The Cern (g-2) measurements

Measurements of the anomalous magnetic moment of the muon are reviewed. The emphasis is put on the first one of a series of three CERN experiments which led to an experimental value ofa=1165922.9 (8.5)·10⁻⁹ (±7.2ppm), and which compares well with the present theoretical resulta=1165919.2 (1.8)·10⁻⁹ (±1.5ppm).     

A RAPID APPROXIMATION FOR PREDICTING THE HYDROCARBON DISCOVERY RATE: PART 1. ASSESSING THE ACCURACY

The hydrocarbon discovery prediction problem is important to firms having to make decisions about the deployment of scarce exploration resources. Traditional methods for estimating the discovery rate rely on the completion of time consuming simulation experiments. A rapid approximation that does not require the completion of simulation exists and has been shown to have some promise as a prediction tool. This paper investigates the accuracy of the approximation method under a wide variety of distributional and drilling efficiency assumptions. The results indicate that the approximation produces predictions close to those of simulation under most of the tested conditions. This suggests that resource exploration firms could conveniently use the method for a wide variety of planning purposes without incurring the same costs in time and personnel required for simulation.     

Magnetic resonance imaging and pulsed Doppler sonography of poststenotic jets: Correlation between signal void and flow velocity distribution

To correlate the appearance of poststenotic jets on gradient echo images with features of localized Doppler spectra of the jets, we studied an in vitro model of steady flow-through stenoses of 86, 96, and 99% area reduction. As fluids, water and a 40% glycerol solution in water were used. MRI was performed with a 1.5 T whole body imager and gradient echo images were obtained in planes parallel to the direction of flow. Doppler spectra were acquired separately from the MR measurements at 1 cm intervals for a distance of 10 cm downstream from the stenosis. Poststenotic signal void was observed for water and for the 40% glycerol solution only if the mean velocity within the stenosis exceeded a limit of 50–60 cm/sec. On the MR images, the jets could be divided into two segments: A proximal jet segment of uniform width equal to the diameter of the stenosis, followed by a distal jet segment which was characterized by broadening and then dissipating signal void. Except for the 99% stenosis, a high signal intensity core was present within the proximal jet segment. In the proximal jet segment, the Doppler measurements showed a low temporal fluctuation of the maximal flow velocity and only little flow opposite to the main flow direction. In the distal jet segment, the velocity fluctuation and the intensity of reverse flow increased sharply. The high signal intensity core of the jet was associated with a poststenotic zone of constant maximal flow velocity. The results demonstrate a close relationship between characteristic features of poststenotic jets in MRI and pulsed Doppler sonography.     

Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Variational bounds on shear-driven turbulence and turbulent Boussinesq convection

Based on earlier studies by Hopf (1941), Doering and Constantin (1992, 1994, 1995) have recently formulated a new “background” technique for obtaining upper bounds on turbulent fluid flow quantities. This method produces upper bounds on the limit supremum of long time averages, making no statistical assumptions about the flow in contrast to the well-known Howard-Busse approach. The full optimisation problems posed by this method for the momentum transport in turbulent Couette flow and the heat transport (with zero background flow) in turbulent Boussinesq convection are solved here for the first time at asymptotically large Reynolds number and Rayleigh number within Busse's multiple boundary layer approximation to extract the best (lowest) possible upper bounds available. Intriguingly, the original bounds isolated by Busse (1969, 1970) within the confines of statistical stationarity are recovered exactly using this new formalism. The optimal background velocity profile for turbulent Couette flow is found to be shearless in the interior thus differing from Busse's “ ” mean shear result. In the convective case, an interesting degeneracy in the formulation of the background variational problem leads to an indeterminacy in the optimal background temperature profile. Only for one special choice is the isothermal core feature of Busse's mean profile recovered.     

随机删失下乘积限过程和累积失效率过程振动模的局部渐近性

在随机删失下研究了乘积限过程和累积失效率过程的振动模的局部性质 .给出了这两个过程的振动模的重对数律 ,并应用这些结果得到了几种核密度估计和Bahadur-Kiefer过程的精确收敛速度     

Liquid crystal side chain polysiloxanes containing various proportions of non-mesogenic units

Recent studies have established that side chain polymeric liquid crystals composed of mesogenic and non-mesogenic side groups keep their liquid-crystalline properties even for a low proportion of mesogens. We show that the detailed structures of three kinds of new diluted liquid crystal polysiloxanes depend on the nature of the co-substituent as well as on the proportion of the silicon sites occupied by the mesogenic groups. Mixtures of these systems with low molar mass liquid crystals were also investigated in terms of compatibility and/or stabilization of smectic A phases.