We present here the explicit parametric solutions of second order differential equations
invariant under time translation and rescaling and third order differential equations
invariant under time translation and the two homogeneity symmetries. The computtion of first integrals gives in the most general...
The singularity analysis is carried out for a system of four first-order quadratic ODEs
with a parameter, which was proposed recently by Golubchik and Sokolov. A transfomation of dependent variables is revealed by the analysis, after which the transformed
system possesses the Painlevé property and...
Among simple Z-graded Lie superalgebras of polynomial growth, there are several
which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element
C2: these are the Lie superalgebra kL
(1|6) of vector fields on the (1|6)-dimensional
supercircle preserving the contact form, and the...
Let A be an associative simple (central) superalgebra over C and L an invariant
linear functional on it (trace). Let a at
be an antiautomorphism of A such that
a, where p(a) is the parity of a, and let L(at
) = L(a). Then A admits
a nondegenerate supersymmetric invariant bilinear...
This is the second part of a series of papers dealing with an extensive class of anlytic difference operators admitting reflectionless eigenfunctions. In the first part, the
pertinent difference operators and their reflectionless eigenfunctions are constructed
from given "spectral data", in analogy...
We obtain the collection of symmetric and symplectic matrix integrals and the colletion of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke,
as specific elements in the Spin-group orbit of the vacuum vector of a fermionic Fock
space. This fermionic Fock space is the same...