DURATION DEPENDENCE IN THE US BUSINESS CYCLE

Durland and McCurdy (1994) investigated the issue of duration dependence in US business cycle phases using a Markov regime switching approach, introduced by Hamilton (1989) and extended to the case of variable transition parameters by Filardo (1994). In Durland and McCurdy’s model duration alone was used as an explanatory of the transition probabilities. They found that recessions were duration dependent whilst expansions were not. In this paper, we explicitly incorporate the widely-accepted US business cycle phase change dates as determined by the NBER, and use a state-dependent multinomial Logit (and Probit) modelling framework. The model incorporates both duration and movements in two leading indexes - one designed to have a short lead (SLI) and the other designed to have a longer lead (LLI) - as potential explanators. We find that doing so suggests that current duration is not only a significant determinant of transition out of recessions, but that there is some evidence that it is also weakly significant in the case of expansions. Furthermore, we find that SLI has more informational content for the termination of recessions whilst LLI does so for expansions.

Cartan Triples

We introduce the class of Cartan triples as a generalization of the notion of a Cartan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi's theorem to this setting. This context contains that of Fulman's generalization of Cartan MASAs and we discuss his generalization in an appendix.Comment: 37 page

The Tolman Surface Brightness Test for the Reality of the Expansion. II. The Effect of the Point-Spread Function and Galaxy Ellipticity on the Derived Photometric Parameters

To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes of point-spread-functions composed of telescope diffraction, CCD pixel resolutions, and ground-based seeing on the measurements of mean surface brightness. We have done the calculations using two synthetic galaxies of effective radii of 0.70" and 0.25" with point-spread functions of 0.1, 0.3, and 0.9 arcseconds. We have also compared actual observations of three high-redshift galaxies in the cluster Cl 1324 + 3011 (z = 0.76) made both with the Keck telescopes in seeing of about 0.9" and with HST which has a PSF that is approximately ten times smaller. The conclusion is that HST data can be used as far into the galaxy image as a Petrosian metric radius of eta = 1.3 magnitudes, whereas the ground-based data will have systematic errors of up to 2.9 magnitudes in the mean surface brightness at eta values of less than 2.2 magnitudes. In the final section, we compare the differences in derived average surface brightness for nearly circular galaxy images compared with highly flattened images. The comparison is made by using the two reduction procedures of (1) integrating the profile curves using circular apertures, and (2) approximating an ``equivalent circular'' galaxy that is highly elongated by using an ``effective'' radius of sqrt{ab}, where a and b are the semi-major and semi-minor axis, respectively, of the best-fitting ellipse. The conclusion is that the two methods of reduction give nearly identical results and that either method can be used to analyze the low and high-redshift galaxy samples used in the Tolman test.Comment: 15 pages, 9 figures; accepted for publication in Astronomical Journa

CARTAN TRIPLES

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix

Arctic marine climate of the early nineteenth century

The climate of the early nineteenth century is likely to have been significantly cooler than that of today, as it was a period of low solar activity (the Dalton minimum) and followed a series of large volcanic eruptions. Proxy reconstructions of the temperature of the period do not agree well on the size of the temperature change, so other observational records from the period are particularly valuable. Weather observations have been extracted from the reports of the noted whaling captain William Scoresby Jr., and from the records of a series of Royal Navy expeditions to the Arctic, preserved in the UK National Archives. They demonstrate that marine climate in 1810 - 1825 was marked by consistently cold summers, with abundant sea-ice. But although the period was significantly colder than the modern average, there was considerable variability: in the Greenland Sea the summers following the Tambora eruption (1816 and 1817) were noticeably warmer, and had less sea-ice coverage, than the years immediately preceding them; and the sea-ice coverage in Lancaster Sound in 1819 and 1820 was low even by modern standards. © 2010 Author(s)

The Metallicity Dependence of the Fourier Components of RR Lyrae Light Curves is the Oosterhoff/Arp/Preston Period Ratio Effect in Disguise

The correlation of particular Fourier components of the light curves of RR Lyrae variables with metallicity, discovered by Simon and later by Kovacs and his coworkers, is shown to have the same explanation as the period ratios (period shifts in log P) between RRab Lyrae variables that have the same colors, amplitudes, and light-curve shapes but different metallicities. A purpose of this paper is to demonstrate that the model which predicts the period-metallicity relations is the mediating parameters of colors, amplitudes, and light-curve shapes also explains the Simon/Kovacs et al. correlation between period, Phi_31, and metallicity. The proof is made by demonstrating that the combination of the first and third phase terms in a Fourier decomposition of RRab light curves, called Phi_31 by Simon and Lee, varies monotonically across the RR Lyrae instability strip in the same way that amplitude, color, and rise time vary with period within the strip. The premise of the model is that if horizontal branches at the RR Lyrae strip are stacked in luminosity according to the metallicity, then there necessarily must be a log period shift between RR Lyraes with different metallicities at the same Phi_31 values. However, there are exceptions to the model. (...)Comment: 17 pages, 8 figures, 1 table. Accepted for publication in The A

Path-integral calculation of the third virial coefficient of quantum gases at low temperatures

We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of 3He and 4He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at http://jcp.aip.org/ Version 2 includes the corrections detailed in the Erratu

Stochastic models for atomic clocks

For the atomic clocks used in the National Bureau of Standards Time Scales, an adequate model is the superposition of white FM, random walk FM, and linear frequency drift for times longer than about one minute. The model was tested on several clocks using maximum likelihood techniques for parameter estimation and the residuals were acceptably random. Conventional diagnostics indicate that additional model elements contribute no significant improvement to the model even at the expense of the added model complexity