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hep-th1996
Statistical Topology of Real Polynomials. I: Two Variables
George Khimshiashvili, Alexander Ushveridze
We investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradien…
hep-th1996
Bender-Dunne Orthogonal Polynomials and Quasi-Exact Solvability
A. Krajewska, A. Ushveridze, Z. Walczak
The paper is devoted to the further study of the remarkable classes of orthogonal polynomials recently discovered by Bender and Dunne. We show that these polynomials can be generat…
hep-th1996
On the Duality of Quasi-Exactly Solvable Problems
A. Krajewska, A. Ushveridze, Z. Walczak
It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the si…