as a part of his method he constructs an information set following the same ideas introduced by Sakata. In this paper we show that, in the general case of q-ary multidimensional abelian codes, both methods, that based on Groebner basis and that defined in terms of the defining sets, also yield the same information set.