Uniform bounds under increment conditions

We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.

     

Regular population monotonic allocation schemes

The paper introduces a refinement of the notion of population monotonic allocation scheme, called regular population monotonic allocation scheme (regularpmas). This refinement is based on economic situations in which players may have to select new partners from a set of potential players and in which there exist certain capacity constraints. A sufficient condition for the existence of a regularpmas is given. For the class of games with regularpmas, we prove that the core coincides with the Davis and Maschler and the Mas-Colell bargaining sets.     

Pion correlations and resonance effects in \bar{p}p annihilation to 4\pi^0 at rest

We study correlations in the exclusive reaction at rest with complete reconstruction of the kinematics for each event. The inclusive distribution is fairly flat at small invariant mass of the pion pair while a small enhancement in the double differential distribution is observed for small invariant masses of both pion pairs. Dynamical models with resonances in the final state are shown to be consistent with the data while the stochastic HBT mechanism is not supported by the present findings. Received: 26 February 2002 / Revised version: 22 July 2002 / Published online: 30 August 2002     

The influence of slits on sound transmission through a lightweight partition

In this paper the influence on sound reduction index of the length and the depth of sound leaks at the perimeter of lightweight partitions was examined. It was shown that the most important decrease on sound reduction index is caused by the first slit between lightweight partition and one of the structural members. When the length of the slit is increased, the decrease on sound reduction index is less significative. Calculated results show the same effects as measured ones.     

Structure and electrochemical behaviour of 4,7-diazaheptyl-trimethoxy-silane and vinyl-trialkoxy-silane adsorbed at silver surface

Novel self-assembled monolayers were obtained on silver using 4,7-diazaheptyl-trimethoxy-silane (SiN) and vinyl-trialkoxy-silane (SiVA, where the alkyl group is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60-eicozaoxa- hexaheptaconan). It was shown that thus modified metal surface was protected against electrooxidation. A densely packed monolayer remained stable and did not desorb from the Ag electrode on the potential cycling. The structure of SiN and SiVA as well as their complexes with Li⁺ cations were calculated and visualised by the AM1d and PM5 semi-empirical methods.     

Almost Sure Convergence and Square Functions of Averages Of Riemann Sums

Under a very moderate assumption on the Fourier coefficients of a periodic function, we show the convergence almost everywhere of the sequence of averages of its associated Riemann sums. The structure of the set of averages is analyzed by proving a spectral regularization type inequality, which allows to control the corresponding Littlewood-Paley square function.     

A nucleophilic substitution reaction in microemulsions based on either an alcohol ethoxylate or a sugar surfactant

A nucleophilic substitution reaction between 4-tert-butylbenzyl bromide and a series of iodide salts has been performed in oil-in-water microemulsions based on either a fatty alcohol ethoxylate or a sugar surfactant. The reaction kinetics was compared with the kinetics of the same reaction performed in a microhomogeneous reaction medium, d-MeOH. Previous results showing a particularly high reactivity in the microemulsion based on the fatty alcohol ethoxylate was confirmed. It was shown that in both microemulsions the reaction rate was almost independent of the choice of counterion to iodide. This indicates that complexation of the cation with the surfactant headgroup, which, in particular, could have taken place with surfactants containing oligooxyethylene chains (a “crown ether effect”), seems not to be of importance.

¹²⁷I NMR studies, as well as quadrupole splitting experiments performed by ²H NMR, indicate that there is a certain accumulation of iodide at the oil–water interface of the microemulsions. It is difficult to draw any quantitative conclusions in this respect, however.

The results obtained in this study, combined with results from previous investigations of the same reaction, indicate that the unexpectedly high reactivity obtained in the microemulsion based on a surfactant containing an oligooxyethylene headgroup is most probably due to the nucleophile being poorly solvated when present in the headgroup layer of such a microemulsion. Poorly solvated anions are known to be highly reactive nucleophiles.