Testing goodness of fit for the distribution of errors in multivariate linear models

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.     

Determination of bromide by low power surfatron microwave induced plasma after bromine continuous generation

A simple continuous flow generation of volatile bromine is described for the determination of low concentrations of the elements by atmospheric-pressure argon microwave induced plasma (MIP) surfatron. Bromine is continuously generated by mixing the bromide with sulphuric acid and hypochlorite solutions. The bromine vapor is separated from the aqueous phase by a gas-liquid separator and is desiccated by passing it through concentrated sulphuric acid. The detection limit attained was 2 microg/l. and the precision was +/-0.7% (at the 80 microg/l. level). The proposed determination is very selective if oxidizing/reducing agents are absent. The procedure has been tested for bromide determination in two drug preparations. Good agreement between the experimental results and the certified values has been obtained.     

Monodromy,center–focus and integrability problems for quasi-homogeneous polynomial systems

This paper deals with planar quasi-homogeneous polynomial vector fields, and addresses three major questions: the monodromy, the center–focus and the integrability problems. We characterize the monodromic planar quasi-homogeneous polynomial vector fields, and we give a condition to distinguish between a center and a focus in this case. Also, we provide conditions which characterize the integrability of quasi-homogeneous polynomial systems under non-resonance conditions. The results obtained allow us to analyse two monodromic planar systems with degenerate linear part: one of them with nilpotent linearization, and another one with null linear part.     

Analysis of Hopf and Takens–Bogdanov Bifurcations in a Modified van der Pol–Duffing Oscillator

We analyze a modified van der Pol–Duffing electronic circuit, modeled by a tridimensional autonomous system of differential equations with Z₂-symmetry. Linear codimension-one and two bifurcations of equilibria give rise to several dynamical behaviours, including periodic, homoclinic and heteroclinic orbits. The local analysis provides, in first approximation, the different bifurcation sets. These local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Hopf bifurcation shows the presence of cusps of saddle-node bifurcations of periodic orbits. The existence of a codimension-four Hopf bifurcation is also pointed out. In the case of the Takens–Bogdanov bifurcation, several degenerate situations of codimension-three are analyzed in both homoclinic and heteroclinic cases. The existence of a Hopf–Shil'nikov singularity is also shown.     

Differential cognitive impairment for diverse forms of multiple sclerosis

Background  

Cognitive impairment is a common feature in multiple sclerosis (MS) patients and occurs in 60% of all cases. Unfortunately, neurological examination does not always agree with the neuropsychological evaluation in determining the cognitive profile of the patient. On the other hand, psychophysiological techniques such as event-related potentials (ERPs) can help in evaluating cognitive impairment in different pathologies.     

A Tame Degenerate Hopf-Pitchfork Bifurcation in a Modified van der Pol–Duffing Oscillator

We consider a modified van der Pol–Duffing electronic circuit,focusing on the case where a Hopf-pitchfork bifurcation takes places.The analysis of this bifurcation is a simple way to detect andcharacterize purely three-dimensional behaviour (an oscillatory regimein three variables, quasiperiodic motion, etc.).The normal formanalysis provides the classification of different kinds ofHopf-pitchfork bifurcation, organized according to some degeneratecases. One of these degenerate cases is analyzed, by considering acodimension-three unfolding of a reflectionally symmetric planar vectorfield. Later, the implications for three-dimensional flows arepresented. Unlike another degenerate Hopf-pitchfork bifurcationsexhibited by the system, the one studied here does not involvequasiperiodic behaviour, so that the complexity related to quasiperiodicmotion is not present.     

A homogeneity test for bivariate random variables

In this paper, a test for the homogeneity of two bidimensional populations is proposed. It is based on the L ₂-norm of the difference between the empirical characteristic functions associated with independent random samples from each population. We first approximate this norm and then we give two bootstrap algorithms to consistently estimate the null distribution of the resultant test statistic. A simulation study illustrates the goodness of these two bootstrap estimators and compares the proposed test with others.