Note on 'N-pseudoreductions' of the KP hierarchy

The group-theoretical side of N-pseudoreductions is discussed. The resulting equations are shown to be easy transformations of the N-KdV hierarch

Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere

We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials

<i>Caviziphius altirostris</i>, a new beaked whale from the Miocene southern North Sea basin

An odontocete cranium from Miocene deposits in northern Belgium is examined and referred to Caviziphius altirostris, a new genus and species of beaked whale. In the general architecture of its vertex and closed mesorostral canal, Caviziphius resembles the fossil genera Ziphirostrum and Choneziphius, but differs from all known ziphiids by a very deep excavated prenarial basin with a semicircular outline in lateral view. This peculiar cranial architecture of Caviziphius might indicate an advanced and efficient mechanism of sound production in this fossil ziphiid

Preparation, testing, and delivery of low density polyimide foam panels

Plastic foams based on polyimide resins were shown to be stable at relatively high temperatures, and to possess very low flame spread and smoke generation characteristics. A system and process were developed to prepare low-density polyimide foam from a liquid formulation. The system is based on the reaction of micropulverized grade pyromellitic dianhydride with a polymeric diisocyanate. The panels produced were postcured at elevated temperatures to achieve maximum thermal and fire resistance, and incorporation of a fire retardant into the formulation was considered. The effects of a flame retardant (Flameout 5600B1) were investigated, but eliminated in preference to the postcuring approach

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure