154 research outputs found
Nearly commuting projections
It is well known that projection operators are typical elements in Boolean algebras, and a number of relevant theorems have been proved for commutative projections. We propose an extension of the concept of commutativity, which we call near-commutativity. We extend to this concept the main theorems on commutative projections, and in various ways we frame the class of nearly commutative projections in Boolean algebras.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30927/1/0000597.pd
Testing the bounds on quantum probabilities
Bounds on quantum probabilities and expectation values are derived for
experimental setups associated with Bell-type inequalities. In analogy to the
classical bounds, the quantum limits are experimentally testable and therefore
serve as criteria for the validity of quantum mechanics.Comment: 9 pages, Revte
The Schr\"oder functional equation and its relation to the invariant measures of chaotic maps
The aim of this paper is to show that the invariant measure for a class of
one dimensional chaotic maps, , is an extended solution of the Schr\"oder
functional equation, , induced by them. Hence, we give an
unified treatment of a collection of exactly solved examples worked out in the
current literature. In particular, we show that these examples belongs to a
class of functions introduced by Mira, (see text). Moreover, as a new example,
we compute the invariant densities for a class of rational maps having the
Weierstrass functions as an invariant one. Also, we study the relation
between that equation and the well known Frobenius-Perron and Koopman's
operators.Comment: 9 page
Bell inequalities as constraints on unmeasurable correlations
The interpretation of the violation of Bell-Clauser-Horne inequalities is
revisited, in relation with the notion of extension of QM predictions to
unmeasurable correlations. Such extensions are compatible with QM predictions
in many cases, in particular for observables with compatibility relations
described by tree graphs. This implies classical representability of any set of
correlations , , , and the equivalence of the
Bell-Clauser-Horne inequalities to a non void intersection between the ranges
of values for the unmeasurable correlation associated to different
choices for B. The same analysis applies to the Hardy model and to the "perfect
correlations" discussed by Greenberger, Horne, Shimony and Zeilinger. In all
the cases, the dependence of an unmeasurable correlation on a set of variables
allowing for a classical representation is the only basis for arguments about
violations of locality and causality.Comment: Some modifications have been done in order to improve clarity of
presentation and comparison with other approache
A Bio-Logical Theory of Animal Learning
This article provides the foundation for a new predictive theory of animal learning that is based upon a simple logical model. The knowledge of experimental subjects at a given time is described using logical equations. These logical equations are then used to predict a subject’s response when presented with a known or a previously unknown situation. This new theory suc- cessfully anticipates phenomena that existing theories predict, as well as phenomena that they cannot. It provides a theoretical account for phenomena that are beyond the domain of existing models, such as extinction and the detection of novelty, from which “external inhibition” can be explained. Examples of the methods applied to make predictions are given using previously published results. The present theory proposes a new way to envision the minimal functions of the nervous system, and provides possible new insights into the way that brains ultimately create and use knowledge about the world
Infinite ergodic theory and Non-extensive entropies
We bring into account a series of result in the infinite ergodic theory that
we believe that they are relevant to the theory of non-extensive entropie
How much contextuality?
The amount of contextuality is quantified in terms of the probability of the
necessary violations of noncontextual assignments to counterfactual elements of
physical reality.Comment: 5 pages, 3 figure
The Jacobi last multiplier for difference equations
We present a discretization of the Jacobi last multiplier, with some
applications to the computation of solutions of difference equations.Comment: 9 page
Hahn's Symmetric Quantum Variational Calculus
We introduce and develop the Hahn symmetric quantum calculus with
applications to the calculus of variations. Namely, we obtain a necessary
optimality condition of Euler-Lagrange type and a sufficient optimality
condition for variational problems within the context of Hahn's symmetric
calculus. Moreover, we show the effectiveness of Leitmann's direct method when
applied to Hahn's symmetric variational calculus. Illustrative examples are
provided.Comment: This is a preprint of a paper whose final and definite form will
appear in the international journal Numerical Algebra, Control and
Optimization (NACO). Paper accepted for publication 06-Sept-201
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