Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Learning to See: Making Sense of the Mathematics of Change in Middle School

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the students and their teacher negotiated the mathematical meanings of these representations, in interaction with the software and other representational tools available in the classroom. The class developed ways of selectively attending to specific features of stacks of centimeter cubes, hand-drawn graphs, and graphs (labeled velocity vs. time) on the computer screen. In addition, the class became adept at imagining the motions that corresponded to various velocity vs. time graphs. In this article, we describe this development as a process of learning to see mathematical representations of motion. The main question this article addresses is: How do students learn to see mathematical representations in ways that are consistent with the discipline of mathematics? This revised version was published online in July 2006 with corrections to the Cover Date.     

Peptides-XXXXVI: Studies in the synthesis of an analogue of hen egg white lysozyme

The previously synthesised (1–37), (38–75), (76–93), (94–104), (105–117) and (118–129) fragments of the analogue were combined making extensive use of the DCCI/HONSu method. The final coupling involved the (1–75) and (76–129) sub-fragments. Aggregation of the latter fragment caused problems in purification by routine gel filtration methods employing Enzacryl K2 or Sephadex LH60. The fully protected (1–129) product was partially purified by washing, then deprotectcd and purified by gel filtration and ion exchange chromatography. Satisfactory removal of the acetamidomethyl group used for cysteine protection could not be achieved.     

The dipole moment of HNO in its ÃA″ excited state determined using optical—optical double resonance stark spectroscopy

The Stark splittings and rotational asymmetry splittings of a number of levels of the ùA″ excited state of HNO have been measured using the sub-Doppler technique of optical—optical double resonance, μ_a is found to be 1.08 ± 0.01 D for the 100 vibronic state, and 1.05 ± 0.01 D for the 020 vibronic state. These values are to be compared with a recently determined ground state value of μ_a = 0.996 D. The asymmetry splittings of some of the levels studied are considerably larger than predicted from the known rotational constants, indicating minor rotational perturbations.     

Accuracy, latency, and listener-search behavior in localization in the horizontal and vertical planes

Thirty-six listeners localized continuous filtered noise bursts centered on 2.3 or 8.3 kHz under normal listening conditions or while wearing earmuffs. The noise bursts were from any one of 20 loudspeakers, 18 degrees apart, visible to the listeners, and arranged in the horizontal and vertical planes. Listeners were free to move, while remaining seated, throughout all trials. The noise bursts were terminated by the listeners. Measures of accuracy and latency showed that earmuff listening had a significant effect whereas, overall, signal frequency had no significant effect. There was, however, an apparent downward shift of the 2.3-kHz signals presented above the midline in the vertical plane. Analysis of video records of listeners' behavior revealed a strong tendency for initial orientation by head or eye movement to correlate with final response, even when both were inaccurate. The paradigm adopted in this latter aspect of the study illustrates an "ecological" approach to the study of auditory phenomena.     

Fabrication of "hairy" colloidosomes with shells of polymeric microrods

Novel colloidosome microcapsules with aqueous gel cores and integral shells of rodlike polymeric particles have been prepared and characterized. The synthesis is based on templating water-in-oil emulsions stabilized by rodlike particles followed by gelling of the aqueous phase, dissolution of the oil phase in ethanol, and redispersion of the obtained colloidosome capsules in water. Such capsules may find applications as vehicles for delivery and controlled release of drugs, cosmetics, and food supplements.