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.     

On finite {1,2,3}-semiaffine planes

In this paper, we investigate {1,2,3}-semiaffine planes. All such planes of order n >51 shall be classified. It turns out that they are embeddable into projective planes of the same order n in the most natural way.Work supported by National Research Project on Strutture Geometriche Combinatoria, loro applicazioni of Italian M.P.I. and G.N.S.A.G.A. of C.N.R.     

Ruthenium complexes of analogues of the antitumor antibiotic streptonigrin

The complexes Ru(L1-CH3)(CO)3Cl, RuL2(CO)2Cl2, and RuL3(CO)2Cl2 (L1= 6-methoxy-5,8-quinolinedione, L2 = 7-amino-6-methoxy-5,8-quinolinedione, L3 = 6,6'-dimethoxycarbonyl-2,2'-bipyridine) were prepared by reaction of L1-L3 with the tricarbonyldichlororuthenium(II) dimer. L1-L3 act as bidentates through the ortho oxygen atoms, the pyridyl nitrogen and the adjacent quinone oxygen, and the bipyridyl nitrogens, respectively. RuL3(CO)2Cl2 is characterized by X-ray crystallography. 15N NMR correlation spectra give upfield shifts of around 60 ppm for the pyridyl nitrogens that are coordinated to the metal, while 13C NMR correlation spectra give a downfield shift of 10 ppm for the quinone carbonyl group that is coordinated to the metal. The electrochemistry of RuL2(CO)2Cl2 is examined, and the implications for the formation of metal complexes of the antitumor antibiotic streptonigrin, which cleaves DNA in the presence of metal ions, are discussed.     

Formation of dimers that contain unbridged W(IV)/W(IV) double bonds

A tungsten neopentylidene complex has been found to decompose to yield a heterochiral dimer that contains a W=W double bond and no bridging ligands. Decompositions of related bisalkoxide complexes also yield compounds that contain an "unsupported" W=W double bond, while a sample of [Mo(NAr)(CH2-t-Bu)(OC6F5)]2 has been found to be a homochiral species related to [W(NAr)(CH2-t-Bu)(OC6F5)]2.     

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.