Finite dimensional polish spaces are extreme boundaries of convex bodies in Euclidean space

It is proved that everyn-dimensional Polish space is homeomorphic to the set of extreme points of a compact convex set inR ^18(n+1). The contribution of M. Levin to this paper is a part of his Ph.D. thesis prepared at the University of Haifa under the supervision of Y. Sternfeld.     

Elastic properties of high-temperature superconductors Pb2Sr2ACu3O8 (A=Ho,Y,Y0.5Ca0.5) derived from high-pressure X-ray diffraction

The crystal structure of the superconducting compounds Pb₂Sr₂ACu₃O₈, where A=Ho, Y and Y_0.5Ca_0.5, has been studied at room temperature in the pressure range up to 50 GPa. A transition from orthorhombic to tetragonal structure is observed at about 10 GPa for all these components. The transition is reversible and without any discontinuous volume change. The value of the bulk modulus for the two compounds with A=Ho and Y is in the range 160–164 GPa, whereas for A=Y_0.5 Ca_0.5 a larger value of 195 GPa has been measured.     

Stabilization energies of charged multiexciton complexes calculated at configuration interaction level

Recombination and stabilization energies of multiexcitons confined in positively and negatively charged semiconductor InGaAs/GaAs quantum dot (QD) samples have been studied by employing large-scale configuration interaction (CI) calculations. The CI calculations show that at most six electrons or two holes can be confined in the QD. Multiply charged multiexciton complexes with up to five excess electrons or two excess holes are also found to be stable, even when a few electron–hole pairs are present in the QD. The chemical potential functions for charged QD samples do not possess the pronounced stepped form as obtained for the corresponding neutral multiexciton complexes. The negatively and the positively charged excitons (negative and positive trions) lie lower in energy as compared to a neutral exciton and a single non-interacting charge carrier in the lowest single-particle state of another quantum dot. The other charged multiexciton complexes studied are not confined with respect to the corresponding neutral multiexciton and a non-interacting charge carrier. To include the contributions from the heavy-hole light-hole (HH–LH) coupling, a perturbative treatment of the band-mixing effects was implemented. The perturbation-theory calculations show that the HH–LH coupling does not shift the energies in the present InGaAs/GaAs QD sample.     

Gluon bremsstrahlung in e+e− annihilation: (II). Gluon polarization

The linear and circular polarizations of gluons emitted in electron-positron annihilation, $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{g}$, are evaluated, including neutral current and beam polarization effects. For the lower part of the gluon bremsstrahlung spectrum, the linear polarization is found to be large and the plane of polarization to be almost parallel to the q$\text{q}$g event plane. The neutral current induced circular polarization is in the upper part of the gluon spectrum of the order of 10–15% at 40 GeV total energy and reaches ～50% at asymptotic energies.     

Study of some two-nucleon pick-up reactions in the 1p shell with 39.8 MeV protons

Differential cross sections at a proton energy of 39.8 MeV (lab) have been measured for the following reactions (energies in MeV): ¹²C(p,τ)¹⁰B(g.s., 0.72, 1.74, 2.15, 3.59), ¹⁴C(p, t)¹²C(g.s., 4.43), ¹⁴N(p, τ)¹²C(g.s., 4.43), and ¹⁶O(p,τ)¹⁴N(g.s., 2.31, 3.95). A zero-range DWBA analysis of the data has been performed using the 1p shell wave functions of Cohen and Kurath. The fits we find are overall somewhat worse in shape than those found in the (p, t) survey of the 1p shell performed by Kahana and Kurath, the principal reason being that of the (p, τ) transitions which proceed with both L = 0 and L = 2 components we find several which occur with a much weaker L = 0 strength than the calculations predict. When ratios of experimental integrated cross sections to DWBA integrated cross sections are compared for all transitions, an rms deviation about the mean of 39% of the mean is found, whereas if only ratios for transitions from a given target nucleus are compared, then the rms deviations are considerably smaller.     

Quasi-free scattering of polarized protons

Cross section and analyzing power, energy-sharing spectra have been measured for the ¹⁶O($\text{p}$, 2p) reaction at an incident energy of 200 MeV for twenty-four different pairs of angles of the detected final-state protons. This general survey is intended to test the validity of the distorted wave impulse approximation (DWIA), particularly with respect to the predicted j-dependent analyzing power caused by the distorting optical potentials and nuclear spin-orbit coupling. Although the data in general confirm this j-dependence, agreement in detail between DWIA calculations and the analyzing power data becomes worse as the momentum of the recoiling nucleus increases. Predictably, the cross-section calculations show more sensitivity to the optical-model parameters than do the analyzing powers. Within the present limits imposed by scanty elastic scattering data, there seems to remain a choice between predicted ($\text{p}$, 2p) cross sections which either are unreasonably large or which have the incorrect energy-sharing shapes. More comprehensive elastic scattering and total reaction cross section data are clearly needed.     

Kazama-Yang monopole-fermion bound states: (I). Analytic results

We present explicit, approximate, remarkably precise results for the Kazama-Yang monopole-fermion binding energies and wave functions. The results are valid for the states of lowest angular momentum and for the binding energy M ? E ? M. They agree very well with the numerically calculated values.     

Dominated estimates of convex combinations of commuting isometries

The principal result of this paper is that the convex combination of two positive, invertible, commuting isometries ofL _p(X,F, μ) 1<p<+∞, one of which is periodic, admits a dominated estimate with constantp/p−1. In establishing this, the following analogue of Linderholm’s theorem is obtained: Let σ and ε be two commuting non-singular point transformations of a Lebesgue Space with τ periodic. Then given ε>O, there exists a periodic non-singular point transformation σ′ such that σ′ commutes with τ and μ(x:σ′x≠σx}<ε. Byan approximation argument, the principal result is applied to the convex combination of two isometries ofL _p (0, 1) induced by point transformations of the form τx=x ^k,k>0 to show that such convex combinations admit a dominated estimate with constantp/p−1. Research supported in part by NSF Grant No. GP-7475. A portion of the contents of this paper is based on the author’s doctoral dissertation written under the direction of Professor R. V. Chacon of the University of Minnesota.