17,625 research outputs found
Maximal quadratic modules on *-rings
We generalize the notion of and results on maximal proper quadratic modules
from commutative unital rings to -rings and discuss the relation of this
generalization to recent developments in noncommutative real algebraic
geometry. The simplest example of a maximal proper quadratic module is the cone
of all positive semidefinite complex matrices of a fixed dimension. We show
that the support of a maximal proper quadratic module is the symmetric part of
a prime -ideal, that every maximal proper quadratic module in a
Noetherian -ring comes from a maximal proper quadratic module in a simple
artinian ring with involution and that maximal proper quadratic modules satisfy
an intersection theorem. As an application we obtain the following extension of
Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let be an
element of the Weyl algebra which is not negative semidefinite
in the Schr\" odinger representation. It is shown that under some conditions
there exists an integer and elements such
that is a finite sum of hermitian squares. This
result is not a proper generalization however because we don't have the bound
.Comment: 11 page
Stability of Filters for the Navier-Stokes Equation
Data assimilation methodologies are designed to incorporate noisy
observations of a physical system into an underlying model in order to infer
the properties of the state of the system. Filters refer to a class of data
assimilation algorithms designed to update the estimation of the state in a
on-line fashion, as data is acquired sequentially. For linear problems subject
to Gaussian noise filtering can be performed exactly using the Kalman filter.
For nonlinear systems it can be approximated in a systematic way by particle
filters. However in high dimensions these particle filtering methods can break
down. Hence, for the large nonlinear systems arising in applications such as
weather forecasting, various ad hoc filters are used, mostly based on making
Gaussian approximations. The purpose of this work is to study the properties of
these ad hoc filters, working in the context of the 2D incompressible
Navier-Stokes equation. By working in this infinite dimensional setting we
provide an analysis which is useful for understanding high dimensional
filtering, and is robust to mesh-refinement. We describe theoretical results
showing that, in the small observational noise limit, the filters can be tuned
to accurately track the signal itself (filter stability), provided the system
is observed in a sufficiently large low dimensional space; roughly speaking
this space should be large enough to contain the unstable modes of the
linearized dynamics. Numerical results are given which illustrate the theory.
In a simplified scenario we also derive, and study numerically, a stochastic
PDE which determines filter stability in the limit of frequent observations,
subject to large observational noise. The positive results herein concerning
filter stability complement recent numerical studies which demonstrate that the
ad hoc filters perform poorly in reproducing statistical variation about the
true signal
Biased EPR entanglement and its application to teleportation
We consider pure continuous variable entanglement with non-equal correlations
between orthogonal quadratures. We introduce a simple protocol which equates
these correlations and in the process transforms the entanglement onto a state
with the minimum allowed number of photons. As an example we show that our
protocol transforms, through unitary local operations, a single squeezed beam
split on a beam splitter into the same entanglement that is produced when two
squeezed beams are mixed orthogonally. We demonstrate that this technique can
in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure
ANTICIPATION EFFECT ON KNEE JOINT STABILITY DURING PLANNED AND UN-PLANNED MOVEMENT TESTS IN LABORATORY
The purpose of this study was to investigate the anticipation effect on knee stability during functional test in laboratory. Ten healthy male subjects were recruited and instructed to perform a series of planned and un-planned stop-jumping tasks. Knee joint kinematics was measured by a motion analysis system. The subjects demonstrated different abduction and rotation angles for reactive tasks. This suggested that if knee abduction or rotational stability is considered as a primary measurement in documenting knee stability, such as in the investigation of rehabilitation progress after anterior cruciate ligament reconstruction, both planned and un-planned tasks should be considered as to take the anticipation effect into account
A Scalable, Self-Analyzing Digital Locking System for use on Quantum Optics Experiments
Digital control of optics experiments has many advantages over analog control
systems, specifically in terms of scalability, cost, flexibility, and the
integration of system information into one location. We present a digital
control system, freely available for download online, specifically designed for
quantum optics experiments that allows for automatic and sequential re-locking
of optical components. We show how the inbuilt locking analysis tools,
including a white-noise network analyzer, can be used to help optimize
individual locks, and verify the long term stability of the digital system.
Finally, we present an example of the benefits of digital locking for quantum
optics by applying the code to a specific experiment used to characterize
optical Schrodinger cat states.Comment: 7 pages, 5 figure
XAX: a multi-ton, multi-target detection system for dark matter, double beta decay and pp solar neutrinos
A multi-target detection system XAX, comprising concentric 10 ton targets of
136Xe and 129/131Xe, together with a geometrically similar or larger target of
liquid Ar, is described. Each is configured as a two-phase
scintillation/ionization TPC detector, enhanced by a full 4pi array of
ultra-low radioactivity Quartz Photon Intensifying Detectors (QUPIDs) replacing
the conventional photomultipliers for detection of scintillation light. It is
shown that background levels in XAX can be reduced to the level required for
dark matter particle (WIMP) mass measurement at a 10^-10 pb WIMP-nucleon cross
section, with single-event sensitivity below 10^-11 pb. The use of multiple
target elements allows for confirmation of the A^2 dependence of a coherent
cross section, and the different Xe isotopes provide information on the
spin-dependence of the dark matter interaction. The event rates observed by Xe
and Ar would modulate annually with opposite phases from each other for WIMP
mass >~100 GeV/c^2. The large target mass of 136Xe and high degree of
background reduction allow neutrinoless double beta decay to be observed with
lifetimes of 10^27-10^28 years, corresponding to the Majorana neutrino mass
range 0.01-0.1 eV, the most likely range from observed neutrino mass
differences. The use of a 136Xe-depleted 129/131Xe target will also allow
measurement of the pp solar neutrino spectrum to a precision of 1-2%.Comment: 16 pages with 17 figure
Self-aligned nanoscale SQUID on a tip
A nanometer-sized superconducting quantum interference device (nanoSQUID) is
fabricated on the apex of a sharp quartz tip and integrated into a scanning
SQUID microscope. A simple self-aligned fabrication method results in
nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An
aluminum nanoSQUID with an effective area of 0.034 m displays flux
sensitivity of 1.8 \mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly
promising probe for nanoscale magnetic imaging and spectroscopy.Comment: 14 manuscript pages, 5 figure
And the winner is: galaxy mass
The environment is known to affect the formation and evolution of galaxies
considerably best visible through the well-known morphology-density
relationship. We study the effect of environment on the evolution of early-type
galaxies for a sample of 3,360 galaxies morphologically selected by visual
inspection from the SDSS in the redshift range 0.05<z<0.06, and analyse
luminosity-weighted age, metallicity, and alpha/Fe ratio as function of
environment and galaxy mass. We find that on average 10 per cent of early-type
galaxies are rejuvenated through minor recent star formation. This fraction
increases with both decreasing galaxy mass and decreasing environmental
density. However, the bulk of the population obeys a well-defined scaling of
age, metallicity, and alpha/Fe ratio with galaxy mass that is independent of
environment. Our results contribute to the growing evidence in the recent
literature that galaxy mass is the major driver of galaxy formation. Even the
morphology-density relationship may actually be mass-driven, as the consequence
of an environment dependent characteristic galaxy mass coupled with the fact
that late-type galaxy morphologies are more prevalent in low-mass galaxies.Comment: 5 pages, proceedings of JENAM 2010, Symposium 2: "Environment and the
formation of galaxies: 30 years later
EXCESSIVE TIBIAL ROTATION IS RESTORED AFTER ANATOMICAL DOUBLE BUNDLE ANTERIOR CRUCIATE LIGAMENT RECONSTRUCTION
Recent studies suggested that tibial rotaion was not restored after single bundle anterior cruciate ligament (ACL) reconstruction. This study aimed to determine if excessive tibial rotation would be restored by anatomical double bundle ACL reconstruction. Ten male subjects with unilateral ACL injury were prospectively assessed with a high demanding task before and after ACL reconstruction. Knee kinematics during pivoting movement was measured by a motion analysis system. The tibial rotation was reduced in the reconstructed knee after ACL reconstruction than the deficient knee (
Wigner Crystallization of a two dimensional electron gas in a magnetic field: single electrons versus electron pairs at the lattice sites
The ground state energy and the lowest excitations of a two dimensional
Wigner crystal in a perpendicular magnetic field with one and two electrons per
cell is investigated. In case of two electrons per lattice site, the
interaction of the electrons {\em within} each cell is taken into account
exactly (including exchange and correlation effects), and the interaction {\em
between} the cells is in second order (dipole) van der Waals approximation. No
further approximations are made, in particular Landau level mixing and {\em
in}complete spin polarization are accounted for. Therefore, our calculation
comprises a, roughly speaking, complementary description of the bubble phase
(in the special case of one and two electrons per bubble), which was proposed
by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation.
The phase diagram shows that in GaAs the paired phase is energetically more
favorable than the single electron phase for, roughly speaking, filling factor
larger than 0.3 and density parameter smaller than 19 effective Bohr
radii (for a more precise statement see Fig.s 4 and 5). If we start within the
paired phase and increase magnetic field or decrease density, the pairs first
undergo some singlet- triplet transitions before they break.Comment: 11 pages, 7 figure
- …