74,072,717 research outputs found
Free-Field Representation of Group Element for Simple Quantum Group
A representation of the group element (also known as ``universal -matrix'') which satisfies , is given in the form where , and and
are the generators of quantum group associated respectively with
Cartan algebra and the {\it simple} roots. The ``free fields'' $\chi,\
\vec\phi,\ \psi\psi^{(s)}\psi^{(s')} =
q^{-\vec\alpha_{i(s)} \vec\alpha_{i(s')}} \psi^{(s')}\psi^{(s)}, &
\chi^{(s)}\chi^{(s')} = q^{-\vec\alpha_{i(s)}\vec\alpha_{i(s')}}
\chi^{(s')}\chi^{(s)}& {\rm for} \ s<s', \\ q^{\vec h\vec\phi}\psi^{(s)} =
q^{\vec h\vec\alpha_{i(s)}} \psi^{(s)}q^{\vec h\vec\phi}, & q^{\vec
h\vec\phi}\chi^{(s)} = q^{\vec h \vec\alpha_{i(s)}}\chi^{(s)}q^{\vec
h\vec\phi}, & \\ &\psi^{(s)} \chi^{(s')} = \chi^{(s')}\psi^{(s)} & {\rm for\
any}\ s,s'.d_Ggg \rightarrow g'\cdot g''{\cal
R}{\cal R} (g\otimes I)(I\otimes g) =
(I\otimes g)(g\otimes I){\cal R}$Comment: 68 page
Convergence of the restricted Nelder-Mead algorithm in two dimensions
The Nelder-Mead algorithm, a longstanding direct search method for
unconstrained optimization published in 1965, is designed to minimize a
scalar-valued function f of n real variables using only function values,
without any derivative information. Each Nelder-Mead iteration is associated
with a nondegenerate simplex defined by n+1 vertices and their function values;
a typical iteration produces a new simplex by replacing the worst vertex by a
new point. Despite the method's widespread use, theoretical results have been
limited: for strictly convex objective functions of one variable with bounded
level sets, the algorithm always converges to the minimizer; for such functions
of two variables, the diameter of the simplex converges to zero, but examples
constructed by McKinnon show that the algorithm may converge to a nonminimizing
point.
This paper considers the restricted Nelder-Mead algorithm, a variant that
does not allow expansion steps. In two dimensions we show that, for any
nondegenerate starting simplex and any twice-continuously differentiable
function with positive definite Hessian and bounded level sets, the algorithm
always converges to the minimizer. The proof is based on treating the method as
a discrete dynamical system, and relies on several techniques that are
non-standard in convergence proofs for unconstrained optimization.Comment: 27 page
Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set
We report a measurement of the bottom-strange meson mixing phase \beta_s
using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays
in which the quark-flavor content of the bottom-strange meson is identified at
production. This measurement uses the full data set of proton-antiproton
collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment
at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity.
We report confidence regions in the two-dimensional space of \beta_s and the
B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2,
-1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in
agreement with the standard model expectation. Assuming the standard model
value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +-
0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +-
0.009 (syst) ps, which are consistent and competitive with determinations by
other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012
The twisted fourth moment of the Riemann zeta function
We compute the asymptotics of the fourth moment of the Riemann zeta function
times an arbitrary Dirichlet polynomial of length Comment: 28 pages. v2: added reference
Evolution of the Scale Factor with a Variable Cosmological Term
Evolution of the scale factor a(t) in Friedmann models (those with zero
pressure and a constant cosmological term Lambda) is well understood, and
elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58,
689 (1986)]. Developments in particle physics and inflationary theory, however,
increasingly indicate that Lambda ought to be treated as a dynamical quantity.
We revisit the evolution of the scale factor with a variable Lambda-term, and
also generalize the treatment to include nonzero pressure. New solutions are
obtained and evaluated using a variety of observational criteria. Existing
arguments for the inevitability of a big bang (ie., an initial state with a=0)
are substantially weakened, and can be evaded in some cases with Lambda_0 (the
present value of Lambda) well below current experimental limits.Comment: 29 pages, 12 figures (not included), LaTeX, uses Phys Rev D style
files (revtex.cls, revtex.sty, aps.sty, aps10.sty, prabib.sty). To appear in
Phys Rev
Matrix-F5 algorithms and tropical Gr\"obner bases computation
Let be a field equipped with a valuation. Tropical varieties over can
be defined with a theory of Gr\"obner bases taking into account the valuation
of . Because of the use of the valuation, this theory is promising for
stable computations over polynomial rings over a -adic fields.We design a
strategy to compute such tropical Gr\"obner bases by adapting the Matrix-F5
algorithm. Two variants of the Matrix-F5 algorithm, depending on how the
Macaulay matrices are built, are available to tropical computation with
respective modifications. The former is more numerically stable while the
latter is faster.Our study is performed both over any exact field with
valuation and some inexact fields like or In the latter case, we track the loss in precision,
and show that the numerical stability can compare very favorably to the case of
classical Gr\"obner bases when the valuation is non-trivial. Numerical examples
are provided
Afterglow upper limits for four short duration, hard spectrum gamma-ray bursts
We present interplanetary network localization, spectral, and time history
information for four short-duration, hard spectrum gamma-ray bursts, GRB000607,
001025B, 001204, and 010119. All of these events were followed up with
sensitive radio and optical observations (the first and only such bursts to be
followed up in the radio to date), but no detections were made, demonstrating
that the short bursts do not have anomalously intense afterglows. We discuss
the upper limits, and show that the lack of observable counterparts is
consistent both with the hypothesis that the afterglow behavior of the short
bursts is like that of the long duration bursts, many of which similarly have
no detectable afterglows, as well as with the hypothesis that the short bursts
have no detectable afterglows at all. Small number statistics do not allow a
clear choice between these alternatives, but given the present detection rates
of various missions, we show that progress can be expected in the near future.Comment: 19 pages, 4 figures; Revised version, accepted by the Astrophysical
Journa
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