14,266 research outputs found
From Many-Valued Consequence to Many-Valued Connectives
Given a consequence relation in many-valued logic, what connectives can be
defined? For instance, does there always exist a conditional operator
internalizing the consequence relation, and which form should it take? In this
paper, we pose this question in a multi-premise multi-conclusion setting for
the class of so-called intersective mixed consequence relations, which extends
the class of Tarskian relations. Using computer-aided methods, we answer
extensively for 3-valued and 4-valued logics, focusing not only on conditional
operators, but on what we call Gentzen-regular connectives (including negation,
conjunction, and disjunction). For arbitrary N-valued logics, we state
necessary and sufficient conditions for the existence of such connectives in a
multi-premise multi-conclusion setting. The results show that mixed consequence
relations admit all classical connectives, and among them pure consequence
relations are those that admit no other Gentzen-regular connectives.
Conditionals can also be found for a broader class of intersective mixed
consequence relations, but with the exclusion of order-theoretic consequence
relations.Comment: Updated version [corrections of an incorrect claim in first version;
two bib entries added
Energy efficiency of consecutive fragmentation processes
We present a first study on the energy required to reduce a unit mass
fragment by consecutively using several devices, as it happens in the mining
industry. Two devices are considered, which we represent as different
stochastic fragmentation processes. Following the self-similar energy model
introduced by Bertoin and Martinez, we compute the average energy required to
attain a size x with this two-device procedure. We then asymptotically compare,
as x goes to 0 or 1, its energy requirement with that of individual
fragmentation processes. In particular, we show that for certain range of
parameters of the fragmentation processes and of their energy cost-functions,
the consecutive use of two devices can be asymptotically more efficient than
using each of them separately, or conversely
Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity
In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients
Experimental studies of the resultant contact forces in drillbit-rock interaction
Peer reviewedPostprin
Hints for families of GRBs improving the Hubble diagram
As soon as their extragalactic origins were established, the hope to make
Gamma - Ray Bursts (GRBs) standardizeable candles to probe the very high - z
universe has opened the search for scaling relations between redshift
independent observable quantities and distance dependent ones. Although some
remarkable success has been achieved, the empirical correlations thus found are
still affected by a significant intrinsic scatter which downgrades the
precision in the inferred GRBs Hubble diagram. We investigate here whether this
scatter may come from fitting together objects belonging to intrinsically
different classes. To this end, we rely on a cladistics analysis to partition
GRBs in homogenous families according to their rest frame properties. Although
the poor statistics prevent us from drawing a definitive answer, we find that
both the intrinsic scatter and the coefficients of the \,-\,
and \,-\, correlations significantly change depending on which
subsample is fitted. It turns out that the fit to the full sample leads to a
scaling relation which approximately follows the diagonal of the region
delimited by the fits to each homogenous class. We therefore argue that a
preliminary identification of the class a GRB belongs to is necessary in order
to select the right scaling relation to be used in order to not bias the
distance determination and hence the Hubble diagram.Comment: 10 pages, 6 figures, 4 tables, accepted for publication on MNRA
Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)
We propose a monotonic logic of internalised non-monotonic or instant
interactive proofs (LiiP) and reconstruct an existing monotonic logic of
internalised monotonic or persistent interactive proofs (LiP) as a minimal
conservative extension of LiiP. Instant interactive proofs effect a fragile
epistemic impact in their intended communities of peer reviewers that consists
in the impermanent induction of the knowledge of their proof goal by means of
the knowledge of the proof with the interpreting reviewer: If my peer reviewer
knew my proof then she would at least then (in that instant) know that its
proof goal is true. Their impact is fragile and their induction of knowledge
impermanent in the sense of being the case possibly only at the instant of
learning the proof. This accounts for the important possibility of
internalising proofs of statements whose truth value can vary, which, as
opposed to invariant statements, cannot have persistent proofs. So instant
interactive proofs effect a temporary transfer of certain propositional
knowledge (knowable ephemeral facts) via the transmission of certain individual
knowledge (knowable non-monotonic proofs) in distributed systems of multiple
interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract:
DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591
Proof mining in metric fixed point theory and ergodic theory
In this survey we present some recent applications of proof mining to the
fixed point theory of (asymptotically) nonexpansive mappings and to the
metastability (in the sense of Terence Tao) of ergodic averages in uniformly
convex Banach spaces.Comment: appeared as OWP 2009-05, Oberwolfach Preprints; 71 page
Friedel Oscillations and Charge Density Waves in Chains and Ladders
The density matrix renormalization group method for ladders works much more
efficiently with open boundary conditions. One consequence of these boundary
conditions is groundstate charge density oscillations that often appear to be
nearly constant in magnitude or to decay only slightly away from the
boundaries. We analyse these using bosonization techniques, relating their
detailed form to the correlation exponent and distinguishing boundary induced
generalized Friedel oscillations from true charge density waves. We also
discuss a different approach to extracting the correlation exponent from the
finite size spectrum which uses exclusively open boundary conditions and can
therefore take advantage of data for much larger system sizes. A general
discussion of the Friedel oscillation wave-vectors is given, and a convenient
Fourier transform technique is used to determine it. DMRG results are analysed
on Hubbard and t-J chains and 2 leg t-J ladders. We present evidence for the
existence of a long-ranged charge density wave state in the t-J ladder at a
filling of n=0.75 and near J/t \approx 0.25.Comment: Revtex, 15 pages, 15 postscript figure
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