Indefinitely Oscillating Martingales

We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from the martingale literature. We discuss two applications. First, our results imply that the limit of the minimum description length operator may not exist. Second, we give bounds on how often one can change one's belief in a given hypothesis when observing a stream of data.Comment: ALT 2014, extended technical repor

Molecular astronomy of cool stars and sub-stellar objects

The optical and infrared spectra of a wide variety of `cool' astronomical objects including the Sun, sunspots, K-, M- and S-type stars, carbon stars, brown dwarfs and extrasolar planets are reviewed. The review provides the necessary astronomical background for chemical physicists to understand and appreciate the unique molecular environments found in astronomy. The calculation of molecular opacities needed to simulate the observed spectral energy distributions is discussed

The Cause and Prevention of Dental Caries.

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Chandra Observations of the Crab-like Supernova Remnant G21.5-0.9

Chandra observations of the Crab-like supernova remnant G21.5-0.9 reveal a compact central core and spectral variations indicative of synchrotron burn-off of higher energy electrons in the inner nebula. The central core is slightly extended, perhaps indicating the presence of an inner wind-shock nebula surrounding the pulsar. No pulsations are observed from the central region, yielding an upper limit of ~40% for the pulsed fraction. A faint outer shell may be the first evidence of the expanding ejecta and blast wave formed in the initial explosion, indicating a composite nature for G21.5-0.9.Comment: 4 pages, 2 figures, formatted with emulateapj, submitted to ApJ

The Pacific Center of Action of the Northern Hemisphere Annular Mode: Real or Artifact?

The leading empirical orthogonal function (EOF) of the sea level pressure (SLP) field, referred to as the Arctic Oscillation (AO) or Northern Hemisphere annular mode (NAM), consists of a dipole between the polar cap region and the surrounding zonal ring centered along 458N. Embedded within the outer ring are centers of action over the Euro-Atlantic and Pacific sectors in which SLP fluctuates in phase. That the observed SLP fluctuations at these two centers of action are virtually uncorrelated raises the question of whether the Pacific center in the annular mode could be an artifact of EOF analysis. It is argued that sea level pressure fluctuations at the Pacific and Euro-Atlantic centers of action of the AO/ NAM would be more strongly correlated were it not for the fact that SLP variability over the North Pacific is dominated by a pattern in which fluctuations over the North Atlantic and North Pacific are inversely related. Evidence of the coexistence of such a pattern, which resembles an augmented version of the Pacific–North American pattern, is presented

Effects of Negative Energy Components in the Constituent Quark Model

Relativistic covariance requires that in the constituent quark model for mesons the positive energy states as well as the negative energy states are included. Using relativistic quasi-potential equations the contribution of the negative energy states is studied for the light and charmonium mesons. It is found that these states change the meson mass spectrum significantly but leave its global structure untouched.Comment: 14 pages revtex 3.0, 4 figures uudecoded attached in postscript format, THU-93/1

Evidence for Past Subduction Earthquakes at a Plate Boundary with Widespread Upper Plate Faulting: Southern Hikurangi Margin, New Zealand

At the southern Hikurangi margin, New Zealand, we use salt marsh stratigraphy, sedimentology, micropaleontology, and radiocarbon dating to document evidence of two earthquakes producing coseismic subsidence and (in one case) a tsunami over the past 1000 yrs. The earthquake at 520-470 yrs before present (B.P.) produced 0.25 +/- 0.1 m of subsidence at Big Lagoon. The earthquake at 880-800 yrs B.P. produced 0.45 +/- 0.1 m of subsidence at Big Lagoon and was accompanied by a tsunami that inundated >= 360 m inland with a probable height of >= 3.3 m. Distinguishing the effects of upper plate faulting from plate interface earthquakes is a significant challenge at this margin. We use correlation with regional upper plate paleoearthquake chronologies and elastic dislocation modeling to determine that the most likely cause of the subsidence and tsunami events is subduction interface rupture, although the older event may have been a synchronous subduction interface and upper plate fault rupture. The southern Hikurangi margin has had no significant (M > 6.5) documented subduction interface earthquakes in historic times, and previous assumptions that this margin segment is prone to rupture in large to great earthquakes were based on seismic and geodetic evidence of strong contemporary plate coupling. This is the first geologic evidence to confirm that the southern Hikurangi margin ruptures in large earthquakes. The relatively short-time interval between the two subduction earthquakes (similar to 350 yrs) is shorter than in current seismic-hazard models.GNSEQC Biennial ProjectNew Zealand Natural Hazards Research Platform and Foundation for Research Science and TechnologyInstitute for Geophysic

Dynamics of monatomic liquids

We present a theory of the dynamics of monatomic liquids built on two basic ideas: (1) The potential surface of the liquid contains three classes of intersecting nearly-harmonic valleys, one of which (the ``random'' class) vastly outnumbers the others and all whose members have the same depth and normal mode spectrum; and (2) the motion of particles in the liquid can be decomposed into oscillations in a single many-body valley, and nearly instantaneous inter-valley transitions called transits. We review the thermodynamic data which led to the theory, and we discuss the results of molecular dynamics (MD) simulations of sodium and Lennard-Jones argon which support the theory in more detail. Then we apply the theory to problems in equilibrium and nonequilibrium statistical mechanics, and we compare the results to experimental data and MD simulations. We also discuss our work in comparison with the QNM and INM research programs and suggest directions for future research.Comment: 53 pages, 16 figures. Differs from published version in using American English spelling and grammar (published version uses British English

Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

The truncation of a pair potential at a distance r_cut is well-known to imply in general an impulsive correction to the pressure and other moments of the first derivatives of the potential. That depending on r_cut the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and d=2 dimensions

A Study of the Direct-Fitting Method for Measurement of Galaxy Velocity Dispersions

We have measured the central stellar velocity dispersions of 33 nearby spiral and elliptical galaxies, using a straightforward template-fitting algorithm operating in the pixel domain. The spectra, obtained with the Double Spectrograph at Palomar Observatory, cover both the Ca triplet and the Mg b region, and we present a comparison of the velocity dispersion measurements from these two spectral regions. Model fits to the Ca triplet region generally yield good results with little sensitivity to the choice of template star. In contrast, the Mg b region is more sensitive to template mismatch and to details of the fitting procedure such as the order of a polynomial used to match the continuum shape of the template to the object. As a consequence of the correlation of the [Mg/Fe] ratio with velocity dispersion, it is difficult to obtain a satisfactory model fit to the Mg b lines and the surrounding Fe blends simultaneously, particularly for giant elliptical galaxies with large velocity dispersions. We demonstrate that if the metallicities of the galaxy and template star are not well matched, then direct template-fitting results are improved if the Mg b lines themselves are excluded from the fit and the velocity dispersion is determined from the surrounding weaker lines.Comment: 14 pages. To appear in A