Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya

Preliminaries Consider the local SR-geometry (U, D, g), where U is a neighborhood of 0 ∈ R 3 , D is a Martinet-type distribution, which can be taken in the normal form D = Ker ω, ω = dz − y 2 2 dx, and g is a C ω metric on D, which can be written (see Expanding F 1 and F 2 in Taylor series according to the previous weights and identifying at the order p two elements whose Taylor series are the same at the order p, we obtain the following normal forms of order −1 and 0: • Normal form of order −1: (flat case); • Normal form of order 0: 2 dx 2 + (1 + βx + γy) 2 dy 2 , α, β, γ ∈ R. 1.1. Geodesics equations. The energy minimization problem equivalent to the SR-problem is the following optimal control problem: from Pontryagin's maximum principle [9], minimizing solutions are solutions of the following equations: where H ν is the pseudo-Hamiltonian where ν is a constant normalized to 0 or 1/2. A solution of the previous equations is called an extremal; when ν = 1/2 (resp. ν = 0), the solutions are called normal (resp. abnormal), and their projections onto the state space are called the geodesics. They can be easily computed

Optimal control of quantum superpositions in a bosonic Josephson junction

We show how to optimally control the creation of quantum superpositions in a bosonic Josephson junction within the two-site Bose-Hubbard model framework. Both geometric and purely numerical optimal control approaches are used, the former providing a generalization of the proposal of Micheli et al [Phys. Rev. A 67, 013607 (2003)]. While this method is shown not to lead to significant improvements in terms of time of formation and fidelity of the superposition, a numerical optimal control approach appears more promising, as it allows to create an almost perfect superposition, within a time short compared to other existing protocols. We analyze the robustness of the optimal solution against atom number variations. Finally, we discuss to which extent these optimal solutions could be implemented with the state of art technology.Comment: Several comments added, structure re-organize

Saturation of a spin 1/2 particle by generalized Local control

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.Comment: 12 pages, 4 figures, submitted to new journal of physics (2011

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Outcome of alimentary tract duplications operated on by minimally invasive surgery: a retrospective multicenter study by the GECI (Groupe d'Etude en Coeliochirurgie Infantile).

BACKGROUND: Alimentary tract duplications (ATD) are a rare cause of intestinal obstruction in childhood. There are many case reports but few series about laparoscopy or thoracoscopy for ATD. The aim of our study was to report the outcome of minimally invasive surgery (MIS) for ATD. METHODS: This was a retrospective multicenter study from the GECI (Groupe d\u27Etude en Coeliochirurgie Infantile). We reviewed the charts of 114 patients operated on by MIS for ATD from 1994 to 2009. RESULTS: Sixty-two patients (54 %) had a prenatal diagnosis. Forty-nine patients (43 %) were symptomatic before surgery: 33 of those patients (63 %) with postnatal diagnosis compared to 16 (25 %) with prenatal diagnosis (P < 0.01). In this last group, the median age at onset of symptoms was 16 days (range = 0-972). One hundred and two patients had laparoscopy (esophageal to rectal duplications) and 12 patients had thoracoscopy for esophageal duplications. The mean operative time was 90 min (range = 82-98). There were 32 (28 %) resection anastomoses, 55 (48 %) enucleations, and 27 (24 %) unroofings. The conversion rate was 32 %, and in a multivariate analysis, it was significantly higher, up to 41 % for patients weighing <10 kg (P < 0.01). Ten patients (8 %) had unintentional perioperative opening of the digestive tract during the dissection. Eight patients had nine postoperative complications, including six small bowel obstructions. The median length of hospital stay was 4 days (range = 1-21) without conversion and 6 days (range = 1-27) with conversion (P = 0.01). The median follow-up was 3 months (range = 1-120). Eighteen of the 27 patients who underwent partial surgery had an ultrasound examination during follow-up. Five (18 %) of them had macroscopic residue. CONCLUSION: This study showed that MIS for ATD is feasible with a low rate of complications. Patients with prenatal diagnosis should have prompt surgery to prevent symptoms, despite a high rate of conversion in small infants

Gamma-ray limits on Galactic 60Fe nucleosynthesis and implications on the Origin of the 26Al emission

The Gamma Ray Imaging Spectrometer (GRIS) recently observed the gamma-ray emission from the Galactic center region. We have detected the 1809 keV Galactic 26Al emission at a significance level of 6.8-sigma but have found no evidence for emission at 1173 keV and 1332 keV, expected from the decay chain of the nucleosynthetic 60Fe. The isotopic abundances and fluxes are derived for different source distribution models. The resulting abundances are between 2.6+-0.4 and 4.5+-0.7 Solar Masses for 26Al and a 2-sigma upper limit for 60Fe between 1.7 and 3.1 Solar Masses. The measured 26Al emission flux is significantly higher than that derived from the CGRO/COMPTEL 1.8 MeV sky map. This suggests that a fraction of the 26Al emission may come from extended sources with a low surface brightness that are invisible to COMPTEL. We obtain a 60Fe to 26Al flux ratio 2-sigma upper limit of 0.14, which is slightly lower than the 0.16 predicted from current nucleosynthesis models assuming that SNII are the major contributors to the galactic 26Al. Since the uncertainties in the predicted fluxes are large (up to a factor of 2), our measurement is still compatible with the theoretical expectations.Comment: to be published in Astroph. Journal Letters, 12 pages, 3 Postscript figures; added reference for introduction, typos adde

Shape polarization in the tin isotopes near N=60N=60 from precision gg-factor measurements on short-lived 11/2−11/2^- isomers

The $g$ factors of $11/2^-$ isomers in semimagic $^{109}$Sn and $^{111}$Sn (isomeric lifetimes $\tau = 2.9(3)$ ns and $\tau = 14.4(7)$ ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses \LaBr detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, $g(11/2^-; {^{109}\textrm{Sn}}) = -0.186(8)$ and $g(11/2^-; {^{111}\textrm{Sn}}) = -0.214(4)$, are significantly lower in magnitude than those of the $11/2^-$ isomers in the heavier isotopes and depart from the value expected for a near pure neutron $h_{11/2}$ configuration. Broken-symmetry density functional theory calculations applied to the sequence of $11/2^-$ states reproduce the magnitude and location of this deviation. The $g(11/2^-)$ values are affected by shape core polarization; the odd $0h_{11/2}$ neutron couples to $J^{\pi}=2^+,4^+,6^+...$ configurations in the weakly-deformed effective core, causing a decrease in the $g$-factor magnitudes.Comment: 8 pages, 7 figures. Accepted in Physics Letters

Esophageal atresia: data from a national cohort

PURPOSE: A prospective national register was established in 2008 to record all new cases of live-birth newborns with esophageal atresia (EA). This epidemiological survey was recommended as part of a national rare diseases plan. METHODS: All 38 national centers treating EA participated by completing for each patient at first discharge a questionnaire validated by a national committee of experts. Data were centralized by the national reference center for esophageal anomalies. Quantitative and qualitative analyses were performed, with P-values of less than 0.05 considered statistically significant. Results of the 2008-2009 data collection are presented in this report. RESULTS: Three hundred seven new living cases of EA were recorded between January 1, 2008, and December 31, 2009. The male/female sex ratio was 1.3, and the live-birth prevalence of EA was 1.8 per 10,000 births. Major characteristics were comparable to those reported in the literature. Survival was 95%, and no correlation with caseload was noted. CONCLUSIONS: Epidemiologic surveys of congenital anomalies such as EA, which is a rare disease, provide valuable data for public health authorities and fulfill one important mission of reference centers. When compared with previous epidemiological data, this national population-based registry suggests that the incidence of EA remains stable