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The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P, L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In(More)
We study the connections between Gelfand–Dickey (GD) systems and their modified counterparts , the Drinfeld–Sokolov (DS) systems in the case of general matrix–valued coefficients with entries in a commutative algebra over an arbitrary field. Our main results describe auto–Bäcklund transformations for the GD hierarchy based on Miura–type transformations(More)
A rapid procedure for the defined isolation and characterization of single bovine chromosome fragment specific probes is described. This has been developed as a technical prerequisite for the directed generation of bovine DNA sequences. The specific regions lql3–24, 5q21–24, 6q31–32, 7q21–22, 12q24-ter, and 20ql2-ter of bovine GTG-banded metaphase(More)
In this paper two classical theorems by Levinson and Marchenko for the inverse problem of the Schrödinger equation on a compact interval are extended to finite trees. Specifically, (1) the Dirichlet eigenvalues and the Neumann data of the eigenfunctions determine the potential uniquely (a Levinson-type result) and (2) the Dirichlet eigenvalues and a set of(More)
If the differential expressions P and L are polynomials (over C) of another differential expression they will obviously commute. To have a P which does not arise in this way but satisfies [P, L] = 0 is rare. Yet the question of when it happens has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P, L). In(More)