The dependence of the sixth equation of Painlevé on its four parameters (2α,−2β, 2γ, 1− 2δ) = (θ ∞ , θ 0 , θ 2 1 , θ 2 x) is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar “Lax” pair of Fuchs, but the second order matrix Lax pair of Jimbo and Miwa presents a meromorphic dependence on θ∞ (and a holomorphic dep...

By regarding the classical non abelian cohomology of groups from a 2-dimensional categorical viewpoint, we are led to a non abelian cohomology of groupoids which continues to satisfy classification, interpretation and representation theorems generalizing the classical ones. This categorical approach is based on the fact that if groups are regarded as categories, then, on the one hand, crossed m...

The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a wellknown Lax representation – the three-particle open Toda lattice – is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certai...

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian ...

The ability of lymphokine-activatedkiller (LAK) cells to mediate antibody-dependent cellular cytotoxicity and its efficacy against a LAX resistant tumor were investigated. Cells ofthe MH134 murine hepatoma line are scarcely lysed by LAX cells generated in vitro by incubatiOn of G3H/HeN mousespleen cells with humanrecombinantinterleukin2 (rIL 2). However, the splenic LAX cells potently lysed the...