The weak closure of the set of left translation operators

It is known that for an amenable locally compact group , is not in the weak closure of of . In this paper, it is proved that the converse of this is true. In other words, if is a non-amenable locally compact group, then is in the weak closure of . This answers several questions of Ülger. Applications to the algebra and the dual of the reduced group -algebra are obtained.

     

Nonlinear directional coupler in periodically poled lithium niobate

Nonlinear wave propagation was investigated experimentally in coupled waveguides by means of the cascaded nonlinearity in quasi-phase-matched second-harmonic generation. With a specially designed wave-vector-mismatch distribution along the propagation axis, cascading was optimized for low fundamental depletion. High-contrast, ultrafast all-optical switching with switching powers of tens of watts was observed.     

Integrable Equations Arising from Motions of Plane Curves. II

Integrable equations satisfied by the curvature of plane curves or curves on the real line under inextensible motions in some Klein geometries are identified. These include the Euclidean, similarity, and projective geometries on the real line, and restricted conformal, conformal, and projective geometries in the plane. Together with Chou and Qu [Physica D 162 (2002), 9–33], we determine inextensible motions and their associated integrable equations in all Klein geometries in the plane. The relations between several pairs of these geometries provide a natural geometric explanation of the existence of transformations of Miura and Cole-Hopf type.     

Sn/Ge(111) surface charge-density-wave phase transition

Angle-resolved photoemission has been utilized to study the surface electronic structure of 1 / 3 monolayer of Sn on Ge(111) in both the room-temperature (sqrt[3]xsqrt[3] )R30 degrees phase and the low-temperature ( 3x3) charge-density-wave phase. The results reveal a gap opening around the ( 3x3) Brillouin zone boundary, suggesting a Peierls-like transition despite the well-documented lack of Fermi nesting. A highly sensitive electronic response to doping by intrinsic surface defects is the cause for this unusual behavior, and a detailed calculation illustrates the origin of the ( 3x3) symmetry.     

Two-dimensional numerical visualization on the interaction of blast waves with obstacles

In this study, the complex phenomena of propagation and interaction of the blast waves impacting on obstacles were visualized and investigated using a numerical method. Three different distances between an immovable wall and a bomb shelter with a square block inside were considered while a blast source is located in front of wall at the same distance from shelter. The transitional shock phenomena were simulated by means of a multi-block mesh system and a flux computational model. Spatial discretization was performed using the Roe’s upwind schemes; time integration was achieved via the second-order explicit Hancock method. Proof of the numerical results indicated that those results were in close agreement with the experimental data obtained for the wedge flow. For the cases proved, the geometries of the reflected wave patterns followed by the incident blast waves crossing the immovable wall and impacting inside of bomb shelters were similar. However the height of wall has a dominating impact on the effect associated with different incident blast waves from the same blast source. Meanwhile, different reflected overpressure-time histories and streamlines were observed and analyzed for the results obtained.     

Raman scattering from one-dimensional carbon systems

Although the Raman effect was discovered nearly 80 years ago, it is only recently that the special characteristics of Raman scattering for one-dimensional systems have been seriously considered. This review focuses on the special interest of the Raman effect for one-dimensional systems that is of particular relevance to carbon nanostructures. Two examples of Raman scattering in one-dimensional systems are given. The first illustrates the use of Raman spectroscopy to reveal the remarkable structure and properties of carbon nanotubes arising from their one-dimensionality. Some of the recent advances in using Raman spectroscopy to study doping and intercalation to modify nanotube properties are reviewed, in the context of a one-dimensional system. The second example is the Raman spectra of a linear chain of carbon atoms and the special properties of this interesting system. New approaches toward applying Raman spectroscopy to carbon nanostructures are also emphasized.     

Performance of default risk model with barrier option framework and maximum likelihood estimation: Evidence from Taiwan

We investigate the performance of a default risk model based on the barrier option framework with maximum likelihood estimation. We provide empirical validation of the model by showing that implied default barriers are statistically significant for a sample of construction firms in Taiwan over the period 1994-2004. We find that our model dominates the commonly adopted models, Merton model, Z-score model and ZETA model. Moreover, we test the n-year-ahead prediction performance of the model and find evidence that the prediction accuracy of the model improves as the forecast horizon decreases. Finally, we assess the effect of estimated default risk on equity returns and find that default risk is able to explain equity returns and that default risk is a variable worth considering in asset-pricing tests, above and beyond size and book-to-market.