Recent results on the generalized Kadomtsev-Petviashvili equations

We survey some recent results concerning the generalized Kadomtsev-Petviashvili equations, which are natural extensions of KdV type equations to higher dimensions. We will focus on rigorous results of the Cauchy problem and on the existence and properties of localized solitary waves.     

Combined Designs and Labour Programming

In this paper, the problem of labour scheduling is solved using Combinatorial analysis with Combined designs; characteristic applications to scheduling industrial labour, itinerary distribution and supervision are given.     

Polyimidines: A new class of polymers. III. A comparison of isomers of polypyromellitimidines

The cis (3,3,5,5-), trans (3,3,7,7-), oxo, and thio analogs of tetraphenylpyromellitide were polymerized with 1, 6-hexane diamine, p-phenylene diamine, and p,p'-diaminodiphenyl ether under various conditions. A comparison was then made of reactivity of the isomers and of the properties of the polymers. In general the thio monomers were more soluble and reactive than the oxo. They also gave more thermally stable polymers. The cis isomers of the monomers were more soluble than the trans, but the trans were more reactive. The least stable of the 12 polymers prepared was that from the cis–oxo monomer and 1,6-hexane diamine. It gave a 10% weight loss at 300°C in air and 340°C in nitrogen by TGA. The most stable polymer was from the reaction of the cis–thio pyromellitide with p,p'-diaminodiphenyl ether, which showed 10% weight losses by TGA at 560 and 650°C in air and nitrogen, respectively. The polymers were stable in hot dilute hydrochloric acid and sodium hydroxide. They were all soluble in chloroform, dimethylformamide, and sulfuric acid. Polymers that contained sulfur were also soluble in carbon tetrachloride, benzene, xylene, and toluene. Brittle films could be cast from solution or melt-pressed.     

Robust polarization-based quantum key distribution over a collective-noise channel

We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting to interferometry or two-way quantum communication, thereby circumventing, respectively, the need for high precision timing and the threat of Trojan horse attacks.     

Hyperbolicity and change of type in the flow of viscoelastic fluids

The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.Dedicated to Walter Noll on the Occasion of his 60^th Birthday     

Frequency response of a cold-wire in a flow seeded with oil particles

Experiments have been carried out to investigate the effects of aging on the frequency response of a fine cold-wire located in a flow seeded with oil particles used for laser Doppler anemometry. Transfer functions are shown to depend strongly on the running time. Photo-micrographs show that the contamination effect is due to discrete droplets, the diameter of which increases with running time. Reduction of frequency response is shown to affect at first the high-frequency range and then an intermediate range of frequencies that are larger than the inverse of the oil droplets time constant. Good agreement is found between experimental results and predictions derived from a simple model of the contaminated wire. This contamination process requires testing and cleaning the wire steadily in order to keep a significant frequency response and, if needed, to correct temperature fluctuations.