46,639 research outputs found
inverse orbit generating functions almost always have natural boundaries
The function sends to resp. according
as is odd, resp. even, where . The map
sends integers to integers, and for let mean that is in the forward orbit of under iteration of
We consider the generating functions which are holomorphic in the unit disk. We give
sufficient conditions on for the functions have the unit
circle as a natural boundary to analytic continuation. For the
function these conditions hold for all to show that
has the unit circle as a natural boundary except possibly for and . The Conjecture is equivalent to the assertion that
is a rational function of for the remaining values .Comment: 15 page
The Identity Correspondence Problem and its Applications
In this paper we study several closely related fundamental problems for words
and matrices. First, we introduce the Identity Correspondence Problem (ICP):
whether a finite set of pairs of words (over a group alphabet) can generate an
identity pair by a sequence of concatenations. We prove that ICP is undecidable
by a reduction of Post's Correspondence Problem via several new encoding
techniques.
In the second part of the paper we use ICP to answer a long standing open
problem concerning matrix semigroups: "Is it decidable for a finitely generated
semigroup S of square integral matrices whether or not the identity matrix
belongs to S?". We show that the problem is undecidable starting from dimension
four even when the number of matrices in the generator is 48. From this fact,
we can immediately derive that the fundamental problem of whether a finite set
of matrices generates a group is also undecidable. We also answer several
question for matrices over different number fields. Apart from the application
to matrix problems, we believe that the Identity Correspondence Problem will
also be useful in identifying new areas of undecidable problems in abstract
algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the
published journal version of this article, see footnote 3 on page 1
Pair plasma cushions in the hole-boring scenario
Pulses from a 10 PW laser are predicted to produce large numbers of
gamma-rays and electron-positron pairs on hitting a solid target. However, a
pair plasma, if it accumulates in front of the target, may partially shield it
from the pulse. Using stationary, one-dimensional solutions of the two-fluid
(electron-positron) and Maxwell equations, including a classical radiation
reaction term, we examine this effect in the hole-boring scenario. We find the
collective effects of a pair plasma "cushion" substantially reduce the
reflectivity, converting the absorbed flux into high-energy gamma-rays. There
is also a modest increase in the laser intensity needed to achieve threshold
for a non-linear pair cascade.Comment: 17 pages, 5 figures. Accepted for publication in Plasma Physics and
Controlled Fusion. Typos corrected, reference update
Strong violations of Bell-type inequalities for Werner-like states
We investigate the violation of Bell-type inequalities for two-qubit
Werner-like states parametrized by the positive parameter 0<p<1. We use an
unbalanced homodyne detection scheme to obtain the quantum mechanical
probabilities. A violation of the Bell-Wigner and Janssens inequalities is
obtained for a large range of the parameter p. The range given by these
inequalities is greater than the one given by the Clauser-Horne inequality. The
range in which a violation is attained actually coincides with the range where
the Werner-like states are known to be nonseparabel, i.e., for p>1/3. However,
the improvement over the Clauser-Horne inequality is achieved at the price of
restricting the class of possible local hidden variable theories.Comment: Revised manuscript, accepted for publication in PR
Quantum Correlation Bounds for Quantum Information Experiments Optimization: the Wigner Inequality Case
Violation of modified Wigner inequality by means binary bipartite quantum
system allows the discrimination between the quantum world and the classical
local-realistic one, and also ensures the security of Ekert-like quantum key
distribution protocol. In this paper we study both theoretically and
experimentally the bounds of quantum correlation associated to the modified
Wigner's inequality finding the optimal experimental configuration for its
maximal violation. We also extend this analysis to the implementation of
Ekert's protocol
A note on heat and mass transfer from a sphere in Stokes\ud flow at low Péclet number
We consider the low Péclet number, Pe ≪ 1, asymptotic solution for steady-state heat and mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of van Dyke’s rule up to terms of O(Pe3) shows that the O(Pe3 log Pe) terms in the expression for the average Nusselt/Sherwood number are double those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase significantly the range of validity of the expansion
Macroscopic modelling of the surface tension of polymer-surfactant systems
Polymer-surfactant mixtures are increasingly being used in a wide range of applications. Weakly-interacting systems, such as SDS/PEO and SDS/PVP, comprise ionic surfactants and neutral polymers, while strongly-interacting systems, such as SDS/POLYDMDAAC and C12TAB/NaPSS, comprise ionic surfactants and oppositely charged ionic polymers. The complex nature of interactions in the mixtures leads to interesting and surprising surface tension profiles as the concentrations of polymer and surfactant are varied. The purpose of our research has been to develop a model to explain these surface tension profiles and to understand how they relate to the formation of different complexes in the bulk solution. In this paper we shouw how an existing model based on the law of mass action can be extended to model the surface tension of weakly-interacting systems, and we also extend it further to produce a model for the surface tension of strongly interacting systems. Applying the model to a variety of strongly-interacting systems gives remarkable agreement with the experimental results. The model provides a sound theoretical basis for comparing and contrasting the behaviour of different systems and greatly enhances our understanding of the features observed
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