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System of spheres-based multiple contractions
We propose a new class of multiple contraction operations — the
system of spheres-based multiple contractions — which are a generalization
of Grove’s system of spheres-based (singleton) contractions to the case of
contractions by (possibly non-singleton) sets of sentences. Furthermore, we
show that this new class of functions is a subclass of the class of the partial
meet multiple contractions.info:eu-repo/semantics/publishedVersio
Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions
t In some recent works (Reis 2011, Ferme and Reis, J. Philos. Log. ´ 41, 29–52,
2012, Ferme and Reis, Rev. Symb. Log. ´ 6, 460–487, 2013) two new kinds of multiple
contraction functions have been proposed, namely the system of spheres-based multiple
contractions and the epistemic entrenchment-based multiple contractions, as generalizations
(to the case of multiple contraction) of the well-known classes of systems of spheres-based
and of epistemic entrenchment-based (singleton) contractions. Additionally, a representa tion theorem for the class of epistemic entrenchment-based multiple contraction has been
proposed, and it has been shown that the two newly proposed constructions are equivalent, in
the sense that a multiple contraction function is a system of spheres-based multiple contrac tion if and only if it is an epistemic entrenchment-based multiple contraction. In this paper
we present two axiomatic characterizations for those multiple contraction functions which
differ from the one mentioned above and, in particular, make use of some more intuitive
postulates.info:eu-repo/semantics/publishedVersio
Epistemic entrenchment-based multiple contractions
In this article we present a new class of multiple contraction functions—the epistemic entrenchment-based multiple contractions—which are a generalization of the epistemic
entrenchment-based contractions (Gardenfors, 1988; G ¨ ardenfors & Makinson, 1988) to the case of ¨
contractions by (possibly nonsingleton) sets of sentences and provide an axiomatic characterization
for that class of functions. Moreover, we show that the class of epistemic entrenchment-based multi ple contractions coincides with the class of system of spheres-based multiple contractions introduced
in Ferme & Reis (2012).info:eu-repo/semantics/publishedVersio
On theory multiple contraction
The one which is considered the standard model of theory change was presented in
[AGM85] and is known as the AGM model. In particular, that paper introduced
the class of partial meet contractions. In subsequent works several alternative constructive models for that same class of functions were presented, e.g.: safe/kernel
contractions ([AM85, Han94]), system of spheres-based contractions ([Gro88]) and
epistemic entrenchment-based contractions ([G ar88, GM88]).
Besides, several generalizations of such model were investigated. In that regard
we emphasise the presentation of models which accounted for contractions by sets of
sentences rather than only by a single sentence, i.e. multiple contractions. However, until now, only two of the above mentioned models have been generalized in the
sense of addressing the case of contractions by sets of sentences: The partial meet
multiple contractions were presented in [Han89, FH94], while the kernel multiple
contractions were introduced in [FSS03].
In this thesis we propose two new constructive models of multiple contraction
functions, namely the system of spheres-based and the epistemic entrenchment-based
multiple contractions which generalize the models of system of spheres-based and of
epistemic entrenchment-based contractions, respectively, to the case of contractions
(of theories) by sets of sentences. Furthermore, analogously to what is the case
in what concerns the corresponding classes of contraction functions by one single
sentence, those two classes are identical and constitute a subclass of the class of
partial meet multiple contractions.
Additionally, and as the rst step of the procedure that is here followed to
obtain an adequate de nition for the system of spheres-based multiple contractions,
we present a possible worlds semantics for the partial meet multiple contractions
analogous to the one proposed in [Gro88] for the partial meet contractions (by one
single sentence).
Finally, we present yet an axiomatic characterization for the new class(es) of
multiple contraction functions that are here introduced.Eduardo Ferm
Complexity of triangulations of the projective space
It is known that any two triangulations of a compact 3-manifold are related
by finite sequences of certain local transformations. We prove here an upper
bound for the length of a shortest transformation sequence relating any two
triangulations of the 3-dimensional projective space, in terms of the number of
tetrahedra.Comment: 10 pages, 3 figures. Revised version, to appear in Top. App
On the evolution of the empirical measure for the Hard-Sphere dynamics
We prove that the evolution of marginals associated to the empirical measure
of a finite system of hard spheres is driven by the BBGKY hierarchical
expansion. The usual hierarchy of equations for measures is obtained as a
corollary. We discuss the ambiguities arising in the corresponding notion of
microscopic series solution to the Boltzmann-Enskog equation
Buckling Instabilities of a Confined Colloid Crystal Layer
A model predicting the structure of repulsive, spherically symmetric,
monodisperse particles confined between two walls is presented. We study the
buckling transition of a single flat layer as the double layer state develops.
Experimental realizations of this model are suspensions of stabilized colloidal
particles squeezed between glass plates. By expanding the thermodynamic
potential about a flat state of confined colloidal particles, we derive
a free energy as a functional of in-plane and out-of-plane displacements. The
wavevectors of these first buckling instabilities correspond to three different
ordered structures. Landau theory predicts that the symmetry of these phases
allows for second order phase transitions. This possibility exists even in the
presence of gravity or plate asymmetry. These transitions lead to critical
behavior and phases with the symmetry of the three-state and four-state Potts
models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with
cubic interactions. Experimental detection of these structures is discussed.Comment: 24 pages, 8 figures on request. EF508
A Topological Representation Theorem for Oriented Matroids
We present a new direct proof of a topological representation theorem for
oriented matroids in the general rank case. Our proof is based on an earlier
rank 3 version. It uses hyperline sequences and the generalized Sch{\"o}nflies
theorem. As an application, we show that one can read off oriented matroids
from arrangements of embedded spheres of codimension one, even if wild spheres
are involved.Comment: 21 pages, 4 figure
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Microfluidic mixing of low viscosity Boger fluids
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.This study is focused on the development of low viscosity Boger fluids and on the investigation of their elasticity on emulsion formation. Non-Newtonian continuous phases (Boger fluids) made of two different molecular weight Polyacrylamide in water plus glycerol solutions were used. While, as Newtonian continuous phase, a water plus glycerol solution showing the same viscosity as the non-Newtonian one was prepared and as dispersed phase silicon oil was used. Visualization of these emulsions flowing through a micromixer was useful in order to extract quantitative informations of their behavior, such as the velocity profile and droplets’ size distribution. Then the formation of vortex upstream of a divergent-convergent configuration has been shown as the wall migration effect, which drives droplets away from the walls and toward the center of the microcapillary investigated
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