Coupling Poisson and Jacobi structures on foliated manifolds

Let M be a differentiable manifold endowed with a foliation F. A Poisson structure P on M is F-coupling if the image of the annihilator of TF by the sharp-morphism defined by P is a normal bundle of the foliation F. This notion extends Sternberg's coupling symplectic form of a particle in a Yang-Mills field. In the present paper we extend Vorobiev's theory of coupling Poisson structures from fiber bundles to foliations and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. Then we discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.Comment: LateX, 38 page

Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products

International audienceLet $E$ be an elliptic curve, $\mathcal{K}_1$ its Kummer curve $E/\{\pm1\}$, $E^2$ its square product, and $\mathcal{K}_2$ the split Kummer surface $E^2/\{\pm1\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\mathcal{K}_1$, we study the explicit arithmetic of $\mathcal{K}_2$

Detection of Multi-TeV Gamma Rays from Markarian 501 during an Unforeseen Flaring State in 1997 with the Tibet Air Shower Array

In 1997, the BL Lac Object Mrk 501 entered a very active phase and was the brightest source in the sky at TeV energies, showing strong and frequent flaring. Using the data obtained with a high density air shower array that has been operating successfully at Yangbajing in Tibet since 1996, we searched for gamma-ray signals from this source during the period from February through August in 1997. Our observation detected multi-TeV $\gamma$-ray signals at the 3.7-Sigma level during this period. The most rapid increase of the excess counts was observed between April 7 and June 16 and the statistical significance of the excess counts in this period was 4.7-Sigma. Among several observations of flaring TeV gamma-rays from Mrk 501 in 1997, this is the only observation using a conventional air shower array. We present the energy spectrum of gamma-rays which will be worthy to compare with those obtained by imaging atmospheric Cerenkov telescopes.Comment: 9 pages, 7 figures, To appear in Ap

Observation of Multi-Tev Diffuse Gamma Rays from the Galactic Plane with the Tibet Air Shower Array

Data from the Tibet-III air shower array (with energies around 3 TeV) and from the Tibet-II array (with energies around 10 TeV) have been searched for diffuse gamma rays from the Galactic plane. These arrays have an angular resolution of about 0.9 degrees. The sky regions searched are the inner Galaxy, 20 degrees <= l <= 55 degrees, and outer Galaxy, 140 degrees <= l <= 225 degrees, and |b| <= 2 degrees or <= 5 degrees. No significant Galactic plane gamma-ray excess was observed. The 99% confidence level upper limits for gamma-ray intensity obtained are (for |b| <= 2 degrees) 1.1 times 10^{-15} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 4.1 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the inner Galaxy, and 3.6 times 10^{-16} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 3 TeV and 1.3 times 10^{-17} cm^{-2}s^{-1}sr^{-1}MeV^{-1} at 10 TeV for the outer Galaxy, assuming a differential spectral index of 2.4. The upper limits are significant in the multi-TeV region when compared to those from Cherenkov telescopes in the lower energy region and other air shower arrays in the higher energy region; however, the results are not sufficient to rule out the inverse Compton model with a source electron spectral index of 2.0.Comment: 22 pages, 8 figures, Accepted for publication in Ap

Observation of Multi-Tev Gamma Rays from the Crab Nebula Using the Tibet Air Shower Array

The Tibet experiment, operating at Yangbajing (4,300 m above sea level), is the lowest energy air shower array and the new high density array constructed in 1996 has sensitivity to $\gamma$-ray air showers at energies as low as 3 TeV. With this new array, the Crab Nebula was observed in multi-TeV $\gamma$-rays and a signal was detected at the 5.5 $\sigma$ level. We also obtained the energy spectrum of $\gamma$-rays in the energy region above 3 TeV which partially overlaps those observed with imaging atmospheric Cherenkov telescopes. This is the first observation of $\gamma$-ray signals from point sources with a conventional air shower array using scintillation detectors.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter

Primary proton spectrum between 200 TeV and 1000 TeV observed with the Tibet burst detector and air shower array

Since 1996, a hybrid experiment consisting of the emulsion chamber and burst detector array and the Tibet-II air-shower array has been operated at Yangbajing (4300 m above sea level, 606 g/cm^2) in Tibet. This experiment can detect air-shower cores, called as burst events, accompanied by air showers in excess of about 100 TeV. We observed about 4300 burst events accompanied by air showers during 690 days of operation and selected 820 proton-induced events with its primary energy above 200 TeV using a neural network method. Using this data set, we obtained the energy spectrum of primary protons in the energy range from 200 to 1000 TeV. The differential energy spectrum obtained in this energy region can be fitted by a power law with the index of -2.97 $\pm$ 0.06, which is steeper than that obtained by direct measurements at lower energies. We also obtained the energy spectrum of helium nuclei at particle energies around 1000 TeV.Comment: 25 pages, 22 figures, Accepted for publication in Phys. Rev.

Measurement of air shower cores to study the cosmic ray composition in the knee energy region

Since 1996, a hybrid experiment consisting of an emulsion chamber and a burst detector array and the Tibet-II air shower array has been operated at Yangbajing (4300 m above sea level) in Tibet. This experiment can detect air-shower cores, called burst events, accompanied by air showers in excess of about 100 TeV. Using the burst event data observed by this experiment, we discuss the primary cosmic ray composition around the knee in comparison with the Monte Carlo simulations. In this paper, we show that all the features of burst events are wholly compatible with the heavy enriched composition in the knee energy region.Comment: 20 pages, 21 figures, to appear in Physical Review

Locally Administrated Perindopril Improves Healing in an Ovariectomized Rat Tibial Osteotomy Model

Angiotensin-converting enzyme inhibitors are widely prescribed to regulate blood pressure. High doses of orally administered perindopril have previously been shown to improve fracture healing in a mouse femur fracture model. In this study, perindopril was administered directly to the fracture area with the goal of stimulating fracture repair. Three months after being ovariectomized (OVX), tibial fractures were produced in Sprague–Dawley rats and subsequently stabilized with intramedullary wires. Perindopril (0.4 mg/kg/day) was injected locally at the fractured site for a treatment period of 7 days. Vehicle reagent was used as a control. Callus quality was evaluated at 2 and 4 weeks post-fracture. Compared with the vehicle group, perindopril treatment significantly increased bone formation, increased biomechanical strength, and improved microstructural parameters of the callus. Newly woven bone was arranged more tightly and regularly at 4 weeks post-fracture. The ultimate load increased by 66.1 and 76.9% (p<0.01), and the bone volume over total volume (BV/TV) increased by 29.9% and 24.3% (p<0.01) at 2 and 4 weeks post-fracture, respectively. These findings suggest that local treatment with perindopril could promote fracture healing in ovariectomized rats

Numerical Analysis of Ca2+ Signaling in Rat Ventricular Myocytes with Realistic Transverse-Axial Tubular Geometry and Inhibited Sarcoplasmic Reticulum

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubule microanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes