869 research outputs found
Sums of two squares and a power
We extend results of Jagy and Kaplansky and the present authors and show that
for all there are infinitely many positive integers , which cannot
be written as for positive integers , where for
a congruence condition is imposed on . These
examples are of interest as there is no congruence obstruction itself for the
representation of these . This way we provide a new family of
counterexamples to the Hasse principle or strong approximation.Comment: 6 pages, to appear in the memorial volume "From Arithmetic to
Zeta-Functions - Number Theory in Memory of Wolfgang Schwarz
Dendrimers Clicked Together Divergently
ABSTRACT: Dendrimers containing 1,4-triazole linkages between each generation were grown divergently via the Click chemistry inspired Huisgen 1,3-dipolar cycloaddition reaction in the presence of a Cu(I) catalyst. The monomeric unit (1-propargylbenzene-3,5-dimethanol) contained the alkyne functionality, while the core (1,2-bis(2-azidoethoxy)ethane) and growing dendrimers presented the azide groups necessary for this type of Click reaction. The first generation dendrimer was also functionalized with alkyne termini to demonstrate an alternative pathway allowed by this chemistry. Synthesis and characterization, with infrared (IR), 1H and 13C NMR spectroscopies, high-resolution mass spectrometry, gel permeation chromatography (GPC), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA), are reported for these divergently grown dendrimers
The Otterbein Miscellany - June 1974
https://digitalcommons.otterbein.edu/miscellany/1002/thumbnail.jp
Assimilation of healthy and indulgent impressions from labelling influences fullness but not intake or sensory experience
Background: Recent evidence suggests that products believed to be healthy may be over-consumed relative to believed indulgent or highly caloric products. The extent to which these effects relate to expectations from labelling, oral experience or assimilation of expectations is unclear. Over two experiments, we tested the hypotheses that healthy and indulgent information could be assimilated by oral experience of beverages and influence sensory evaluation, expected satiety, satiation and subsequent appetite. Additionally, we explored how expectation-experience congruency influenced these factors.
Results: Results supported some assimilation of healthiness and indulgent ratings—study 1 showed that indulgent ratings enhanced by the indulgent label persisted post-tasting, and this resulted in increased fullness ratings.
In study 2, congruency of healthy labels and oral experience promoted enhanced healthiness ratings. These healthiness and indulgent beliefs did not influence sensory analysis or intake—these were dictated by the products themselves. Healthy labels, but not experience, were associated with decreased expected satiety.
Conclusions: Overall labels generated expectations, and some assimilation where there were congruencies between expectation and experience, but oral experience tended to override initial expectations to determine ultimate sensory evaluations and intake. Familiarity with the sensory properties of the test beverages may have resulted in the use of prior knowledge, rather than the label information, to guide evaluations and behaviour
First LIGO search for gravitational wave bursts from cosmic (super)strings
We report on a matched-filter search for gravitational wave bursts from
cosmic string cusps using LIGO data from the fourth science run (S4) which took
place in February and March 2005. No gravitational waves were detected in 14.9
days of data from times when all three LIGO detectors were operating. We
interpret the result in terms of a frequentist upper limit on the rate of
gravitational wave bursts and use the limits on the rate to constrain the
parameter space (string tension, reconnection probability, and loop sizes) of
cosmic string models.Comment: 11 pages, 3 figures. Replaced with version submitted to PR
Search for Gravitational Wave Bursts from Soft Gamma Repeaters
We present the results of a LIGO search for short-duration gravitational
waves (GWs) associated with Soft Gamma Repeater (SGR) bursts. This is the first
search sensitive to neutron star f-modes, usually considered the most efficient
GW emitting modes. We find no evidence of GWs associated with any SGR burst in
a sample consisting of the 27 Dec. 2004 giant flare from SGR 1806-20 and 190
lesser events from SGR 1806-20 and SGR 1900+14 which occurred during the first
year of LIGO's fifth science run. GW strain upper limits and model-dependent GW
emission energy upper limits are estimated for individual bursts using a
variety of simulated waveforms. The unprecedented sensitivity of the detectors
allows us to set the most stringent limits on transient GW amplitudes published
to date. We find upper limit estimates on the model-dependent isotropic GW
emission energies (at a nominal distance of 10 kpc) between 3x10^45 and 9x10^52
erg depending on waveform type, detector antenna factors and noise
characteristics at the time of the burst. These upper limits are within the
theoretically predicted range of some SGR models.Comment: 6 pages, 1 Postscript figur
A Joint Search for Gravitational Wave Bursts with AURIGA and LIGO
The first simultaneous operation of the AURIGA detector and the LIGO
observatory was an opportunity to explore real data, joint analysis methods
between two very different types of gravitational wave detectors: resonant bars
and interferometers. This paper describes a coincident gravitational wave burst
search, where data from the LIGO interferometers are cross-correlated at the
time of AURIGA candidate events to identify coherent transients. The analysis
pipeline is tuned with two thresholds, on the signal-to-noise ratio of AURIGA
candidate events and on the significance of the cross-correlation test in LIGO.
The false alarm rate is estimated by introducing time shifts between data sets
and the network detection efficiency is measured with simulated signals with
power in the narrower AURIGA band. In the absence of a detection, we discuss
how to set an upper limit on the rate of gravitational waves and to interpret
it according to different source models. Due to the short amount of analyzed
data and to the high rate of non-Gaussian transients in the detectors noise at
the time, the relevance of this study is methodological: this was the first
joint search for gravitational wave bursts among detectors with such different
spectral sensitivity and the first opportunity for the resonant and
interferometric communities to unify languages and techniques in the pursuit of
their common goal.Comment: 18 pages, IOP, 12 EPS figure
All-sky LIGO Search for Periodic Gravitational Waves in the Early S5 Data
We report on an all-sky search with the LIGO detectors for periodic
gravitational waves in the frequency range 50--1100 Hz and with the frequency's
time derivative in the range -5.0E-9 Hz/s to zero. Data from the first eight
months of the fifth LIGO science run (S5) have been used in this search, which
is based on a semi-coherent method (PowerFlux) of summing strain power.
Observing no evidence of periodic gravitational radiation, we report 95%
confidence-level upper limits on radiation emitted by any unknown isolated
rotating neutron stars within the search range. Strain limits below 1.E-24 are
obtained over a 200-Hz band, and the sensitivity improvement over previous
searches increases the spatial volume sampled by an average factor of about 100
over the entire search band. For a neutron star with nominal equatorial
ellipticity of 1.0E-6, the search is sensitive to distances as great as 500
pc--a range that could encompass many undiscovered neutron stars, albeit only a
tiny fraction of which would likely be rotating fast enough to be accessible to
LIGO. This ellipticity is at the upper range thought to be sustainable by
conventional neutron stars and well below the maximum sustainable by a strange
quark star.Comment: 6 pages, 1 figur
Search for Gravitational Waves Associated with 39 Gamma-Ray Bursts Using Data from the Second, Third, and Fourth LIGO Runs
We present the results of a search for short-duration gravitational-wave
bursts associated with 39 gamma-ray bursts (GRBs) detected by gamma-ray
satellite experiments during LIGO's S2, S3, and S4 science runs. The search
involves calculating the crosscorrelation between two interferometer data
streams surrounding the GRB trigger time. We search for associated
gravitational radiation from single GRBs, and also apply statistical tests to
search for a gravitational-wave signature associated with the whole sample. For
the sample examined, we find no evidence for the association of gravitational
radiation with GRBs, either on a single-GRB basis or on a statistical basis.
Simulating gravitational-wave bursts with sine-gaussian waveforms, we set upper
limits on the root-sum-square of the gravitational-wave strain amplitude of
such waveforms at the times of the GRB triggers. We also demonstrate how a
sample of several GRBs can be used collectively to set constraints on
population models. The small number of GRBs and the significant change in
sensitivity of the detectors over the three runs, however, limits the
usefulness of a population study for the S2, S3, and S4 runs. Finally, we
discuss prospects for the search sensitivity for the ongoing S5 run, and beyond
for the next generation of detectors.Comment: 24 pages, 10 figures, 14 tables; minor changes to text and Fig. 2;
accepted by Phys. Rev.
Search for gravitational waves from binary inspirals in S3 and S4 LIGO data
We report on a search for gravitational waves from the coalescence of compact
binaries during the third and fourth LIGO science runs. The search focused on
gravitational waves generated during the inspiral phase of the binary
evolution. In our analysis, we considered three categories of compact binary
systems, ordered by mass: (i) primordial black hole binaries with masses in the
range 0.35 M(sun) < m1, m2 < 1.0 M(sun), (ii) binary neutron stars with masses
in the range 1.0 M(sun) < m1, m2 < 3.0 M(sun), and (iii) binary black holes
with masses in the range 3.0 M(sun)< m1, m2 < m_(max) with the additional
constraint m1+ m2 < m_(max), where m_(max) was set to 40.0 M(sun) and 80.0
M(sun) in the third and fourth science runs, respectively. Although the
detectors could probe to distances as far as tens of Mpc, no gravitational-wave
signals were identified in the 1364 hours of data we analyzed. Assuming a
binary population with a Gaussian distribution around 0.75-0.75 M(sun), 1.4-1.4
M(sun), and 5.0-5.0 M(sun), we derived 90%-confidence upper limit rates of 4.9
yr^(-1) L10^(-1) for primordial black hole binaries, 1.2 yr^(-1) L10^(-1) for
binary neutron stars, and 0.5 yr^(-1) L10^(-1) for stellar mass binary black
holes, where L10 is 10^(10) times the blue light luminosity of the Sun.Comment: 12 pages, 11 figure
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