12,664 research outputs found
On wild ramification in quaternion extensions
Quaternion extensions are often the smallest extensions to exhibit special
properties. In the setting of the Hasse-Arf Theorem, for instance, quaternion
extensions are used to illustrate the fact that upper ramification numbers need
not be integers. These extensions play a similar role in Galois module
structure. To better understand these examples, we catalog the ramification
filtrations that are possible in totally ramified extensions of dyadic number
fields. Interestingly, we find that the catalog depends, for sharp lower
bounds, upon the refined ramification filtration, which is associated with the
biquatratic subfield. Moreover these examples, as counter-examples to the
conclusion of Hasse-Arf, occur only when the refined filtration is, in two
different ways, extreme.Comment: 19 pages. This is an extensive revision of the earlier draf
THE CONSTITUTIONAL SIGNIFICANCE OF DELEGATED LEGISLATION IN ENGLAND
The Committee on Ministers\u27 Powers defined delegated legislation as the exercise by a subordinate authority, such as a Minister, of the legislative power delegated to him by Parliament. This definition followed logically from the terms of reference which required the Committee to report what safeguards are desirable or necessary to secure the constitutional principles of the sovereignty of Parliament and the supremacy of the Law. \u27 Behind these two statements lie certain assumptions which coloured the Report of the Committee and influenced its recommendations. One of these assumptions is that Ministers of the Crown are subordinate to Parliament so that any great increase in their powers may threaten Parliamentary sovereignty. A second assumption is that the phrase legislative power of Parliament is self-explanatory and free from ambiguity. These two assumptions are closely connected for they appear to answer implicitly the questions of the relationship of the Executive to Parliament and of the functions which the latter body performs under the Constitution today
Intersection Information based on Common Randomness
The introduction of the partial information decomposition generated a flurry
of proposals for defining an intersection information that quantifies how much
of "the same information" two or more random variables specify about a target
random variable. As of yet, none is wholly satisfactory. A palatable measure of
intersection information would provide a principled way to quantify slippery
concepts, such as synergy. Here, we introduce an intersection information
measure based on the G\'acs-K\"orner common random variable that is the first
to satisfy the coveted target monotonicity property. Our measure is imperfect,
too, and we suggest directions for improvement.Comment: 19 pages, 5 figure
Spectroscopy on two coupled flux qubits
We have performed spectroscopy measurements on two coupled flux qubits. The
qubits are coupled inductively, which results in a
interaction. By applying microwave radiation, we observe resonances due to
transitions from the ground state to the first two excited states. From the
position of these resonances as a function of the magnetic field applied we
observe the coupling of the qubits. The coupling strength agrees well with
calculations of the mutual inductance
Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study
The generalized stacking fault (GSF) energy surfaces have received
considerable attention due to their close relation to the mechanical properties
of solids. We present a detailed study of the GSF energy surfaces of silicon
within the framework of density functional theory. We have calculated the GSF
energy surfaces for the shuffle and glide set of the (111) plane, and that of
the (100) plane of silicon, paying particular attention to the effects of the
relaxation of atomic coordinates. Based on the calculated GSF energy surfaces
and the Peierls-Nabarro model, we obtain estimates for the dislocation
profiles, core energies, Peierls energies, and the corresponding stresses for
various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]
EPR studies of manganese centers in SrTiO3: Non-Kramers Mn3+ ions and spin-spin coupled Mn4+ dimers
X- and Q-band electron paramagnetic resonance (EPR) study is reported on the
SrTiO3 single crystals doped with 0.5-at.% MnO. EPR spectra originating from
the S = 2 ground state of Mn3+ ions are shown to belong to the three distinct
types of Jahn-Teller centres. The ordering of the oxygen vacancies due to the
reduction treatment of the samples and consequent formation of oxygen vacancy
associated Mn3+ centres are explained in terms of the localized charge
compensation. The EPR spectra of SrTiO3: Mn crystals show the presence of next
nearest neighbor exchange coupled Mn4+ pairs in the directions.Comment: 17 pages, 8 figure
Linear Chains of Styrene and Methyl-Styrene Molecules and their Heterojunctions on Silicon: Theory and Experiment
We report on the synthesis, STM imaging and theoretical studies of the
structure, electronic structure and transport properties of linear chains of
styrene and methyl-styrene molecules and their heterojunctions on
hydrogen-terminated dimerized silicon (001) surfaces. The theory presented here
accounts for the essential features of the experimental STM data including the
nature of the corrugation observed along the molecular chains and the
pronounced changes in the contrast between the styrene and methyl-styrene parts
of the molecular chains that are observed as the applied bias is varied. The
observed evolution with applied bias of the STM profiles near the ends of the
molecular chains is also explained. Calculations are also presented of electron
transport along styrene linear chains adsorbed on the silicon surface at
energies in the vicinity of the molecular HOMO and LUMO levels. For short
styrene chains this lateral transport is found to be due primarily to direct
electron transmission from molecule to molecule rather than through the silicon
substrate, especially in the molecular LUMO band. Differences between the
calculated position-dependences of the STM current around a junction of styrene
and methyl-styrene molecular chains under positive and negative tip bias are
related to the nature of lateral electron transmission along the molecular
chains and to the formation in the LUMO band of an electronic state localized
around the heterojunction.Comment: 17 pages plus 11 figures. To appear in Physical Review
A Preliminary Report on Unique Hail and Tornadic Storm Observations in Central Illinois and Eastern Indiana on 3 April 1974
published or submitted for publicationis peer reviewedOpe
WISE J163940.83-684738.6: A Y Dwarf identified by Methane Imaging
We have used methane imaging techniques to identify the near-infrared
counterpart of the bright WISE source WISEJ163940.83-684738.6. The large proper
motion of this source (around 3.0arcsec/yr) has moved it, since its original
WISE identification, very close to a much brighter background star -- it
currently lies within 1.5" of the J=14.90+-0.04 star 2MASS16394085-6847446.
Observations in good seeing conditions using methane sensitive filters in the
near-infrared J-band with the FourStar instrument on the Magellan 6.5m Baade
telescope, however, have enabled us to detect a near-infrared counterpart. We
have defined a photometric system for use with the FourStar J2 and J3 filters,
and this photometry indicates strong methane absorption, which unequivocally
identifies it as the source of the WISE flux. Using these imaging observations
we were then able to steer this object down the slit of the FIRE spectrograph
on a night of 0.6" seeing, and so obtain near-infrared spectroscopy confirming
a Y0-Y0.5 spectral type. This is in line with the object's
near-infrared-to-WISE J3--W2 colour. Preliminary astrometry using both WISE and
FourStar data indicates a distance of 5.0+-0.5pc and a substantial tangential
velocity of 73+-8km/s. WISEJ163940.83-684738.6 is the brightest confirmed Y
dwarf in the WISE W2 passband and its distance measurement places it amongst
the lowest luminosity sources detected to date.Comment: Accepted for publication in The Astrophysical Journal, 20 September
201
A second order minimality condition for the Mumford-Shah functional
A new necessary minimality condition for the Mumford-Shah functional is
derived by means of second order variations. It is expressed in terms of a sign
condition for a nonlocal quadratic form on , being a
submanifold of the regular part of the discontinuity set of the critical point.
Two equivalent formulations are provided: one in terms of the first eigenvalue
of a suitable compact operator, the other involving a sort of nonlocal capacity
of . A sufficient condition for minimality is also deduced. Finally, an
explicit example is discussed, where a complete characterization of the domains
where the second variation is nonnegative can be given.Comment: 30 page
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