DETECTABILITY AND ERROR ESTIMATION IN ORBITAL FITS OF RESONANT EXTRASOLAR PLANETS

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than similar to 4. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are currently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically overestimated, although the inner planet`s eccentricity suffers a much smaller effect. If the initial conditions correspond to small-amplitude oscillations around stable apsidal corotation resonances, the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.

A modified signed likelihood ratio test in elliptical structural models

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Development of a sequential injection chromatography (SIC) method for determination of simazine, atrazine, and propazine

This paper describes the development of a sequential injection chromatography (SIC) procedure for separation and quantification of the herbicides simazine, atrazine, and propazine exploring the low backpressure of a 2.5 cm long monolithic C(18) column. The separation of the three compounds was achieved in less than 90 s with resolution > 1.5 using a mobile phase composed by ACN/1.25 mmol/L acetate buffer (pH 4.5) at the volumetric ratio of 35:65 and flow rate of 40 mu L/s. Detection was made at 223 nm using a flow cell with 40 mm of optical path length. The LOD was 10 mu g/L for the three triazines and the quantification limits were of 30 mu g/L for simazine and propazine and 40 mu g/L for atrazine. The sampling frequency is 27 samples per hour, consuming 1.1 mL of ACN per analysis. The proposed methodology was applied to spiked water samples and no statistically significant differences were observed in comparison to a conventional HPLC-UV method. The major metabolites of atrazine and other herbicides did not interfere in the analysis, being eluted from the column either together with the unretained peak, or at retention times well-resolved from the studied compounds.

Implementing stepwise solvent elution in sequential injection chromatography for fluorimetric determination of intracellular free amino acids in the microalgae Tetraselmis gracilis

The concept of sequential injection chromatography (SIC) was exploited to automate the fluorimetric determination of amino acids after pre-column derivatization with ophthaldialdehyde (OPA) in presence of 2-mercaptoethanol (2MCE) using a reverse phase monolithic C(18) stationary phase. The method is low-priced and based on five steps of isocratic elutions. The first step employs the mixture methanol: tetrahydrofuran: 10 mmol L(-1) phosphate buffer (pH 7.2) at the volumetric ratio of 8:1:91; the other steps use methanol: 10 mmol L-1 phosphate buffer (pH 7.2) at volumetric ratios of 20:80, 35:65, SO:SO and 65:35. At a flow rate of 10 mu L s(-1) a 25 mm long-column was able to separate aspartic acid (Asp), glutamic acid (Glu), asparagine (Asn), serine (Ser), glutamine (Gln), glycine (Gly), threonine (Thr), citruline (Ctr), arginine (Arg), alanine (Ala), tyrosine (Tyr), phenylalanine (Phe), ornithine (Orn) and lysine (Lys) with resolution >1.2 as well as methionine (Met) and valine (Val) with resolution of 0.6. Under these conditions isoleucine (Ile) and leucine (Leu) co-eluted. The entire cycle of amino acids derivatization, chromatographic separation and column conditioning at the end of separation lasted 25 min. At a flow rate of 40 mu L s(-1) such time was reduced to 10 min at the cost of resolution worsening for the pairs Ctr/Arg and Orn/Lys. The detection limits varied from 0.092 mu mol L(-1) for Tyr to 0.51 mu mol L(-1) for Orn. The method was successfully applied to the determination of intracellular free amino acids in the green alga Tetraselmis gracilis during a period of seven days of cultivation. Samples spiked with known amounts of amino acids resulted in recoveries between 94 and 112%. (C) 2008 Elsevier B.V. All rights reserved.