30,846 research outputs found
Aligator.jl - A Julia Package for Loop Invariant Generation
We describe the Aligator.jl software package for automatically generating all
polynomial invariants of the rich class of extended P-solvable loops with
nested conditionals. Aligator.jl is written in the programming language Julia
and is open-source. Aligator.jl transforms program loops into a system of
algebraic recurrences and implements techniques from symbolic computation to
solve recurrences, derive closed form solutions of loop variables and infer the
ideal of polynomial invariants by variable elimination based on Gr\"obner basis
computation
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square
functions associated with Poisson semigroups for Bessel operators are defined
by using fractional derivatives. If B is a UMD Banach space we obtain for
B-valued Hardy and BMO spaces equivalent norms involving -radonifying
operators and square functions. We also establish characterizations of UMD
Banach spaces by using Hardy and BMO-boundedness properties of g-functions
associated to Bessel-Poisson semigroup
Probing the ZZgamma and Zgammagamma Couplings Through the Process e+e- --> nu anti-nu gamma
We study the sensitivity for testing the anomalous triple gauge couplings
and via the process
at high energy linear colliders. For integrated luminosities of 500
and center of mass energies between 0.5 and 1.5 , we find that this
process can provide tests of the triple neutral gauge boson couplings of order
, one order of magnitude lower than the standard model prediction.Comment: 12 pages, 6 figure
On the Issue of the \zeta Series Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum
We calculate the trispectrum T_\zeta of the primordial curvature perturbation
\zeta, generated during a {\it slow-roll} inflationary epoch by considering a
two-field quadratic model of inflation with {\it canonical} kinetic terms. We
consider loop contributions as well as tree level terms, and show that it is
possible to attain very high, {\it including observable}, values for the level
of non-gaussianity \tau_{NL} if T_\zeta is dominated by the one-loop
contribution. Special attention is paid to the claim in JCAP {\bf 0902}, 017
(2009) [arXiv:0812.0807 [astro-ph]] that, in the model studied in this paper
and for the specific inflationary trajectory we choose, the quantum
fluctuations of the fields overwhelm the classical evolution. We argue that
such a claim actually does not apply to our model, although more research is
needed in order to understand the role of quantum diffusion. We also consider
the probability that an observer in an ensemble of realizations of the density
field sees a non-gaussian distribution. In that respect, we show that the
probability associated to the chosen inflationary trajectory is non-negligible.
Finally, the levels of non-gaussianity f_{NL} and \tau_{NL} in the bispectrum
B_\zeta and trispectrum T_\zeta of \zeta, respectively, are also studied for
the case in which \zeta is not generated during inflation.Comment: LaTex File, 27 pages, 8 figures. v2: Previous Section 2 has been
removed. Two new sections (3 and 4) discussing the classicality condition
given by Byrnes, Choi, and Hall, in JCAP 0902, 017 (2009), and the
probability that an observer sees a non-gaussian distribution have been
added. v3: Version accepted for publication in Physical Review
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