Asymptotic Behavior of One-Parameter Semigroups and Rigidity of Holomorphic Generators

We study the asymptotic behavior of one-parameter continuous semigroups of holomorphic mappings. We present angular characteristics of their trajectories at their Denjoy–Wolff points, as well as at their regular repelling points (whenever they exist). This enables us to establish new rigidity properties of holomorphic generators via the asymptotic behavior of the semigroups they generate. Received: May 11, 2007. Accepted: July 22, 2007.     

Mode transitions in distributed-feedback tapered master-oscillator power-amplifier: theory and experiments

Theoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.     

Asymmetric cubature formulas for polynomial integration in the triangle and square

We present five new cubature formula in the triangle and square for exact integration of polynomials. The points were computed numerically with a cardinal function algorithm which does not impose any symmetry requirements on the points. Cubature formula are presented which integrate degrees 10, 11 and 12 in the triangle and degrees 10 and 12 in the square. They have positive weights, contain no points outside the domain, and have fewer points than previously known results.     

Improving the dispersion and interfaces in polymer‐carbon nanotube nanocomposites by sample preparation choice

Polymer nanocomposites composed of poly(styrene‐ran‐vinyl phenol) (PSVPh) copolymers and 5 wt % multi‐walled carbon nanotubes (MWNTs) were prepared by three different methods, including melt‐mixing and precipitation. The MWNTs were either oxidized to incorporate oxygenated defects or utilized as received. The mechanical properties of the nanocomposites were measured by dynamic mechanical analysis (DMA), and the extent of intermolecular hydrogen bonding between MWNTs and PSVPh was quantified by infrared (IR). Our DMA results suggest that melt‐mixing leads to more stable morphologies of the final nanocomposites than precipitation. Additionally, the IR analysis of the nanocomposites indicates melt‐mixing can result in the formation of more intermolecular hydrogen bonding between the MWNTs and PSVPh than precipitation, and thus suggests that melt‐mixing leads to more reproducible mechanical properties than precipitation. Our DMA and IR results may provide guidelines to realize the desired morphologies and to improve the properties of polymer carbon nanotube nanocomposites by optimizing intermolecular interactions between MWNTs and polymers using processing. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1747–1759, 2008