Equivariance and Multiplicity for the Scalar Curvature Problem

Given (M, g ₀) a three-dimensional compact Riemannian manifold, assumed not to be conformally diffeomorphic to the standard unit 3-sphere, and G a compactsubgroup of the conformal group of (M, g ₀), we first study conditions for a smooth G-invariant function f to be the scalar curvature of a G-invariant conformalmetric to g ₀. Then, extending previous results of Hebeyand Vaugon, we study conditions for f to be the scalarcurvature of at least two conformal metrics to g ₀.     

Inclusive 2(3He,t) reaction at 2 GeV

The inclusive ²(³He,t) reaction has been studied at 2 GeV for energy transfers up to 500 MeV and scattering angles from 0.25⁰ up to 4⁰. Data are well reproduced by a model based on a coupled-channel approach for describing the NN and N( systems. The effect of final state interaction is important in the low energy part of the spectra. In the delta region, the cross-section is very sensitive to the effects of (-N interaction and (N M NN process. The latter has also a large influence well below the pion threshold. The calculation underestimates the experimental cross-section between the quasi-elastic and the delta peaks; this is possibly due to projectile excitation or purely mesonic exchange currents.     

The (He, t) reaction at intermediate energies : Spin-isospin multipole transitions

Data for the (³He, t) reaction at 900 MeV and 2 GeV on the targets ²⁶Mg, ⁴⁰Ca, ⁴⁸Ca, ⁵⁴Fe, ⁹⁰Zr and ²⁰⁸Pb are presented. A multipole decomposition for the data at 900 MeV has been made and the different distributions have been analysed. From the L = 0 cross section the Gamow-Teller strength distributions are extracted and compared with (p, n) data. The L = 1 and 2 distributions are analysed in a schematic model which describes the general systematics fairly well. The spectra at 2 GeV and Θ = 4° show for all targets a well-developed quasi-elastic peak. The A-dependence of the cross section is analysed in a simple model.     

Pion photoproduction on 3He at and above the 3-3 resonance

The differential cross section for the ${}^3\text{He}\text{(γ, π}{}^{\mathrm{+}}\text{)}{}^3\text{H}$ reaction has been measured at fixed values of q² in the region of the first resonance, and at fixed θ_π versus q² up to 13 fm^?2. The observed shift of the resonance towards lower energies, and the absence of a minimum near 11.6 fm^?2 might be explained by recent theoretical calculations.     

Quasi-free (p,pα) scattering on 24Mg, 28Si, 40Ca and 58Ni at 157 MeV

Sixfold energy spectra have been measured for the (p, pα) reaction at 157 MeV on ²⁴Mg, ²⁸Si, ⁴⁰Ca and ⁵⁸Ni around quasi-free kinematic conditions. For the three s-d shell nuclei the experiment covered a map ranging from 0 to 220 MeV/c in recoil momentum and from 0 to 20 MeV in excitation energy of the final nucleus. Recoil momentum distributions have been obtained for the 0⁺ ground state and the 2⁺ first excited state of ²⁰Ne, ²⁴Mg and ³⁶Ar, and also for the states around 4.4 MeV (mainly 4⁺) of ³⁶Ar. The a spectroscopic factors extracted by a DWIA analysis are about three times larger than those predicted by the SU(3) model; however, they agree quite well in relative magnitude for a number of cases. The disagreement in shape between experiment and theory observed at low recoil momentum for the 2⁺ states might result from another reaction mechanism. The cross sections for ⁵⁸Ni are about a factor often smaller than those for ⁴⁰Ca. The ⁵⁸Ni(p, pα)⁵⁴Fe reaction seems to lead mainly to excited states of the final nucleus.     

Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices

We demonstrate optical switching of electrically resonant terahertz planar metamaterials fabricated on ErAs/GaAs nanoisland superlattice substrates. Photoexcited charge carriers in the superlattice shunt the capacitive regions of the constituent elements, thereby modulating the resonant response of the metamaterials. A switching recovery time of 20 ps results from fast carrier recombination in the ErAs/GaAs superlattice substrates.     

Excitation of theΔ (1232)-resonance in proton-nucleus collisions

The excitation of theΔ resonance is observed in proton collisions on C, Nb and Pb targets at 0.8 and 1.6 GeV incident energies. The mass E₀ and widthΓ of the resonance are determined from the invariant mass spectra of correlated (p, π^±)-pairs in the final state of the collision: The mass E₀ is smaller than that of the free resonance, however by comparing to intra-nuclear cascade calculations, this reduction is traced back to the effects of Fermi motion, NN scattering and pion reabsorption in nuclear matter.     

On adaptive stratification

This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the strata, which should be ideally fitted to the subsets where the functions to integrate is nearly constant, and on the allocation of the number of samples within each strata. When the dimension is large and the function to integrate is complex, finding such partitions and allocating the sample is a highly non-trivial problem. In this work, we investigate a novel method to improve the efficiency of the estimator “on the fly”, by jointly sampling and adapting the strata which are hyperrectangles and the allocation within the strata. The accuracy of estimators when this method is used is examined in detail, in the so-called asymptotic regime (i.e. when both the number of samples and the number of strata are large). It turns out that the limiting variance depends on the directions defining the hyperrectangles but not on the precise abscissa of their boundaries along these directions, which gives a mathematical justification to the common choice of equiprobable strata. So, only the directions are adaptively modified by our algorithm. We illustrate the use of the method for the computation of the price of path-dependent options in models with both constant and stochastic volatility. The use of this adaptive technique yields variance reduction by factors sometimes larger than 1000 compared to classical Monte Carlo estimators.