From nonassociativity to solutions of the KP hierarchy

A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with A' a matrix algebra, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and Quantum Symmetries', Prague, 15-17 June 200

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5

An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the noncommutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the noncommutative KP hierarchy. Relations with Rota-Baxter algebras are established.Comment: 59 pages, relative to the second version a few minor corrections, but quite a lot of amendments, to appear in J. Phys.

Cytochrome P450-mediated metabolism of N-(2-methoxyphenyl)-hydroxylamine, a human metabolite of the environmental pollutants and carcinogens o-anisidine and o-nitroanisole

N-(2-methoxyphenyl)hydroxylamine is a human metabolite of the industrial and environmental pollutants and bladder carcinogens 2-methoxyaniline (o-anisidine) and 2-methoxynitrobenzene (o-nitroanisole). Here, we investigated the ability of hepatic microsomes from rat and rabbit to metabolize this reactive compound. We found that N-(2-methoxyphenyl)hydroxylamine is metabolized by microsomes of both species mainly to o-aminophenol and a parent carcinogen, o-anisidine, whereas 2-methoxynitrosobenzene (o-nitrosoanisole) is formed as a minor metabolite. Another N-(2-methoxyphenyl)hydroxylamine metabolite, the exact structure of which has not been identified as yet, was generated by hepatic microsomes of rabbits, but its formation by those of rats was negligible. To evaluate the role of rat hepatic microsomal cytochromes P450 (CYP) in N-(2-methoxyphenyl)hydroxylamine metabolism, we investigated the modulation of its metabolism by specific inducers of these enzymes. The results of this study show that rat hepatic CYPs of a 1A subfamily and, to a lesser extent those of a 2B subfamily, catalyze N-(2-methoxyphenyl)hydroxylamine conversion to form both its reductive metabolite, o-anisidine, and o-aminophenol. CYP2E1 is the most efficient enzyme catalyzing conversion of N-(2-methoxyphenyl)hydroxylamine to o-aminophenol