Visualization of stress distribution has been realized by a nondestructive mechanoluminescence (ML) from SrAl2O4:Eu, which can emit three magnitudes higher visible light than that of well-known ML substance of quartz. A simulation result confirms that such a ML image successfully reflects the stress distribution. A kinetic model for ML of SrAl2O4:Eu is proposed.

The idea and successful practice of a stress sensor to sense mechanical stress by an artificial skin, i.e., self-diagnosis thin film, has been realized, through the fabrication of a high-luminescence thin piezoelectric film which can reproducibly emit strong visible light upon stressing. The strongest luminescent film consists of nanosized crystallites of ZnS doped with 1.5 at. % Mn, in which Mn acts as the emitting center. The intensity of the emitted luminescence responds to stress applied directly onto the film or to the underlying material reversibly and reproducibly, so it can be used as an artificial skin to sense mechanical stress.

We report the realization of the dynamic image of stress distribution by developing a remarkably strong mechanoluminescence (ML) material of Sr0.975Al2O3.985:Eu0.01, which can emit four orders of magnitude larger intensity than that of the reported strong ML material of quartz crystal. This ML material can be mixed in the target composite or coated on the surface to sense stress by emitting visible light. This method is applicable to the dynamic visualization of stress distribution in a solid not only in the atmosphere but also in an aqueous environment.

We introduce a new class of distributions by generalizing the subexponential class to investigate the asymptotic relation between the tails of an infinitely divisible distribution and its Le ´vy measure. We call a one-sided distribution ì O-subexponential if it has positive tail satisfying lim sup x!1 ì Ã ì(x, 1)=ì(x, 1) , 1. Necessary and sufficient conditions for an infinitely divisible distribution to be O-subexponential are given in a similar way to the subexponential case in work by Embrechts et al. It is of critical importance that the O-subexponential is not closed under convolution roots. This property leads to the difference between our result and that corresponding to the subexponential class. Moreover, under the assumption that an infinitely divisible distribution has exponential tail, it is shown that an infinitely divisible distribution is convolution equivalent if and only if the ratio of its tail and its Le ´vy measure goes to a positive constant as x goes to infinity. Additionally, the upper and lower limits of the ratio of the tails of a semi-stable distribution and its Le ´vy measure are given.

A serious gap in the Proof of Pakes's paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It completes the real analytic approach to Sgibnev's theorem. Then the convolution equivalence of random sums of IID random variables is discussed. Some of the results are applied to random walks and Lévy processes. In particular, results of Bertoin and Doney and of Korshunov on the distribution tail of the supremum of a random walk are improved. Finally, an extension of Rogozin's theorem is proved.