Displaying similar documents to “From recursions to asymptotics: On Szekeres' formula for the number of partitions.”

The moving frames for differential equations. II. Underdetermined and functional equations

Václav Tryhuk, Oldřich Dlouhý (2004)

Archivum Mathematicum

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Continuing the idea of Part I, we deal with more involved pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = L ( x ) y , z ¯ = M ( x ) z , ... applied to the first order differential equations including the underdetermined case (i.e. the Monge equation y ' = f ( x , y , z , z ' ) ) and certain differential equations with deviation (if z = y ( ξ ( x ) ) is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction...

The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension

Anatoliy Samoilenko, Yarema Prykarpatsky, Anatoliy Prykarpatsky (2005)

Open Mathematics

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The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.