A Gerschgorin theorem for linear difference equations and eigenvalues of matrix products

AbstractThe Gerschgorin circle theorem is used here to give sufficient conditions for the solution space of the difference equation x(m+1) = A (m+1)x(m) to admit a type of exponential dichotomy. The result obtained is then used to establish a result on regions of eigenvalue inclusion for the product of finitely many square matrices. An application to differential equations is also given

Understanding Mid-Latitude Space Weather: Storm Impacts Observed at BLO on 31 March 2001

On 30 March 2001 in the late evening an auroral display was observed over the United States of America. The Bear Lake Observatory (BLO) magnetometer in Utah measured changes of 550 nT in less than 30 min. During the same period, BLO ionosonde measurements showed deep high-frequency radio wave absorption up to 7 MHz. BLO\u27s GPS single-frequency receiver experienced geolocation errors of 20 m for over 3 hours. These storm signatures were also accompanied by L-band scintillation effects which approached an S4 value of 0.2, which is large for midlatitudes. Although such measurements have been have been made at midlatitude locations for many decades, our knowledge of the processes and couplings involved in such events remains incomplete and, at best, qualitative. The interpretation of key ionospheric parameters\u27 storm response is discussed in the context of present-day auroral and geospace electrodynamics understanding. We find that at BLO (L = 2.38) the available data raise more questions and can provide almost no answers without observational inputs from other locations. One solution to this impasse is to field a ground-based sensor network to resolve the spatial scales of the geospace electrodynamics. On the basis of the instrument complement at BLO, we argue for a contiguous U.S. deployment of modest magnetic/optical/RF observatories to observe the next solar maximum period\u27s geomagnetic storms and to use these data to explore the physical processes and couplings on space weather effective scales in assimilative models in conjunction with space-based observations

ASTRA: ASTrometry and phase-Referencing Astronomy on the Keck interferometer

ASTRA (ASTrometric and phase-Referencing Astronomy) is an upgrade to the existing Keck Interferometer which aims at providing new self-phase referencing (high spectral resolution observation of YSOs), dual-field phase referencing (sensitive AGN observations), and astrometric (known exoplanetary systems characterization and galactic center general relativity in strong field regime) capabilities. With the first high spectral resolution mode now offered to the community, this contribution focuses on the progress of the dual field and astrometric modes.Comment: 10 pages, 6 figures, 2 tables, SPIE 201

Bostonia: 1993-1994, no. 2-3

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Keck Interferometer Nuller Data Reduction and On-Sky Performance

We describe the Keck Interferometer nuller theory of operation, data reduction, and on-sky performance, particularly as it applies to the nuller exozodiacal dust key science program that was carried out between 2008 February and 2009 January. We review the nuller implementation, including the detailed phasor processing involved in implementing the null-peak mode used for science data and the sequencing used for science observing. We then describe the Level 1 reduction to convert the instrument telemetry streams to raw null leakages, and the Level 2 reduction to provide calibrated null leakages. The Level 1 reduction uses conservative, primarily linear processing, implemented consistently for science and calibrator stars. The Level 2 processing is more flexible, and uses diameters for the calibrator stars measured contemporaneously with the interferometer’s K-band cophasing system in order to provide the requisite accuracy. Using the key science data set of 462 total scans, we assess the instrument performance for sensitivity and systematic error. At 2.0 Jy we achieve a photometrically-limited null leakage uncertainty of 0.25% rms per 10 minutes of integration time in our broadband channel. From analysis of the Level 2 reductions, we estimate a systematic noise floor for bright stars of ~0.2% rms null leakage uncertainty per observing cluster in the broadband channel. A similar analysis is performed for the narrowband channels. We also provide additional information needed for science reduction, including details on the instrument beam pattern and the basic astrophysical response of the system, and references to the data reduction and modeling tools

Perceptions of oral health adequacy and access in Michigan nursing facilities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72951/1/j.1741-2358.2007.00202.x.pd

Asteroseismology of the Beta Cephei star 12 (DD) Lacertae: photometric observations, pulsational frequency analysis and mode identification

We report a multisite photometric campaign for the Beta Cephei star 12 Lacertae. 750 hours of high-quality differential photoelectric Stromgren, Johnson and Geneva time-series photometry were obtained with 9 telescopes during 190 nights. Our frequency analysis results in the detection of 23 sinusoidal signals in the light curves. Eleven of those correspond to independent pulsation modes, and the remainder are combination frequencies. We find some slow aperiodic variability such as that seemingly present in several Beta Cephei stars. We perform mode identification from our colour photometry, derive the spherical degree l for the five strongest modes unambiguously and provide constraints on l for the weaker modes. We find a mixture of modes of 0 <= l <= 4. In particular, we prove that the previously suspected rotationally split triplet within the modes of 12 Lac consists of modes of different l; their equal frequency splitting must thus be accidental. One of the periodic signals we detected in the light curves is argued to be a linearly stable mode excited to visible amplitude by nonlinear mode coupling via a 2:1 resonance. We also find a low-frequency signal in the light variations whose physical nature is unclear; it could be a parent or daughter mode resonantly coupled. The remaining combination frequencies are consistent with simple light-curve distortions. The range of excited pulsation frequencies of 12 Lac may be sufficiently large that it cannot be reproduced by standard models. We suspect that the star has a larger metal abundance in the pulsational driving zone, a hypothesis also capable of explaining the presence of Beta Cephei stars in the LMC.Comment: 12 pages, 7 figures, MNRAS, in pres

Preliminary seismological and geological studies of the San Fernando, California, earthquake of February 9 1971

The San Fernando earthquake was the largest earthquake to occur in the metropolitan Los Angeles area in more than 50 years. It has tentatively been assigned a magnitude, M_L of 6.6, a focal depth of 13.0 km, and an epicentral location about 12 km east of Newhall, California, at 34°24.0'N, 118°23.7'W (Figure 1), but these figures undoubtedly will be modified as further data become available. Although the focal depth is not as well defined as the epicenter, it is consistent with other observations suggesting thrusting on a fault plane dipping north about 45 ° and breaking the surface in the Sylmar-San Fernando area (Figure 1). It should be emphasized that the hypocenter of the main shock represents only the point of initial rupture. Breaking, presumably, then propagated southward and upward from this point, so that the main geological and engineering effects were observed farther south where the fault was shallower and the displacement greater. The location of the main shock is based on readings from permanent stations of the Caltech network, as well as the U. S. Geological Survey station at Point Mugu (SBLG) and the California Department of Water Resources stations at Pyramid (PYR) and Cedar Springs (CSP). Portable Caltech seismographs were installed in the epicentral area as early as 3 hr following the main shock, and, within a few days, there were at least 30 portable units in the region operated by various groups and agencies