176 research outputs found
On sets of numbers rationally represented in a rational base number system
In this work, it is proved that a set of numbers closed under addition and
whose representations in a rational base numeration system is a rational
language is not a finitely generated additive monoid.
A key to the proof is the definition of a strong combinatorial property on
languages : the bounded left iteration property. It is both an unnatural
property in usual formal language theory (as it contradicts any kind of pumping
lemma) and an ideal fit to the languages defined through rational base number
systems
HENRI AUGUSTE DELANNOY, UNE BIOGRAPHIE
Cette biographie traite en annexe du legs de la bibliothèque mathématique de Delannoy à la ville de Guéret.Les travaux du mathématicien Delannoy (1833-1915), qui étaient tombés dans l'oubli, ont suscité récemment un vif intérêt, en raison des nombreux objets qui sont dénombrés par les suites associées à son nom. En effet, ces suites ont émergé dans des travaux aussi divers que la représentation et le raisonnement spatio-temporel en informatique et en linguistique, en biologie ou en physique théorique. Nous nous proposons ici de remettre à l'honneur ce mathématicien méconnu. Son parcours, bien que modeste, nous éclaire sur la société mathématique de la fin du dix-neuvième siècle. Dans ce premier article nous présentons les éléments connus de sa vie, en particulier de son activité de mathématicien. Nous fournissons notamment une revue complète de ses publications. En annexe, le lecteur trouvera la description de la bibliothèque mathématique donnée en héritage par Delannoy à la bibliothèque municipale de Guéret et ce qu'il en est advenu. Dans un second article, nous traiterons de façon approfondie de son apport majeur : l'usage des échiquiers arithmétiques dans la résolution de problèmes combinatoires et probabilistes et les applications actuelles
Integrated AlGaAs source of highly indistinguishable and energy-time entangled photons
The generation of nonclassical states of light in miniature chips is a
crucial step towards practical implementations of future quantum technologies.
Semiconductor materials are ideal to achieve extremely compact and massively
parallel systems and several platforms are currently under development. In this
context, spontaneous parametric down conversion in AlGaAs devices combines the
advantages of room temperature operation, possibility of electrical injection
and emission in the telecom band. Here we report on a chip-based AlGaAs source,
producing indistinguishable and energy-time entangled photons with a brightness
of pairs/s and a signal-to-noise ratio of .
Indistinguishability between the photons is demonstrated via a Hong-Ou-Mandel
experiment with a visibility of , while energy-time entanglement is
tested via a Franson interferometer leading to a value for the Bell parameter
High-detection efficiency and low-timing jitter with amorphous superconducting nanowire single-photon detectors
Recent progress in the development of superconducting nanowire single-photon
detectors (SNSPDs) made of amorphous material has delivered excellent
performances, and has had a great impact on a range of research fields. Despite
showing the highest system detection efficiency (SDE) ever reported with
SNSPDs, amorphous materials typically lead to lower critical currents, which
impacts on their jitter performance. Combining a very low jitter and a high SDE
remains a challenge. Here, we report on highly efficient superconducting
nanowire single-photon detectors based on amorphous MoSi, combining system
jitters as low as 26 ps and a SDE of 80% at 1550 nm. We also report detailed
observations on the jitter behaviour, which hints at intrinsic limitations and
leads to practical implications for SNSPD performance
Why Delannoy numbers?
This article is not a research paper, but a little note on the history of
combinatorics: We present here a tentative short biography of Henri Delannoy,
and a survey of his most notable works. This answers to the question raised in
the title, as these works are related to lattice paths enumeration, to the
so-called Delannoy numbers, and were the first general way to solve Ballot-like
problems. These numbers appear in probabilistic game theory, alignments of DNA
sequences, tiling problems, temporal representation models, analysis of
algorithms and combinatorial structures.Comment: Presented to the conference "Lattice Paths Combinatorics and Discrete
Distributions" (Athens, June 5-7, 2002) and to appear in the Journal of
Statistical Planning and Inference
Prefixes of infinite words and ambiguous context-free languages
Résumé disponible dans les fichiers attaché
Dynamic simulation of the THAI heavy oil recovery process
Toe-to-Heel Air Injection (THAI) is a variant of conventional In-Situ Combustion (ISC) that uses a horizontal production well to recover mobilised partially upgraded heavy oil. It has a number of advantages over other heavy oil recovery techniques such as high recovery potential. However, existing models are unable to predict the effect of the most important operational parameters, such as fuel availability and produced oxygen concentration, which will give rise to unsafe designs. Therefore, we have developed a new model that accurately predicts dynamic conditions in the reservoir and also is easily scalable to investigate different field scenarios. The model used a three component direct conversion cracking kinetics scheme, which does not depend on the stoichiometry of the products and, thus, reduces the extent of uncertainty in the simulation results as the number of unknowns is reduced. The oil production rate and cumulative oil produced were well predicted, with the latter deviating from the experimental value by only 4%. The improved ability of the model to emulate real process dynamics meant it also accurately predicted when the oxygen was first produced, thereby enabling a more accurate assessment to be made of when it would be safe to shut-in the process, prior to oxygen breakthrough occurring. The increasing trend in produced oxygen concentration following a step change in the injected oxygen rate by 33 % was closely replicated by the model. The new simulations have now elucidated the mechanism of oxygen production during the later stages of the experiment. The model has allowed limits to be placed on the air injection rates that ensure stability of operation. Unlike previous models, the new simulations have provided better quantitative prediction of fuel laydown, which is a key phenomenon that determines whether, or not, successful operation of the THAI process can be achieved. The new model has also shown that, for completely stable operation, the combustion zone must be restricted to the upper portion of the sand pack, which can be achieved by using higher producer back pressure
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