Prime normal form and equivalence of simple grammars

AbstractA prefix-free language is prime if it cannot be decomposed into a concatenation of two prefix-free languages. We show that we can check in polynomial time if a language generated by a simple context-free grammar is prime. Our algorithm computes a canonical representation of a simple language, converting its arbitrary simple grammar into prime normal form (PNF); a simple grammar is in PNF if all its nonterminals define primes. We also improve the complexity of testing the equivalence of simple grammars. The best previously known algorithm for this problem worked in O(n13) time. We improve it to O(n7log2n) and O(n5polylogv) time, where n is the total size of the grammars involved, and v is the length of a shortest string derivable from a nonterminal, maximized over all nonterminals

Utilisation de l'imagerie IR pour l'étude de la fatigue des aciers : Premières observations d'effets de surface

International audienceDe nouvelles méthodes de caractérisation de la tenue à la fatigue des matériaux métalliques par mesure thermique sont développées depuis plusieurs années. Elles donnent accès en quelques dizaines de minutes à une estimation de la limite d'endurance et de la dispersion des résultats de fatigue d'un matériau, là où plusieurs jours sont nécessaires traditionnellement. Un des axes de développement de ces méthodes consiste à caractériser à l'aide de ces techniques les effets de surface sur les propriétés à la fatigue. Pour capter l'information due à l'hétérogénéité locale provoquée par le traitement de surface, il est nécessaire de passer d'une vision moyenne à des mesures de champ. Deux points clefs peuvent être considérés pour ce passage. Le premier concerne la mesure et est traité dans cet article. Le second concerne l'identification du champ de sources locales à partir du champ de température mesurée et n'est pas traité ici. Un protocole expérimental de mesure du champ de température d'une tôle mince avec une précision suffisante (incertitude de l'ordre du milliKelvin) est présenté pour discerner des hétérogénéités de propriété à la fatigue (p. ex. surface vs. cœur). L'article expose les différentes sources d'artefacts rencontrés et les techniques utilisées pour les supprimer

Dissipation measurements in steel sheets under cyclic loading by use of infrared microthermography

WOSInternational audienceHeterogeneous dissipation in steel sheets due to cyclic loading is difficult to measure, especially in the transverse direction because of the high conductivity and low thickness of the sheets. The goal of this article is thus to develop an experimental protocol allowing for the dissipation field determination from infra-red thermography. The protocol is based on a specific differential measurement and an asynchronous acquisition. It reduces measurement artefacts due to coating, rigid body motion, convection, and optical deleterious effects. It is eventually applied to different specimens

Probabilistic multiscale models and measurements of self-heating under multiaxial high cycle fatigue

WOSInternational audienceDifferent approaches have been proposed to link high cycle fatigue properties to thermal measurements under cyclic loadings, usually referred to as “self-heating tests.” This paper focuses on two models whose parameters are tuned by resorting to self-heating tests and then used to predict high cycle fatigue properties. The first model is based upon a yield surface approach to account for stress multiaxiality at a microscopic scale, whereas the second one relies on a probabilistic modelling of microplasticity at the scale of slip-planes. Both model identifications are cost effective, relying mainly on quickly-obtained temperature data in self-heating tests. They both describe the influence of the stress heterogeneity, the volume effect and the hydrostatic stress on fatigue limits. The thermal effects and mean fatigue limit predictions are in good agreement with experimental results for in and out-of phase tension-torsion loadings. In the case of fatigue under non-proportional loading paths, the mean fatigue limit prediction error of the critical shear stress approach is three times less than with the yield surface approach

Dialogue essais-modèle pour l'interprétation des liens entre mesure d'auto-échauffement sous chargement cyclique et fatigue polycyclique

WOSInternational audienceUne démarche de développement d'un modèle probabiliste à deux échelles pour la fatigue HCF des aciers est proposée. Elle est basée sur l'utilisation de mesure d'autoéchauffement sous chargements cycliques et est validée sur la base de la prévision des courbes de Wöhler d'un acier dual-phase pour différents rapport de charge

Prediction of self-heating measurements under proportional and non-proportional multiaxial cyclic loadings

WOSInternational audienceSelf-heating measurements under cyclic loadings allow for fast estimations of fatigue properties. These tests are performed under tension–torsion loadings on a medium-carbon steel and a model accounting for heterogeneities is proposed to analyse heat transfer results. Both proportional and non-proportional loading paths are predicted

Angular analysis of the B-0 -> K*(0) e(+) e(-) decay in the low-q(2) region

An angular analysis of the $B^0 \rightarrow K^{*0} e^+ e^-$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 {\mbox{fb}^{-1}}, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared ($q^2$) interval between 0.002 and 1.120${\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}$. The angular observables $F_{\mathrm{L}}$ and $A_{\mathrm{T}}^{\mathrm{Re}}$ which are related to the $K^{*0}$ polarisation and to the lepton forward-backward asymmetry, are measured to be $F_{\mathrm{L}}= 0.16 \pm 0.06 \pm0.03$ and $A_{\mathrm{T}}^{\mathrm{Re}} = 0.10 \pm 0.18 \pm 0.05$, where the first uncertainty is statistical and the second systematic. The angular observables $A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathrm{Im}}$ which are sensitive to the photon polarisation in this $q^2$ range, are found to be $A_{\mathrm{T}}^{(2)} = -0.23 \pm 0.23 \pm 0.05$ and $A_{\mathrm{T}}^{\mathrm{Im}} =0.14 \pm 0.22 \pm 0.05$. The results are consistent with Standard Model predictions.An angular analysis of the B$^{0}$ → K^{*}^{0} e$^{+}$ e$^{−}$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 fb$^{−1}$, collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared (q$^{2}$) interval between 0.002 and 1.120 GeV$^{2}$ /c$^{4}$. The angular observables F$_{L}$ and A$_{T}^{Re}$ which are related to the K^{*}^{0} polarisation and to the lepton forward-backward asymmetry, are measured to be F$_{L}$ = 0.16 ± 0.06 ± 0.03 and A$_{T}^{Re}$  = 0.10 ± 0.18 ± 0.05, where the first uncertainty is statistical and the second systematic. The angular observables A$_{T}^{(2)}$ and A$_{T}^{Im}$ which are sensitive to the photon polarisation in this q$^{2}$ range, are found to be A$_{T}^{(2)}$  = − 0.23 ± 0.23 ± 0.05 and A$_{T}^{Im}$  = 0.14 ± 0.22 ± 0.05. The results are consistent with Standard Model predictions.An angular analysis of the $B^0 \rightarrow K^{*0} e^+ e^-$ decay is performed using a data sample, corresponding to an integrated luminosity of 3.0 {\mbox{fb}^{-1}}, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV during 2011 and 2012. For the first time several observables are measured in the dielectron mass squared ($q^2$) interval between 0.002 and 1.120${\mathrm{\,Ge\kern -0.1em V^2\!/}c^4}$. The angular observables $F_{\mathrm{L}}$ and $A_{\mathrm{T}}^{\mathrm{Re}}$ which are related to the $K^{*0}$ polarisation and to the lepton forward-backward asymmetry, are measured to be $F_{\mathrm{L}}= 0.16 \pm 0.06 \pm0.03$ and $A_{\mathrm{T}}^{\mathrm{Re}} = 0.10 \pm 0.18 \pm 0.05$, where the first uncertainty is statistical and the second systematic. The angular observables $A_{\mathrm{T}}^{(2)}$ and $A_{\mathrm{T}}^{\mathrm{Im}}$ which are sensitive to the photon polarisation in this $q^2$ range, are found to be $A_{\mathrm{T}}^{(2)} = -0.23 \pm 0.23 \pm 0.05$ and $A_{\mathrm{T}}^{\mathrm{Im}} =0.14 \pm 0.22 \pm 0.05$. The results are consistent with Standard Model predictions

Observation of the B0 → ρ0ρ0 decay from an amplitude analysis of B0 → (π+π−)(π+π−) decays

Proton–proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb−1 , are analysed to search for the charmless B0→ρ0ρ0 decay. More than 600 B0→(π+π−)(π+π−) signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B0→ρ0ρ0 decay is observed for the first time with 7.1 standard deviations significance. The fraction of B0→ρ0ρ0 decays yielding a longitudinally polarised final state is measured to be fL=0.745−0.058+0.048(stat)±0.034(syst) . The B0→ρ0ρ0 branching fraction, using the B0→ϕK⁎(892)0 decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94±0.17(stat)±0.09(syst)±0.06(BF))×10−6