Smooth Approximation of Orlicz-Sobolev Maps Between Manifolds

The problem of density of smooth functions in Orlicz-Sobolev spaces of maps between compact manifolds, without topological restrictions, is addressed. Our contribution refines earlier results in the literature via ad hoc Orlicz space techniques.     

Direct measurement of the double emittance minimum in the beam dynamics of the sparc high-brightness photoinjector

In this Letter we report the first experimental observation of the double emittance minimum effect in the beam dynamics of high-brightness electron beam generation by photoinjectors; this effect, as predicted by the theory, is crucial in achieving minimum emittance in photoinjectors aiming at producing electron beams for short wavelength single-pass free electron lasers. The experiment described in this Letter was performed at the SPARC photoinjector site, during the first stage of commissioning of the SPARC project. The experiment was made possible by a newly conceived device, called an emittance meter, which allows a detailed and unprecedented study of the emittance compensation process as the beam propagates along the beam pipe.     

Optimal Gaussian Sobolev embeddings

A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangement-invariant norms with respect to the Gauss measure in Rn, is equivalent to a one-dimensional inequality, for a suitable Hardy-type operator, involving the same norms with respect to the standard Lebesgue measure on the unit interval. This result is exploited to provide a general characterization of optimal range and domain norms in Gaussian Sobolev inequalities. Applications to special instances yield optimal Gaussian Sobolev inequalities in Orlicz and Lorentz(-Zygmund) spaces, point out new phenomena, such as the existence of self-optimal spaces, and provide further insight into classical results.     

Mössbauer effect study of relaxation mechanism in57Fe-doped ammonium alum

The Mössbauer spectra of the ammonium alum doped with approximately 1% of⁵⁷Fe for T. 80K have been considered. The characteristics of the spectra have been reproduced by taking into account that the parameter λ of the spin Hamiltonian is different from zero and that the spin-spin interaction couples the states of each one of the Kramers doublets corresponding to S_z+1/2 and ·S_z±3/2.     

Relaxation phenomena in Cr3+ doped Al2O3−Fe 2 57 O3 systems

Mössbauer absorption spectra have been measured for Cr³⁺ doped Al₂O₃?Fe ₂ ⁵⁷ O₃ systems for different values of the Cr³⁺ concentration at room temperature. The cross relaxation between Fe³⁺ and Cr³⁺ ions, which destroys the paramagnetic hyperfine structure of Fe⁵⁷ observed in undoped Al₂O₃?Fe ₂ ⁵⁷ O₃, is thoroughly studied. The experimental results suggest a new kind of cross-relaxation process involving three spins, i.e. two Fe³⁺.ions and one Cr³⁺. The process, though it is a higher-order one, is highly effective because it is energy-conserving.     

Occurence and correlation of two non-equivalent sites for europium in EuPd3B

Mössbauer spectroscopy has been used to investigate the mechanism which affects the valence state of europium in EuPd₃B. The obtained results are interpreted in terms of a correlation between two non equivalent sites each in a fluctuating valence state.     

Feynman's approach to quantum mechanics: Trajectories,commutation relations and uncertainty principle

Summary In this paper the meaning of trajectory for a quantum-mechanical particle is discussed, starting from the path integral expression of the propagator. By a direct method the trajectories mostly contributing to the total amplitude are found, but it seems impossible to interpret them as paths in the physical space-time; on the contrary, the position-momentum commutation relations directly follow. Moreover, we show that the Heisenberg uncertaint principle can be obtained from the path integral approach. In order to give a better understanding of the characteristic quantum-mechanical features and of the difference from the classical problems, the diffusion equation for a Brownian particle is considered in the first part of the paper. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Low-temperature anharmonic vibrations in the cuprates: a bipolaron model

Il Nuovo Cimento D - Starting from the recent experiments that have revealed large-amplitude anharmonic vibrations in the cuprates, the possibility of formation of bipolarons has been investigated....