655,996 research outputs found
Non-connected toric Hilbert schemes
We construct small (50 and 26 points, respectively) point sets in dimension 5
whose graphs of triangulations are not connected. These examples improve our
construction in J. Amer. Math. Soc., 13:3 (2000), 611--637 not only in size,
but also in that their toric Hilbert schemes are not connected either, a
question left open in that article. Additionally, the point sets can easily be
put into convex position, providing examples of 5-dimensional polytopes with
non-connected graph of triangulations.Comment: 18 pages, 2 figures. Except for Remark 2.6 (see below) changes w.r.t.
version 2 are mostly minor editings suggested by an anonimous referee of
"Mathematische Annalen". The paper has been accepted in that journal. Most of
the contents of Remark 2.6 have been deleted, since there was a flaw in the
argumen
Palatini approach to modified f(R) gravity and its bi-metric structure
f(R) gravity theories in the Palatini formalism has been recently used as an
alternative way to explain the observed late-time cosmic acceleration with no
need of invoking either dark energy or extra spatial dimension. However, its
applications have shown that some subtleties of these theories need a more
profound examination. Here we are interested in the conformal aspects of the
Palatini approach in extended theories of gravity. As is well known,
extremization of the gravitational action a la Palatini, naturally "selects" a
new metric h related to the metric g of the subjacent manifold by a conformal
transformation. The related conformal function is given by the derivative of
f(R). In this work we examine the conformal symmetries of the flat (k=0) FLRW
spacetime and find that its Conformal Killing Vectors are directly linked to
the new metric h and also that each vector yields a different conformal
function.Comment: 3 pages, 1 table, talk given at I CosmoSul: Cosmology and Gravitation
in the Southern Con
Optical tests of Bell's inequalities not resting upon the absurd fair sampling assumption
A simple local hidden-variables model is exhibited which reproduces the
results of all performed tests of Bell\'{}s inequalities involving optical
photon pairs. For the old atomic-cascade experiments, like Aspect\'{}s, the
model agrees with quantum mechanics even for ideal set-ups. For more recent
experiments, using parametric down-converted photons, the agreement occurs only
for actual experiments, involving low efficiency detectors. Arguments are given
against the fair sampling assumption, currently combined with the results of
the experiments in order to claim a contradiction with local realism. New tests
are proposed which are able to discriminate between quantum mechanics and a
restricted, but appealing, family of local hidden-variables models. Such tests
require detectors with efficiencies just above 20%.Comment: 19 page
Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories
The two-body interaction in dilute solutions of polymer chains in good
solvents can be modeled by means of effective bounded potentials, the simplest
of which being that of penetrable spheres (PSs). In this paper we construct two
simple analytical theories for the structural properties of PS fluids: a
low-temperature (LT) approximation, that can be seen as an extension to PSs of
the well-known solution of the Percus-Yevick (PY) equation for hard spheres,
and a high-temperature (HT) approximation based on the exact asymptotic
behavior in the limit of infinite temperature. Monte Carlo simulations for a
wide range of temperatures and densities are performed to assess the validity
of both theories. It is found that, despite their simplicity, the HT and LT
approximations exhibit a fair agreement with the simulation data within their
respective domains of applicability, so that they complement each other. A
comparison with numerical solutions of the PY and the hypernetted-chain
approximations is also carried out, the latter showing a very good performance,
except inside the core at low temperatures.Comment: 14 pages, 8 figures; v2: some figures redone; small change
An exercise on developing an ontology-epistemology about schizophrenia and neuroanatomy
This paper describes preliminary ideas on formalizing some concepts of neuroanatomy into ontological and epistemological terms. We envisage the application of this ontology on the assimilation of facts about medical knowledge about neuroimages from schizophrenic patients
Sonine approximation for collisional moments of granular gases of inelastic rough spheres
We consider a dilute granular gas of hard spheres colliding inelastically
with coefficients of normal and tangential restitution and ,
respectively. The basic quantities characterizing the distribution function
of linear () and angular
() velocities are the second-degree moments defining the
translational () and rotational () temperatures. The
deviation of from the Maxwellian distribution parameterized by
and can be measured by the cumulants associated
with the fourth-degree velocity moments. The main objective of this paper is
the evaluation of the collisional rates of change of these second- and
fourth-degree moments by means of a Sonine approximation. The results are
subsequently applied to the computation of the temperature ratio
and the cumulants of two paradigmatic states: the
homogeneous cooling state and the homogeneous steady state driven by a
white-noise stochastic thermostat. It is found in both cases that the
Maxwellian approximation for the temperature ratio does not deviate much from
the Sonine prediction. On the other hand, non-Maxwellian properties measured by
the cumulants cannot be ignored, especially in the homogeneous cooling state
for medium and small roughness. In that state, moreover, the cumulant directly
related to the translational velocity differs in the quasi-smooth limit
from that of pure smooth spheres (). This singular
behavior is directly related to the unsteady character of the homogeneous
cooling state and thus it is absent in the stochastic thermostat case.Comment: 14 pages, 8 figures; v2: some parts rewritten, new references added;
published in a special topic decicated to Carlo Cercignan
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