2,485 research outputs found
On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces
We study a variant of a problem considered by Dinaburg and Sinai on the
statistics of the minimal solution to a linear Diophantine equation. We show
that the signed ratio between the Euclidean norms of the minimal solution and
the coefficient vector is uniformly distributed modulo one. We reduce the
problem to an equidistribution theorem of Anton Good concerning the orbits of a
point in the upper half-plane under the action of a Fuchsian group.Comment: Minor changes. Final version to appear in proceedings of the
conference on the occasion of Sunada's 60th birthday. Contemp.Math. series of
Amer. Math.So
Live-timer method of automatic dead-time correction for precision counting
Automatic correction for dead time losses in nuclear counting experiments is implemented by a simple live timer arrangement in which each counting interval is extended for compensation for the dead time during that interval. this method eliminates repetitious manual calculations, source of error, and dependence upon paralysis shifts
Observed Faraday Effects in Damped Lyman-Alpha Absorbers and Lyman Limit Systems: The Magnetised Environment of Galactic Building Blocks at Redshift=2
Protogalactic environments are typically identified using quasar absorption
lines, and these galactic building blocks can manifest as Damped Lyman-Alpha
Absorbers (DLAs) and Lyman Limit Systems (LLSs). We use radio observations of
Faraday effects to test whether DLAs and LLSs host a magnetised medium, by
combining DLA and LLS detections throughout the literature with 1.4 GHz
polarization data from the NRAO VLA Sky Survey (NVSS). We obtain a control, a
DLA, and a LLS sample consisting of 114, 19, and 27 lines-of-sight respectively
- all of which are polarized at to ensure Rician bias is
negligible. Using a Bayesian framework, we are unable to detect either coherent
or random magnetic fields in DLAs: the regular coherent magnetic fields within
the DLAs must be G, and the lack of depolarization is consistent
with the weakly magnetised gas in DLAs being non-turbulent and quiescent.
However, we find mild suggestive evidence that LLSs have coherent magnetic
fields: after controlling for the redshift-distribution of our data, we find a
71.5% probability that LLSs have a higher RM than a control sample. We also
find strong evidence that LLSs host random magnetic fields, with a 95.5%
probability that LLS lines-of-sight have lower polarized fractions than a
control sample. The regular coherent magnetic fields within the LLSs must be
G, and the magnetised gas must be highly turbulent with a typical
scale on the order of -20 pc, which is similar to that of the Milky
Way. This is consistent with the standard dynamo pedagogy, whereby magnetic
fields in protogalaxies increase in coherence and strength as a function of
cosmic time. Our results are consistent with a hierarchical galaxy formation
scenario, with the DLAs, LLSs, and strong magnesium II (MgII) systems exploring
three different stages of magnetic field evolution in galaxies.Comment: Submitted to Ap
Testing the Modern Merger Hypothesis via the Assembly of Massive Blue Elliptical Galaxies in the Local Universe
The modern merger hypothesis offers a method of forming a new elliptical
galaxy through merging two equal-mass, gas-rich disk galaxies fuelling a
nuclear starburst followed by efficient quenching and dynamical stabilization.
A key prediction of this scenario is a central concentration of young stars
during the brief phase of morphological transformation from highly-disturbed
remnant to new elliptical galaxy. To test this aspect of the merger hypothesis,
we use integral field spectroscopy to track the stellar Balmer absorption and
4000\AA\ break strength indices as a function of galactic radius for 12 massive
(), nearby (),
visually-selected plausible new ellipticals with blue-cloud optical colours and
varying degrees of morphological peculiarities. We find that these index values
and their radial dependence correlate with specific morphological features such
that the most disturbed galaxies have the smallest 4000\AA\ break strengths and
the largest Balmer absorption values. Overall, two-thirds of our sample are
inconsistent with the predictions of the modern merger hypothesis. Of these
eight, half exhibit signatures consistent with recent minor merger
interactions. The other half have star formation histories similar to local,
quiescent early-type galaxies. Of the remaining four galaxies, three have the
strong morphological disturbances and star-forming optical colours consistent
with being remnants of recent, gas-rich major mergers, but exhibit a weak,
central burst consistent with forming of their stars. The final
galaxy possesses spectroscopic signatures of a strong, centrally-concentrated
starburst and quiescent core optical colours indicative of recent quenching
(i.e., a post-starburst signature) as prescribed by the modern merger
hypothesis.Comment: 25 pages, 37 figures, accepted to MNRA
Federal Tax Concepts as a Guide for State Apportionment of Dividends
In ASARCO, Inc. v. Idaho State Tax Commission, the Supreme Court rejected Idaho’s definition of income, and limited the apportionability of dividends, interest, and capital gains. The Court held that a unitary business relationship did not exist between ASARCO and the dividend payors, but did not address whether such a relationship was a sufficient precondition or a necessary one.
This article addresses two federal tax doctrines that may provide insight into state taxation of dividends: (1) the “effectively connected” doctrine, and (2) the Corn Products doctrine. The article first provides a detailed examination of the facts in ASARCO, and discusses the Court’s holding. The article explains that Idaho’s sweeping definition of income, which conflated business and nonbusiness income, invited the Court’s rejection. Next, the article examines the applicability of Mobil Oil Corp. v. Commissioner of Taxes of Vermont, and how that holding is not dispositive regarding the apportionability of dividends in general. Finally, the article discusses the two aforementioned federal tax doctrines. These two doctrines do not expressly address the characterization of dividends as business income, but implicate the same underlying issue. The article concludes by explaining that the tax treatment of dividends and capital gains as business income is not unique to state taxation
High resolution Ge/Li/ spectrometer reduces rate-dependent distortions at high counting rates
Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts
- …