Growth properties of Sobolev space functions over unbounded domains

Summary We study Sobolev space functions with prescribed growth properties on large spheres. In particular, we prove a weighted Poincaré type inequality for such functions. An extension to weighted Sobolev spaces is sketched.

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Sunto Si studiano funzioni che appartengono a certi spazi di Sobolev e che hanno crescita assegnata su sfere di grande raggio. Per tali funzioni si dimostra una disuguaglianza di tipo Poincaré con peso. Si indica inoltre anche una estensione di tale risultato a funzioni in spazi di Sobolev con peso.

     

Gauge-invariant treatment of the exponential decay of an unstable atomic state

Summary By using a self-consistent projection-operator method, developed recently by the present author, a gauge-invariant Markovian treatment of the spontaneous decay of an unstable atomic state is presented. Without ignoring retardation and electron-spin effects a gauge-invariant result for the probability amplitude of finding the atom in the unstable state is obtained.     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.     

Even denominator filling factors in the thermoelectric power of a 2DEG

We have investigated the interaction of phonons with a 2DEG in the FQH regime with phonon drag thermoelectric power (TEP). We find that the TEP at filling factors with the same even denominator is identical and at other even denominator filling factors they differ only by a constant. Assuming these states to be Composite Fermions (CF), we can explain our observations by extending a zero magnetic field theory for phonon drag to the CF-phonon interaction. This analysis is further corroborated by the observed T⁴ dependence of the CF TEP.     

Compact coaxial driver for small-size Z-pinch

The presented one-capacitor pinch driver, designed as a compact coaxial structure (including spark-gap and discharge section) consistent with the capacitor output, generates a current of 200 kA with 700 ns quarter-period, suitable for studying the optimization of Z-pinch radiative characteristics. The driver is described, measurements of its parameters summarized, and relations to our previous and future activities briefly reviewed.This work was supported in part by the Grant Agency of the Czech Republic under contract No. 202/93/1023.     

Thermal and acoustic effects in optical phase conjugation in Rhodamine 6G solutions with nanosecond pulses

Thermally induced phase conjugation by degenerate four-wave mixing in solutions of Rhodamine 6G in ethanol in the weak absorption region, low-reflectivity regime, and nonosecond time domain is reported. Evidence of oscillatory acoustic modes in the nonlinear medium is presented and existing theories are shown to explain satisfactorily the experimental results.     

Crossing of shears bands in196Pb

High-spin states in¹⁹⁶Pb have been populated using the reaction¹⁷⁰Er(³⁰Si,4n). The previously observed shears bands in this nucleus have been extended and some of their transitions have been reordered. They now form regular bands with band crossings. One of the bands splits into two pathways at high spin.     

HREM studies of the structure and the oxidation process of copper clusters created by inert gas aggregation

Structure and reactivity with oxigen of Cu clusters in the size range of 4.5±2.5 nm created by the inert gas aggregation technique were studied by HREM. The pure Cu clusters investigated under clean conditions show the structures of MTP's with a small lattice dilatation of the (111) plane of 1.25%. For icosahedral and decahedral particles this dilatation corresponds to a splitting of the nearest neighbour distance showing two different values, i.e. dilatation of 2.2% and contraction of 2.8% for the two edges of the deformed tetrahedral subunits, respectively. Oxidation at room temperature and air pressure of 1 bar only begins after a few minutes of exposure to air, after having undergone creation of probably non-stoichiometric intermediate states in the cuprite Cu₂O structure with the bulk values of the bond lengths.