24,701 research outputs found
On a generalization of Valiron's inequality for k-hypermonogenic functions on upper half-space
We present some results on the asymptotic growth behavior of periodic k-hypermonogenic functions on upper half-space. A generalization of the classical Valiron inequality for this class of functions and some basic properties are discussed
How good are MatLab, Octave and Scilab for Computational Modelling?
In this article we test the accuracy of three platforms used in computational
modelling: MatLab, Octave and Scilab, running on i386 architecture and three
operating systems (Windows, Ubuntu and Mac OS). We submitted them to numerical
tests using standard data sets and using the functions provided by each
platform. A Monte Carlo study was conducted in some of the datasets in order to
verify the stability of the results with respect to small departures from the
original input. We propose a set of operations which include the computation of
matrix determinants and eigenvalues, whose results are known. We also used data
provided by NIST (National Institute of Standards and Technology), a protocol
which includes the computation of basic univariate statistics (mean, standard
deviation and first-lag correlation), linear regression and extremes of
probability distributions. The assessment was made comparing the results
computed by the platforms with certified values, that is, known results,
computing the number of correct significant digits.Comment: Accepted for publication in the Computational and Applied Mathematics
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On the propagation of semiclassical Wigner functions
We establish the difference between the propagation of semiclassical Wigner
functions and classical Liouville propagation. First we re-discuss the
semiclassical limit for the propagator of Wigner functions, which on its own
leads to their classical propagation. Then, via stationary phase evaluation of
the full integral evolution equation, using the semiclassical expressions of
Wigner functions, we provide the correct geometrical prescription for their
semiclassical propagation. This is determined by the classical trajectories of
the tips of the chords defined by the initial semiclassical Wigner function and
centered on their arguments, in contrast to the Liouville propagation which is
determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the
one set to print and differs from the previous one (07 Nov 2001) by the
addition of two references, a few extra words of explanation and an augmented
figure captio
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