21,840 research outputs found
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci
In this paper we continue our study of bifurcations of solutions of
boundary-value problems for symplectic maps arising as Hamiltonian
diffeomorphisms. These have been shown to be connected to catastrophe theory
via generating functions and ordinary and reversal phase space symmetries have
been considered. Here we present a convenient, coordinate free framework to
analyse separated Lagrangian boundary value problems which include classical
Dirichlet, Neumann and Robin boundary value problems. The framework is then
used to {prove the existence of obstructions arising from} conformal symplectic
symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary
value problems. Under non-degeneracy conditions, a group action by conformal
symplectic symmetries has the effect that the flow map cannot degenerate in a
direction which is tangential to the action. This imposes restrictions on which
singularities can occur in boundary value problems. Our results generalise
classical results about conjugate loci on Riemannian manifolds to a large class
of Hamiltonian boundary value problems with, for example, scaling symmetries
Oxygen and Sodium Abundances in M13 (NGC 6205) Giants: Linking Globular Cluster Formation Scenarios, Deep Mixing, and Post-RGB Evolution
We present O, Na, and Fe abundances, as well as radial velocities, for 113
red giant branch (RGB) and asymptotic giant branch (AGB) stars in the globular
cluster M13. The abundances and velocities are based on spectra obtained with
the WIYN-Hydra spectrograph, and the observations range in luminosity from the
horizontal branch (HB) to RGB-tip. The results are examined in the context of
recent globular cluster formation scenarios. We find that M13 exhibits many key
characteristics that suggest its formation and chemical enrichment are
well-described by current models. Some of these observations include: the
central concentration of O-poor stars, the notable decrease in [O/Fe] (but
small increase in [Na/Fe]) with increasing luminosity that affects primarily
the "extreme" population, the small fraction of stars with halo-like
composition, and the paucity of O-poor AGB stars. In agreement with recent
work, we conclude that the most O-poor M13 giants are likely He-enriched and
that most (all?) O-poor RGB stars evolve to become extreme HB and AGB-manqu\'e
stars. In contrast, the "primordial" and "intermediate" population stars appear
to experience standard HB and AGB evolution.Comment: Accepted for publication in The Astrophysical Journal Letters. 18
pages; 3 figures; 1 tabl
Hadronic decays of the (pseudo-)scalar charmonium states and in the extended Linear Sigma Model
We study the phenomenology of the ground-state (pseudo-)scalar charmonia
and in the framework of a symmetric
linear sigma model with (pseudo-)scalar and (axial-) vector mesons. Based on
previous results for the spectrum of charmonia and the spectrum and
(OZI-dominant) strong decays of open charmed mesons, we extend the study of
this model to OZI-suppressed charmonia decays. This includes decays into
'ordinary' mesons but also particularly interesting channels with
scalar-isoscalar resonances that may
include sizeable contributions from a scalar glueball. We study the variation
of the corresponding decay widths assuming different mixings between glueball
and quark-antiquark states. We also compute the decay width of the pseudoscalar
into a pseudoscalar glueball. In general, our results for decay widths
are in reasonable agreement with experimental data where available. Order of
magnitude predictions for as yet unmeasured states and channels are potentially
interesting for BESIII, Belle II, LHCb as well as the future PANDA experiment
at the FAIR facility.Comment: 20 pages, 3 figures, 6 tabe
Darboux Integrability of Trapezoidal and Families of Lattice Equations II: General Solutions
In this paper we construct the general solutions of two families of
quad-equations, namely the trapezoidal equations and the
equations. These solutions are obtained exploiting the properties of the first
integrals in the Darboux sense, which were derived in [Gubbiotti G., Yamilov
R.I., J. Phys. A: Math. Theor. 50 (2017), 345205, 26 pages, arXiv:1608.03506].
These first integrals are used to reduce the problem to the solution of some
linear or linearizable non-autonomous ordinary difference equations which can
be formally solved
On the rationality of the moduli space of L\"uroth quartics
We prove that the moduli space M_L of L"uroth quartics in P^2, i.e. the space
of quartics which can be circumscribed around a complete pentagon of lines
modulo the action of PGL_3(CC) is rational, as is the related moduli space of
Bateman seven-tuples of points in P^2.Comment: 7 page
Surface plasma resonance in small rare gas clusters by mixing IR and VUV laser pulses
The ionization dynamics of a Xenon cluster with 40 atoms is analyzed under a
pum p probe scenario of laser pulses where an infrared laser pulse of 50 fs
length follows with a well defined time delay a VUV pulse of the same length
and peak intensity. The mechanism of resonant energy absorption due to the
coinc idence of the IR laser frequency with the frequency of collective motion
of quasi free electrons in the cluster is mapped out by varying the time delay
between the pulses
Comparison of four different algorithms for the calculation of radioimmunoassay standard curves
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