Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical systems. The results are applied to a large class of nonholonomic mechanical systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous approaches and some explanations added. To appear in J. Phys.

Keck Observations of the Hidden Quasar IRAS P09104+4109

We present imaging and spectro- polarimetric observations of the ultraluminous infrared galaxy IRAS P09104+4109 using the Keck 10-m Telescope. We detect the clear presence of broad Hb, Hg, and MgII 2800 emission lines in the polarized flux spectra of the nucleus and of an extranuclear emission region ~ 4" away, confirming the presence of a hidden central quasar. The polarization of the broad Mg II emission line is high (~ 29%), consistent with the remarkably high polarization (~ 30%-40%) observed in the extended continuum emission. The narrow emission lines are polarized in a stratified fashion, with the high ionization lines being polarized 0.7%-1.7% and [O II] essentially unpolarized. The line polarizations are positively correlated with critical density, ionization potential, and velocity width of the emission lines. This indicates that the NLR may be partially shadowed by the putative torus, with the higher ionization lines originating closer to the nucleus. One notable characteristic of the extranuclear knot is that all species of Fe are markedly absent in its spectrum, while they appear prominently in the nucleus. Our favored interpretation is that there is a large amount of dust in the extranuclear regions, allowing gaseous refractory metals to deposit. The extended emission regions are most likely material shredded from nearby cluster members and not gas condensed from the cooling flow or expelled from the obscured quasar. Our data provide strong evidence for matter-bounded clouds in addition to ionization-bounded clouds in the NLR. Ionization by pure velocity shocks can be ruled out. Shocks with photoionizing precursors may be present, but are probably not a dominant contributor to the energy input.Comment: 32 pages, including 9 figs and 2 tables, to be published in the Astronomical Journa

Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap

This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log-periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments.Comment: 38 page

Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first- and second-order moments, the discrete Fourier transform and regression coefficients. The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid