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Let$B$be the unit ball of$C$^{$n$}, I give necessary conditions on sequence$S$of points in$B$to be$H$^{∞}($B$) interpolating in term of a$C$^{$n$}valued holomorphic function zero on$S$(a substitute for the interpolating Blaschke product).

A two-dimensional model of electron motion in a curved quantum wire of length 2<i>D</i> attached to a pair of macroscopic electrodes is studied. The wire is regarded as infinitely thin and supports a potential which is a combination of a constant transversal-mode energy and an attractive curvature-induced term. The system is shown to have at least one resonance which exhibits spectral concentration as <i>D</i>.

Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in [A. Berenstein, D. Kazhdan, Geometric and unipotent crystals. II. From unipotent bicrystals to crystal bases, in: Quantum Groups, in: Contemp. Math., vol. 433, Amer. Math. Soc., Providence, RI, 2007, pp. 1388] constructed a monoid structure on the set of all subsets of I using unipotent -linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxeter groups. Moreover, we will calculate this monoid structure explicitly for each type.

I would like to congratulate Professor Antoniadis for successfully outlining the current state-of-art of wavelet applications in statistics. Since wavelet techniques were introduced to statistics in the early 90s, the applications of wavelet techniques have mushroomed. There is a vast forest of wavelet theory and techniques in statistics and one can find himself easily lost in the jungle. The review by Antoniadis, ranging from linear wavelets to nonlinear wavelets, addressing both theoretical issues and practical relevance, gives in-depth coverage of the wavelet applications in statistics and guides one entering easily into the realm of wavelets.