Lyapunov's center theorem for resonant equilibrium

AbstractLyapunov's center theorem relative to the existence of families of periodic orbits emanating from an equilibrium is generalized to cases where a resonance occurs between two basic frequencies. Analytical Hamiltonian systems are considered and the theorems depend on the nonannulation of an invariant of the system.The proof is performed in two steps. In a first step the theorems are shown to be valid for some approximation of the Hamiltonian system. These results are described in a previous paper (Henrard, 1970) and are only summarized here. In a second step Poincaré's perturbation theorem is generalized in order to transfer to the original system the conclusions relatives to its approximations.In the conclusion, our results are compared with similar results published recently

El cinema com a eina

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Rafel Salas Llompart, "El sector viu un moment dolç, però hi falten pel·lícules"

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Analytical study of the proximity of exoplanetary systems to mean-motion resonances

Aims.In a previous paper (Libert & Henrard 2005, Celest. Mech. & Dyn. Astron., 93, 187) we used a twelfth-order expansion of the perturbative potential in powers of eccentricities to represent the secular effects of two coplanar planets. This expansion was applied successfully to non resonant exoplanetary systems. This study was based on a first order (in the masses of the planets) model and will fail for systems too close to a resonance. In this paper we test the effects of the proximity of a mean-motion resonance on the secular motion of the planets. Methods.We analyse the proximity of several exoplanetary systems to a mean-motion resonance zone by using a first-order (in the mass ratios) Lie algorithm on the perturbative potential expanded to the twelfth order in the eccentricities. This perturbation method evaluates the difference between osculating elements and averaged ones. It permits us to decide whether resonant contributions dominate the terms of this difference or not. Results.This study is applied to several exosystems. We find that HD 168443, HD 38529, HD 74156, HD 217107, and HD 190360 are far away from a mean-motion resonance zone. υ Andromedae and HD 12661 are rather close to the 5/1 resonance, HD 169830 to the 9/1 one. Hence, a secular theory is enough to depict correctly the behaviour of all these systems. On the other hand, HD 108874 and HD 202206 suffer from large perturbations in their motion due to the closeness of the 4/1 and 5/1 resonances, respectively. We also perform a complete investigation of the proximity of the υ Andromedae system to mean-motion resonances, by studying the changes in behaviour due to different values of the outer semi-major axis. The υ Andromedae system begins to be really influenced by the 5/1 resonant terms when the value of the outer semi-major axis decreases from 2.53 to 2.445

Localized state and charge transfer in nitrogen-doped graphene

Nitrogen-doped epitaxial graphene grown on SiC(000?1) was prepared by exposing the surface to an atomic nitrogen flux. Using Scanning Tunneling Microscopy (STM) and Spectroscopy (STS), supported by Density Functional Theory (DFT) calculations, the simple substitution of carbon by nitrogen atoms has been identified as the most common doping configuration. High-resolution images reveal a reduction of local charge density on top of the nitrogen atoms, indicating a charge transfer to the neighboring carbon atoms. For the first time, local STS spectra clearly evidenced the energy levels associated with the chemical doping by nitrogen, localized in the conduction band. Various other nitrogen-related defects have been observed. The bias dependence of their topographic signatures demonstrates the presence of structural configurations more complex than substitution as well as hole-doping.Comment: 5 pages, accepted in PR

Comparison of 6 Mortality Risk Scores for Prediction of 1-Year Mortality Risk in Older Adults With Multimorbidity.

Importance The most appropriate therapy for older adults with multimorbidity may depend on life expectancy (ie, mortality risk), and several scores have been developed to predict 1-year mortality risk. However, often, these mortality risk scores have not been externally validated in large sample sizes, and a head-to-head comparison in a prospective contemporary cohort is lacking. Objective To prospectively compare the performance of 6 scores in predicting the 1-year mortality risk in hospitalized older adults with multimorbidity. Design, Setting, and Participants This prognostic study analyzed data of participants in the OPERAM (Optimising Therapy to Prevent Avoidable Hospital Admissions in Multimorbid Older People) trial, which was conducted between December 1, 2016, and October 31, 2018, in surgical and nonsurgical departments of 4 university-based hospitals in Louvain, Belgium; Utrecht, the Netherlands; Cork, Republic of Ireland; and Bern, Switzerland. Eligible participants in the OPERAM trial had multimorbidity (≥3 coexisting chronic diseases), were aged 70 years or older, had polypharmacy (≥5 long-term medications), and were admitted to a participating ward. Data were analyzed from April 1 to September 30, 2020. Main Outcomes and Measures The outcome of interest was any-cause death occurring in the first year of inclusion in the OPERAM trial. Overall performance, discrimination, and calibration of the following 6 scores were assessed: Burden of Illness Score for Elderly Persons, CARING (Cancer, Admissions ≥2, Residence in a nursing home, Intensive care unit admit with multiorgan failure, ≥2 Noncancer hospice guidelines) Criteria, Charlson Comorbidity Index, Gagné Index, Levine Index, and Walter Index. These scores were assessed using the following measures: Brier score (0 indicates perfect overall performance and 0.25 indicates a noninformative model); C-statistic and 95% CI; Hosmer-Lemeshow goodness-of-fit test and calibration plots; and sensitivity, specificity, and positive and negative predictive values. Results The 1879 patients in the study had a median (IQR) age of 79 (74-84) years and 835 were women (44.4%). The median (IQR) number of chronic diseases was 11 (8-16). Within 1 year, 375 participants (20.0%) died. Brier scores ranged from 0.16 (Gagné Index) to 0.24 (Burden of Illness Score for Elderly Persons). C-statistic values ranged from 0.62 (95% CI, 0.59-0.65) for Charlson Comorbidity Index to 0.69 (95% CI, 0.66-0.72) for the Walter Index. Calibration was good for the Gagné Index and moderate for other mortality risk scores. Conclusions and Relevance Results of this prognostic study suggest that all 6 of the 1-year mortality risk scores examined had moderate prognostic performance, discriminatory power, and calibration in a large cohort of hospitalized older adults with multimorbidity. Overall, none of these mortality risk scores outperformed the others, and thus none could be recommended for use in daily clinical practice

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

Search for R-Parity Violating Decays of Supersymmetric Particles in e+e−e^{+}e^{-} Collisions at Centre-of-Mass Energies near 183 GeV

Searches for pair-production of supersymmetric particles under the assumption that R-parity is violated via a single dominant $LL{\bar E}$, $LQ{\bar D}$ or ${\bar U} {\bar D} {\bar D}$ coupling are performed using the data collected by the \ALEPH\ collaboration at centre-of-mass energies of 181--184~\gev. The observed candidate events in the data are in agreement with the Standard Model expectations. Upper limits on the production cross-sections and lower limits on the masses of charginos, sleptons, squarks and sneutrinos are de rived