Pion pair production with higher order radiative corrections in low energy $e^+e^-$ collisions

The complete QED initial state (IS), final state (FS) and initial–final state (IFS) interference corrections to the process are presented. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section (), the pion angular distribution () and the invariant mass distribution () are investigated in the regime of experimentally realistic kinematical cuts. It is shown that in addition to the full corrections also the and leading-log photonic corrections as well as the contributions from IS -pair production have to be taken into account if at least per cent accuracy is required. For the data analysis we focus on an inclusive treatment of all photons. The theoretical error concerning our treatment of radiative corrections is then estimated to be 2 per mill for both the measurement of the total cross section and the invariant mass distribution. In addition we discuss the model uncertainty due to the pion substructure. Altogether the precision of the theoretical prediction matches the requirements of low energy experiments like the ones going on at DANE or VEPP-2M. Received: 6 September 2001 / Revised version: 24 January 2002 / Published online: 5 April 2002     

The radiative return at small angles: virtual corrections

Virtual corrections for electron-positron annihilation into one real and one off-shell photon of invariant mass are evaluated. Special attention is paid to those configurations where the real photon is collinear with the beam direction. This calculation is an important ingredient of a Monte Carlo program, which simulates events with tagged photons from initial-state radiation, including NLO corrections. Received: 24 April 2002 / Published online: 12 July 2002     

Raman spectra of MgB2 at high pressure and topological electronic transition

Raman spectra of MgB₂ ceramic samples were measured as a function of pressure up to 32 GPa at room temperature. The spectrum at normal conditions contains a very broad peak at ∼590 cm⁻¹ related to the E _2g phonon mode. The frequency of this mode exhibits a strong linear dependence in the pressure region from 5 to 18 GPa, whereas, beyond this region, the slope of the pressure-induced frequency shift is reduced by about a factor of two. The pressure dependence of the phonon mode up to ∼5 GPa exhibits a change in the slope, as well as a “hysteresis” effect in the frequency vs. pressure behavior. These singularities in the E _2g mode behavior under pressure support the suggestion that MgB₂ may undergo a pressure-induced topological electronic transition.     

A NEW METHOD FOR SEPARATING LONGITUDINAL WAVES IN A LARGE DIAMETER HOPKINSON BAR

This paper outlines various methods for separating fundamental longitudinal waves propagating along a Hopkinson pressure bar. Advantages and disadvantages of the different methods are presented and discussed in detail. A new method is then proposed for separating the fundamental waves in the frequency domain. This new method is based on the assumption that wave propagation can be adequately described by the first mode of the Pochhammer-Chree theory. The method requires two-point strain gauge measurements on the pressure bar. Fourier components of the positive wave at one gauge location are determined either from the corresponding Fourier components of the measured strain histories or from their derivatives. The method also makes use of the derivative of the wave number with respect to the circular frequency of the pressure bar. Important points of the implementation of the technique are described. Numerical accuracy of the proposed method is verified by considering a simple example with analytical solution and by comparing measured data derived from a large diameter Hopkinson pressure bar. The proposed method will find application in dynamic material tests using the split Hopkinson pressure bar technique.     

Liquid chromatographic analysis of prednisolone, prednisone and their 20-reduced metabolites in perfusion media

A reversed-phase liquid chromatographic assay was developed to quantitate prednisolone, prednisone and the 20 alpha-dihydro and 20 beta-dihydro reduced metabolites of both parent compounds in tissue culture media from in vitro perfusions of the human placental lobule. Steroids were extracted from perfusate, using reversed-phase cartridges, with average recoveries of 95.2% or greater. The internal standard for the analyses was 6 alpha-methylprednisolone. In this assay cortisol coelutes with prednisolone, however, no other significant interferences were found. Assay of each steroid was linear in the range 0-1 microgram/ml. Intra-assay coefficients of variation were measured at 10 and 750 ng/ml with ranges of 3.4% (20 alpha-dihydroprednisone) to 8.8% (20 beta-dihydroprednisolone) and 4.1% (20 beta-dihydroprednisone) to 8.8% (prednisone). The corresponding inter-assay coefficients of variation were 3.3% (20 alpha-dihydroprednisone) to 9.1% (20 beta-dihydroprednisolone) and 1.9% (prednisolone) to 3.5% (prednisone). The analyses utilized two C18 columns which were linked together and maintained at 40 degrees C.     

Perfect fluid spacetimes admitting curvature collineations

Some basic concepts about curvature collineations are reviewed and the existing results on this topic are applied to the case of perfect fluids, giving a characterization of those amongst them which admit proper curvature collineations.     

Optimization over the efficient set using an active constraint approach

In this work the problem of maximizing a nonlinear objective over the set of efficient solutions of a multicriteria linear program is considered. This is a nonlinear program with nonconvex constraints. The approach is to develop an active constraint algorithm which utilizes the fact that the efficient structure in decision space can be associated in a natural way with hyperplanes in the space of objective values. Examples and numerical experience are included.