17,156 research outputs found
Chebyshev, Legendre, Hermite and other orthonormal polynomials in D-dimensions
We propose a general method to construct symmetric tensor polynomials in the
D-dimensional Euclidean space which are orthonormal under a general weight. The
D-dimensional Hermite polynomials are a particular case of the present ones for
the case of a gaussian weight. Hence we obtain generalizations of the Legendre
and of the Chebyshev polynomials in D dimensions that reduce to the respective
well-known orthonormal polynomials in D=1 dimensions. We also obtain new
D-dimensional polynomials orthonormal under other weights, such as the
Fermi-Dirac, Bose-Einstein, Graphene equilibrium distribution functions and the
Yukawa potential. We calculate the series expansion of an arbitrary function in
terms of the new polynomials up to the fourth order and define orthonormal
multipoles. The explicit orthonormalization of the polynomials up to the fifth
order (N from 0 to 4) reveals an increasing number of orthonormalization
equations that matches exactly the number of polynomial coefficients indication
the correctness of the present procedure.Comment: 20 page
Boundary conditions in first order gravity: Hamiltonian and Ensemble
In this work two different boundary conditions for first order gravity,
corresponding to a null and a negative cosmological constant respectively, are
studied. Both boundary conditions allows to obtain the standard black hole
thermodynamics. Furthermore both boundary conditions define a canonical
ensemble. Additionally the quasilocal energy definition is obtained for the
null cosmological constant case.Comment: To be published in Phys, Rev.
Modelling the exposure to Cronobacter sakazakii by consumption of a cocoa-milk-based beverage processed by pulsed electric fields
peer-reviewedM.C. Pina-Pérez is grateful to CSIC for providing a DOCTOR contract linked to the INNPACTO project IPT-2011-1724-060000. This study was carried out with funds from BISOSTAD project PSE-060000-2009-003, Generalitat Valenciana I+D+I emergent research groups GV/2010/064 and CYCIT project AGL2010-22206-C02-01.Infants’ exposure (Nf ) to Cronobacter sakazakii via the consumption of infant-rich-inpolyphenols
cocoa-milk-based beverages (CCX-M) treated with high-intensity pulsed
electric fields (PEF) was evaluated. Monte Carlo simulation enabled the prediction
of the variability in C. sakazakii load in beverages at the time of consumption to be
estimated. Different scenarios (initial contamination levels; PEF treatment conditions;
and time-temperature combinations of CCX-M beverages storage after treatment) were
simulated. Cocoa addition and PEF treatment resulted in the most influential input
factors to control bacterial final load. Cronobacter spp. exposure risk was reduced by
a maximum of 100 times at 95% of iterations due to addition of cocoa at 5 g/100 mL,
corresponding to scenario 3 (PEF: 15 kV/cm–3,000 μs; storage 120 h at 8 °C). Moreover,
the probability of illness for a healthy population was reduced from 2.15 × 10-8,
in the baseline scenario, to 4.78 × 10-10 due to cocoa addition and application of
15 kV/cm–3,000 μs PEF treatment.BISOSTAD projec
Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
It is shown that the addition of a topological invariant (Gauss-Bonnet term)
to the anti-de Sitter (AdS) gravity action in four dimensions recovers the
standard regularization given by holographic renormalization procedure. This
crucial step makes possible the inclusion of an odd parity invariant
(Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti)
self-dual condition on the Weyl tensor. This argument allows to find the dual
point of the theory where the holographic stress tensor is related to the
boundary Cotton tensor as , which
has been observed in recent literature in solitonic solutions and hydrodynamic
models.
A general procedure to generate the counterterm series for AdS gravity in any
even dimension from the corresponding Euler term is also briefly discussed.Comment: 13 pages, no figures; enlarged discussion on self-duality condition
for AAdS spacetimes, references added, final version for PR
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