1,740 research outputs found
evolution of chiral-odd twist-3 distribution
We study the dependence of the chiral-odd twist-3 distribution
.The anomalous dimension matrix for the corresponding twist-3
operators is calculated in the one-loop level. This study completes the
calculation of the anomalous dimension matrices for all the twist-3
distributions together with the known results for the other twist-3
distributions and . We also have confirmed that in the
large limit the -evolution of is wholely governed by the
lowest eigenvalue of the anomalous dimension matrix which takes a very simple
analytic form as in the case of and .Comment: 16 pages LaTeX, 4 postscript figure
Rational approximation of
Let denote the minimax (i.e., best supremum norm) error in
approximation of on by rational functions of type
with . We show that in an appropriate limit independently of , where is
Halphen's constant. This is the same formula as for minimax approximation of
on .Comment: 5 page
Liouville/Toda central charges from M5-branes
We show that the central charge of the Liouville and ADE Toda theories can be
reproduced by equivariantly integrating the anomaly eight-form of the
corresponding six-dimensional N=(0,2) theories, which describe the low-energy
dynamics of M5-branes.Comment: 9 page
Rational minimax approximation via adaptive barycentric representations
Computing rational minimax approximations can be very challenging when there
are singularities on or near the interval of approximation - precisely the case
where rational functions outperform polynomials by a landslide. We show that
far more robust algorithms than previously available can be developed by making
use of rational barycentric representations whose support points are chosen in
an adaptive fashion as the approximant is computed. Three variants of this
barycentric strategy are all shown to be powerful: (1) a classical Remez
algorithm, (2) a "AAA-Lawson" method of iteratively reweighted least-squares,
and (3) a differential correction algorithm. Our preferred combination,
implemented in the Chebfun MINIMAX code, is to use (2) in an initial phase and
then switch to (1) for generically quadratic convergence. By such methods we
can calculate approximations up to type (80, 80) of on in
standard 16-digit floating point arithmetic, a problem for which Varga, Ruttan,
and Carpenter required 200-digit extended precision.Comment: 29 pages, 11 figure
An algorithm for real and complex rational minimax approximation
Rational minimax approximation of real functions on real intervals is an
established topic, but when it comes to complex functions or domains, there
appear to be no algorithms currently in use. Such a method is introduced here,
the {\em AAA-Lawson algorithm,} available in Chebfun. The new algorithm solves
a wide range of problems on arbitrary domains in a fraction of a second of
laptop time by a procedure consisting of two steps. First, the standard AAA
algorithm is run to obtain a near-best approximation and a set of support
points for a barycentric representation of the rational approximant. Then a
"Lawson phase" of iteratively reweighted least-squares adjustment of the
barycentric coefficients is carried out to improve the approximation to
minimax
Reciprocal-log approximation and planar PDE solvers
This article is about both approximation theory and the numerical solution of
partial differential equations (PDEs). First we introduce the notion of {\em
reciprocal-log} or {\em log-lightning approximation} of analytic functions with
branch point singularities at points by functions of the form , which have poles potentially distributed
along a Riemann surface. We prove that the errors of best reciprocal-log
approximations decrease exponentially with respect to and that exponential
or near-exponential convergence (i.e., at a rate ) also
holds for near-best approximations with preassigned singularities constructed
by linear least-squares fitting on the boundary. We then apply these results to
derive a "log-lightning method" for numerical solution of Laplace and related
PDEs in two-dimensional domains with corner singularities. The convergence is
near-exponential, in contrast to the root-exponential convergence for the
original lightning methods based on rational functions.Comment: 20 pages, 11 figure
Classical and Quantum Correlations of Scalar Field in the Inflationary Universe
We investigate classical and quantum correlations of a quantum field in the
inflationary universe using a particle detector model. By considering the
entanglement and correlations between two comoving detectors interacting with a
scalar field, we find that the entanglement between the detectors becomes zero
after their physical separation exceeds the Hubble horizon. Furthermore, the
quantum discord, which is defined as the quantum part of total correlation,
approaches zero on super horizon scale. These behaviors support appearance of
classical nature of the quantum fluctuation generated during the inflationary
era.Comment: 21 pages, accepted for publication in Phys. Rev.
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Glaucomatous vertical vessel density asymmetry of the temporal raphe detected with optical coherence tomography angiography.
Changes in retinal vasculature and ocular circulation may play an important role in the glaucoma development and progression. We evaluated the vertical asymmetry across the temporal raphe of the deep retinal layer vessel density, using swept-source optical coherence tomography angiography (SS-OCTA), and its relationship with the central visual field (VF) loss. Thirty-four eyes of 27 patients with open-angle glaucoma were included. SS-OCTA macular scanning was performed within a 3 Ă 3âmm (300 Ă 300 pixels) volume, centred on the fovea. The relationships between the vertical asymmetrical deep retinal vessel density reduction (ADRVD) across the temporal raphe and various ocular parameters were analysed. Twenty-two glaucomatous eyes with ADRVDs had central VF loss. Contrarily, ADRVDs were not found in any of the 12 eyes without central VF loss. Thirteen eyes (59.1%) with central VF loss had ADRVDs topographically corresponding to the central VF loss and macular ganglion cell complex thinning. The glaucomatous eyes with ADRVDs exhibited inferior rather than superior central VF loss (Pâ=â0.032). Thus, ADRVD specifically indicates the glaucomatous central visual loss. Further analysis of ADRVD may improve our understanding on glaucoma pathogenesis, offering new treatment insights
Rigid Limit in N=2 Supergravity and Weak-Gravity Conjecture
We analyze the coupled N=2 supergravity and Yang-Mills system using
holomorphy, near the rigid limit where the former decouples from the latter. We
find that there appears generically a new mass scale around g M_{pl} where g is
the gauge coupling constant and M_{pl} is the Planck scale. This is in accord
with the weak-gravity conjecture proposed recently. We also study the scale
dependence of the gauge theory prepotential from its embedding into
supergravity.Comment: 17 pages, minor correction
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