3,552 research outputs found
Stationarity-conservation laws for certain linear fractional differential equations
The Leibniz rule for fractional Riemann-Liouville derivative is studied in
algebra of functions defined by Laplace convolution. This algebra and the
derived Leibniz rule are used in construction of explicit form of
stationary-conserved currents for linear fractional differential equations. The
examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1
dimensions are discussed in detail. The results are generalized to the mixed
fractional-differential and mixed sequential fractional-differential systems
for which the stationarity-conservation laws are obtained. The derived currents
are used in construction of stationary nonlocal charges.Comment: 28 page
Principles of Discrete Time Mechanics: II. Classical field Theory
We apply the principles discussed in an earlier paper to the construction of
discrete time field theories. We derive the discrete time field equations of
motion and Noether's theorem and apply them to the Schrodinger equation to
illustrate the methodology. Stationary solutions to the discrete time
Schrodinger wave equation are found to be identical to standard energy
eigenvalue solutions except for a fundamental limit on the energy. Then we
apply the formalism to the free neutral Klein Gordon system, deriving the
equations of motion and conserved quantities such as the linear momentum and
angular momentum. We show that there is an upper bound on the magnitude of
linear momentum for physical particle-like solutions. We extend the formalism
to the charged scalar field coupled to Maxwell's electrodynamics in a gauge
invariant way. We apply the formalism to include the Maxwell and Dirac fields,
setting the scene for second quantisation of discrete time mechanics and
discrete time Quantum Electrodynamics.Comment: 23 pages, LateX, To be published in J.Phys.A: Math.Gen: contact email
address: [email protected]
Extensions and degenerations of spectral triples
For a unital C*-algebra A, which is equipped with a spectral triple and an
extension T of A by the compacts, we construct a family of spectral triples
associated to T and depending on the two positive parameters (s,t).
Using Rieffel's notation of quantum Gromov-Hausdorff distance between compact
quantum metric spaces it is possible to define a metric on this family of
spectral triples, and we show that the distance between a pair of spectral
triples varies continuously with respect to the parameters. It turns out that a
spectral triple associated to the unitarization of the algebra of compact
operators is obtained under the limit - in this metric - for (s,1) -> (0, 1),
while the basic spectral triple, associated to A, is obtained from this family
under a sort of a dual limiting process for (1, t) -> (1, 0).
We show that our constructions will provide families of spectral triples for
the unitarized compacts and for the Podles sphere. In the case of the compacts
we investigate to which extent our proposed spectral triple satisfies Connes' 7
axioms for noncommutative geometry.Comment: 40 pages. Addedd in ver. 2: Examples for the compacts and the Podle`s
sphere plus comments on the relations to matricial quantum metrics. In ver.3
the word "deformations" in the original title has changed to "degenerations"
and some illustrative remarks on this aspect are adde
Lack of consensus in social systems
We propose an exactly solvable model for the dynamics of voters in a
two-party system. The opinion formation process is modeled on a random network
of agents. The dynamical nature of interpersonal relations is also reflected in
the model, as the connections in the network evolve with the dynamics of the
voters. In the infinite time limit, an exact solution predicts the emergence of
consensus, for arbitrary initial conditions. However, before consensus is
reached, two different metastable states can persist for exponentially long
times. One state reflects a perfect balancing of opinions, the other reflects a
completely static situation. An estimate of the associated lifetimes suggests
that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let
Reverberation Mapping Measurements of Black Hole Masses in Six Local Seyfert Galaxies
We present the final results from a high sampling rate, multi-month,
spectrophotometric reverberation mapping campaign undertaken to obtain either
new or improved Hbeta reverberation lag measurements for several relatively
low-luminosity AGNs. We have reliably measured thetime delay between variations
in the continuum and Hbeta emission line in six local Seyfert 1 galaxies. These
measurements are used to calculate the mass of the supermassive black hole at
the center of each of these AGNs. We place our results in context to the most
current calibration of the broad-line region (BLR) R-L relationship, where our
results remove outliers and reduce the scatter at the low-luminosity end of
this relationship. We also present velocity-resolved Hbeta time delay
measurements for our complete sample, though the clearest velocity-resolved
kinematic signatures have already been published.Comment: 52 pages (AASTeX: 29 pages of text, 8 tables, 7 figures), accepted
for publication in the Astrophysical Journa
Forecasting the Early Impact of COVID-19 on Physician Supply in EU Countries
Background
Many countries faced health workforce challenges even before the pandemic, such as impending retirements, negative population growth, or sub-optimal allocation of resources across health sectors. Current quantitative models are often of limited use, either because they require extensive individual-level data to be properly calibrated, or (in the absence of such data) because they are too simplistic to capture important demographic changes or disruptive epidemiological shocks such as the SARS-CoV-2 pandemic.
Method
We propose a population-dynamic and stock-flow-consistent approach to physician supply forecasting that is complex enough to account for dynamically changing behaviour, while requiring only publicly available time-series data for full calibration. We demonstrate the utility of this model by applying it to 21 European countries to forecast the supply of generalist and specialist physicians to 2040, and the impact of increased health care utilisation due to Covid on this supply.
Results
Compared with the workforce needed to maintain physician density at 2019 levels, we find that in many countries there is indeed a significant trend towards decreasing generalist density at the expense of increasing specialist density. The trends for specialists are exacerbated by expectations of negative population growth in many Southern and Eastern European countries. Compared to the expected demographic changes in the population and the health workforce, we expect a limited impact of Covid on these trends, even under conservative modelling assumptions. Finally, we generalise the approach to a multiprofessional, multi-regional and multi-sectoral model for Austria, where we find an additional suboptimal distribution in the supply of contracted versus non-contracted (private) physicians.
Conclusion
It is therefore vital to develop tools for decision-makers to influence the allocation and supply of doctors across specialties and sectors to address these imbalances
A Revised Broad-Line Region Radius and Black Hole Mass for the Narrow-Line Seyfert 1 NGC 4051
We present the first results from a high sampling rate, multi-month
reverberation mapping campaign undertaken primarily at MDM Observatory with
supporting observations from telescopes around the world. The primary goal of
this campaign was to obtain either new or improved Hbeta reverberation lag
measurements for several relatively low luminosity AGNs. We feature results for
NGC 4051 here because, until now, this object has been a significant outlier
from AGN scaling relationships, e.g., it was previously a ~2-3sigma outlier on
the relationship between the broad-line region (BLR) radius and the optical
continuum luminosity - the R_BLR-L relationship. Our new measurements of the
lag time between variations in the continuum and Hbeta emission line made from
spectroscopic monitoring of NGC 4051 lead to a measured BLR radius of R_BLR =
1.87 (+0.54 -0.50) light days and black hole mass of M_BH = 1.73 (+0.55 -0.52)
x 10^6 M_sun. This radius is consistent with that expected from the R_BLR-L
relationship, based on the present luminosity of NGC 4051 and the most current
calibration of the relation by Bentz et al. (2009a). We also present a
preliminary look at velocity-resolved Hbeta light curves and time delay
measurements, although we are unable to reconstruct an unambiguous
velocity-resolved reverberation signal.Comment: 38 pages, 7 figures, accepted for publication in ApJ, changes from v1
reflect suggestions from anonymous refere
Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics
We study fractional configurations in gravity theories and Lagrange
mechanics. The approach is based on Caputo fractional derivative which gives
zero for actions on constants. We elaborate fractional geometric models of
physical interactions and we formulate a method of nonholonomic deformations to
other types of fractional derivatives. The main result of this paper consists
in a proof that for corresponding classes of nonholonomic distributions a large
class of physical theories are modelled as nonholonomic manifolds with constant
matrix curvature. This allows us to encode the fractional dynamics of
interactions and constraints into the geometry of curve flows and solitonic
hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and
up-dated reference
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