18 research outputs found
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