A Strong Szego Theorem for Jacobi Matrices

We use a classical result of Gollinski and Ibragimov to prove an analog of the strong Szego theorem for Jacobi matrices on $l^2(\N)$. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary and sufficient conditions on the spectral measure such that $\sum_{k=n}^\infty b_k$ and $\sum_{k=n}^\infty (a_k^2 - 1)$ lie in $l^2_1$, the linearly-weighted $l^2$ space.Comment: 26 page

An evaluation of human factors research for ultrasonic inservice inspection

This work was undertaken to determine if human factors research has yielded information applicable to upgrading requirements in ASME Boiler and Pressure Vessel Code Section XI, improving methods and techniques in Section V, and/or suggesting relevant research. A preference was established for information and recommendations which have become accepted and standard practice. Manual Ultrasonic Testing/Inservice Inspection (UT/ISI) is a complex task subject to influence by dozens of variables. This review frequently revealed equivocal findings regarding effects of environmental variables as well as repeated indications that inspection performance may be more, and more reliably, influenced by the workers` social environment, including managerial practices, than by other situational variables. Also of significance are each inspector`s relevant knowledge, skills, and abilities, and determination of these is seen as a necessary first step in upgrading requirements, methods, and techniques as well as in focusing research in support of such programs, While understanding the effects and mediating mechanisms of the variables impacting inspection performance is a worthwhile pursuit for researchers, initial improvements in industrial UTASI performance may be achieved by implementing practices already known to mitigate the effects of potentially adverse conditions. 52 refs., 2 tabs

High angular resolution mm- and submm-observations of dense molecular gas in M82

Researchers observed CO(7-6), CO(3-2), HCN(3-2) and HCO+(3-2) line emission toward the starburst nucleus of M82 and have obtained an upper limit to H13CN(3-2). These are the first observations of the CO(7-6), HCN(3-2) and HCO+(3-2) lines in any extragalactic source. Researchers took the CO(7-6) spectrum in January 1988 at the Infrared Telescope Facility (IRTF) with the Max Planck Institute for Extraterrestrial Physics/Univ. of California, Berkeley 800 GHz Heterodyne Receiver. In March 1989 researchers used the Institute for Radio Astronomy in the Millimeter range (IRAM) 30 m telescope to observe the CO(3-2) line with the new MPE 350 GHz Superconductor Insulator Superconductor (SIS) receiver and the HCN(3-2) and HCO+(3-2) lines with the (IRAM) 230 GHz SIS receiver (beam 12" FWHM, Blundell et al. 1988). The observational parameters are summarized

Existence of superposition solutions for pulse propagation in nonlinear resonant media

Existence of self-similar, superposed pulse-train solutions of the nonlinear, coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the oscillator strengths of the transitions, is established. Some of these excitations are specific to the resonant media, with energy levels in the configurations of $\Lambda$ and $N$ and arise because of the interference effects of cnoidal waves, as evidenced from some recently discovered identities involving the Jacobian elliptic functions. Interestingly, these excitations also admit a dual interpretation as single pulse-trains, with widely different amplitudes, which can lead to substantially different field intensities and population densities in different atomic levels.Comment: 11 Pages, 6 Figures, presentation changed and 3 figures adde

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc

A class of Schrodinger operators with decaying oscillatory potentials

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.Comment: 18 page

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure

An updated radiocarbon-based ice margin chronology for the last deglaciation of the North American Ice Sheet Complex

The North American Ice Sheet Complex (NAISC; consisting of the Laurentide, Cordilleran and Innuitian ice sheets) was the largest ice mass to repeatedly grow and decay in the Northern Hemisphere during the Quaternary. Understanding its pattern of retreat following the Last Glacial Maximum is critical for studying many facets of the Late Quaternary, including ice sheet behaviour, the evolution of Holocene landscapes, sea level, atmospheric circulation, and the peopling of the Americas. Currently, the most up-to-date and authoritative margin chronology for the entire ice sheet complex is featured in two publications (Geological Survey of Canada Open File 1574 [Dyke et al., 2003]; ‘Quaternary Glaciations – Extent and Chronology, Part II’ [Dyke, 2004]). These often-cited datasets track ice margin recession in 36 time slices spanning 18 ka to 1 ka (all ages in uncalibrated radiocarbon years) using a combination of geomorphology, stratigraphy and radiocarbon dating. However, by virtue of being over 15 years old, the ice margin chronology requires updating to reflect new work and important revisions. This paper updates the aforementioned 36 ice margin maps to reflect new data from regional studies. We also update the original radiocarbon dataset from the 2003/2004 papers with 1541 new ages to reflect work up to and including 2018. A major revision is made to the 18 ka ice margin, where Banks and Eglinton islands (once considered to be glacial refugia) are now shown to be fully glaciated. Our updated 18 ka ice sheet increased in areal extent from 17.81 to 18.37 million km2, which is an increase of 3.1% in spatial coverage of the NAISC at that time. Elsewhere, we also summarize, region-by-region, significant changes to the deglaciation sequence. This paper integrates new information provided by regional experts and radiocarbon data into the deglaciation sequence while maintaining consistency with the original ice margin positions of Dyke et al. (2003) and Dyke (2004) where new information is lacking; this is a pragmatic solution to satisfy the needs of a Quaternary research community that requires up-to-date knowledge of the pattern of ice margin recession of what was once the world’s largest ice mass. The 36 updated isochrones are available in PDF and shapefile format, together with a spreadsheet of the expanded radiocarbon dataset (n = 5195 ages) and estimates of uncertainty for each interval

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc