859 research outputs found
On the Fourier Spectra of the Infinite Families of Quadratic APN Functions
It is well known that a quadratic function defined on a finite field of odd
degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN).
For the even degree case there is no apparent relationship between the values
in the Fourier spectrum of a function and the APN property. In this article we
compute the Fourier spectrum of the new quadranomial family of APN functions.
With this result, all known infinite families of APN functions now have their
Fourier spectra and hence their nonlinearities computed.Comment: 12 pages, submitted to Adavances in the Mathematics of communicatio
Multiphoton detachment of electrons from negative ions
A simple analytical solution for the problem of multiphoton detachment from
negative ions by a linearly polarized laser field is found. It is valid in the
wide range of intensities and frequencies of the field, from the perturbation
theory to the tunneling regime, and is applicable to the excess-photon as well
as near-threshold detachment. Practically, the formulae are valid when the
number of photons is greater than two. They produce the total detachment rates,
relative intensities of the excess-photon peaks, and photoelectron angular
distributions for the hydrogen and halogen negative ions, in agreement with
those obtained in other, more numerically involved calculations in both
perturbative and non-perturbative regimes. Our approach explains the extreme
sensitivity of the multiphoton detachment probability to the asymptotic
behaviour of the bound-state wave function. Rapid oscillations in the angular
dependence of the -photon detachment probability are shown to arise due to
interference of the two classical trajectories which lead to the same final
state after the electron emerges at the opposite sides of the atom when the
field is close to maximal.Comment: 27 pages, Latex, and PostScript figures fig1.ps, fig2.ps, fig3.ps,
accepted for publication in Phys. Rev.
On the Derivative Imbalance and Ambiguity of Functions
In 2007, Carlet and Ding introduced two parameters, denoted by and
, quantifying respectively the balancedness of general functions
between finite Abelian groups and the (global) balancedness of their
derivatives , (providing an
indicator of the nonlinearity of the functions). These authors studied the
properties and cryptographic significance of these two measures. They provided
for S-boxes inequalities relating the nonlinearity to ,
and obtained in particular an upper bound on the nonlinearity which unifies
Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the
Workshop WCC 2009 and in its postproceedings in 2011, a further study of these
parameters was made; in particular, the first parameter was applied to the
functions where is affine, providing more nonlinearity parameters.
In 2010, motivated by the study of Costas arrays, two parameters called
ambiguity and deficiency were introduced by Panario \emph{et al.} for
permutations over finite Abelian groups to measure the injectivity and
surjectivity of the derivatives respectively. These authors also studied some
fundamental properties and cryptographic significance of these two measures.
Further studies followed without that the second pair of parameters be compared
to the first one.
In the present paper, we observe that ambiguity is the same parameter as
, up to additive and multiplicative constants (i.e. up to rescaling). We
make the necessary work of comparison and unification of the results on ,
respectively on ambiguity, which have been obtained in the five papers devoted
to these parameters. We generalize some known results to any Abelian groups and
we more importantly derive many new results on these parameters
Aligned spin neutron star-black hole mergers: a gravitational waveform amplitude model
The gravitational radiation emitted during the merger of a black hole with a
neutron star is rather similar to the radiation from the merger of two black
holes when the neutron star is not tidally disrupted. When tidal disruption
occurs, gravitational waveforms can be broadly classified in two groups,
depending on the spatial extent of the disrupted material. Extending previous
work by some of us, here we present a phenomenological model for the
gravitational waveform amplitude in the frequency domain encompassing the three
possible outcomes of the merger: no tidal disruption, "mild" and "strong" tidal
disruption. The model is calibrated to 134 general-relativistic numerical
simulations of binaries where the black hole spin is either aligned or
antialigned with the orbital angular momentum. All simulations were produced
using the SACRA code and piecewise polytropic neutron star equations of state.
The present model can be used to determine when black-hole binary waveforms are
sufficient for gravitational-wave detection, to extract information on the
equation of state from future gravitational-wave observations, to obtain more
accurate estimates of black hole-neutron star merger event rates, and to
determine the conditions under which these systems are plausible candidates as
central engines of gamma-ray bursts, macronovae and kilonovae.Comment: 15 pages, 7 figures, 1 tabl
- …