Search

The problem about a body in a three dimensional infinite channel is considered in the framework of the theory of linear water-waves. The body has a rough surface characterized by a small parameter epsilon > 0 while the distance of the body to the water surface is also of order epsilon. Under a certain symmetry assumption, the accumulation effect for trapped mode frequencies is established, namely it is proved that, for any given d > 0 and integer N > 0, there exists a number epsilon(d, N) > 0 such that the problem has at least N eigenvalues in the interval (0, d) of the continuous spectrum in the case epsilon is an element of (0, epsilon (d, N)). The corresponding eigenfunctions decay exponentially at infinity, have finite energy, and imply trapped modes. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Synthesis and characterization of a new gold-2-mercapto-1-methyl imidazole are reported. This new organic material shows an extraordinary fluorescence activity (superfluorescence) up to 220°C with an unusual quantum yield of 0.2. Both fluorescence and NMR spectroscopy were applied to understand the behavior of the gold-2-mercapto-1-methylimidazole complex. Results suggest that the superfluorescence activity can be attributed to the shrinking of the HOMO-LUMO band gap energy following complexation of the organic imidazole system with gold. Copyright © 2010 John Wiley & Sons, Ltd.

Examples of periodic elastic waveguides are constructed, the essential spectrum of which has a gap, i.e. an open interval in the positive real semiaxis intersecting with the discrete spectrum only. The gap is detected with the help of an inequality of Korn's type and the max-min principle for eigenvalues of self-adjoint positive operators. Under a certain symmetry assumption, it is demonstrated that the first band of the essential spectrum can include eigenvalues in the point spectrum. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim