Results 31 to 40 of about 6,848 (171)
Binary Bell polynomials and Darboux covariant Lax pairs [PDF]
Glasgow Mathematical Journal, 2001 Hirota representations of soliton equations have proved very useful. They produced many of the known families of multisoliton solutions, and have often led to a disclosure of the underlying Lax systems and infinite sets of conserved quantities. A striking feature is the ease with which direct insight can be gained into the nature of the eigenvalue ...
Lambert, Franklin +2 more
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Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
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Finding non-polynomial positive invariants and lyapunov functions for polynomial systems through Darboux polynomials [PDF]
2014 American Control Conference, 2014 In this paper, we focus on finding positive invari-ants and Lyapunov functions to establish reachability and stability properties, respectively, of polynomial ordinary differential equations (ODEs). In general, the search for such functions is a hard problem.
Goubault, Eric +3 more
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Multi-indexed (q-)Racah Polynomials [PDF]
, 2012 As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials.
Andrews G E +24 more
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Integral of Legendre polynomials and its properties [PDF]
Mathematics and Computational SciencesThis paper is concerned with deriving a new system of orthogonal polynomials whose inflection points coincide with their interior roots, primitives of Legendre polynomials.
Abdelhamid Rehouma
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Divergence-free polynomial derivations [PDF]
, 2017 In this paper we present some new and old properties of divergences and divergence-free ...
Nowicki, Andrzej
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Dual Szegö pairs of sequences of rational matrix-valued functions
International Journal of Mathematics and Mathematical Sciences, 2006 We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices.
Andreas Lasarow
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Uniform treatment of Darboux’s method and the Heisenberg polynomials [PDF]
Proceedings of the American Mathematical Society, 2013 We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux's method.
Liu, Sai-Yu, Wong, R., Zhao, Yu-Qiu
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Darboux transformation of symmetric Jacobi matrices and Toda lattices
Frontiers in Applied Mathematics and StatisticsLet J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
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On algebraic integrals of a differential equation
Discrete and Continuous Models and Applied Computational Science, 2019 We consider the problem of integrating a given differential equation in algebraic functions, which arose together with the integral calculus, but still is not completely resolved in finite form.
Mikhail D Malykh +2 more
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