Results 91 to 100 of about 8,235 (175)

Spectral analysis for the exceptional Xm-Jacobi equation

Electronic Journal of Differential Equations, 2015
We provide the mathematical foundation for the $X_m$-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional $X_m$-Jacobi orthogonal polynomials as eigenfunctions.
Constanze Liaw, Lance Littlejohn, Jessica Stewart Kelly   +2 more
doaj  

Factorization of Dual Quaternion Polynomials Without Study's Condition. [PDF]

Adv Appl Clifford Algebr, 2021
Siegele J, Pfurner M, Schröcker HP.
europepmc   +1 more source

Derivations on Polynomial Rings and the Darboux Polynomials [PDF]

Revista Ciencias Exatas e Naturais, 2017
Wálmisson Régis de Almeida, Marcelo Oliveira Veloso   +1 more
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Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system. [PDF]

Open Res Eur, 2021
Constantinescu D, Tigan G, Zhang X.
europepmc   +1 more source

Christoffel-Darboux type identities for independence polynomial

, 2014
In this paper we introduce some Christoffel-Darboux type identities for independence polynomials. As an application, we give a new proof of a theorem of M. Chudnovsky and P. Seymour, claiming that the independence polynomial of a claw-free graph has only real roots. Another application is related to a conjecture of Merrifield and Simmons.
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Efficient Nyström-type method for the solution of highly oscillatory Volterra integral equations of the second kind. [PDF]

PLoS One, 2023
Wu Q, Sun M.
europepmc   +1 more source

Darboux equivalence for matrix-valued orthogonal polynomials

In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see when and how any given sequence of polynomials is Darboux related to a diagonal matrix of classic orthogonal ...
Parisi, Ignacio Bono, Pacharoni, Inés, Zurrián, Ignacio   +2 more
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Automated Reasoning For The Existence Of Darboux Polynomials

Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation
Given a polynomial ordinary differential equation (ODE), we devise generic polynomial reduction algorithms to automatically investigate the intertwined relationship between the total degree of (nontrivial) Darboux polynomials and the polynomials defining the ODE.
Ghorbal, Khalil, Bridoux, Maxime
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Hypergraphs and Lotka-Volterra Systems with Linear Darboux Polynomials

Journal of Dynamics and Differential Equations
Abstract We associate parametric classes of n-component Lotka-Volterra systems which admit k additional linear Darboux polynomials, with admissible loopless hypergraphs of order n and size k. We study the equivalence relation on admissible hypergraphs induced by linear transformations of the associated LV-systems, for
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On Computation of Darboux Polynomials for Full Toda Lattice

Communications in Nonlinear Science and Numerical Simulation
One of the oldest methods for computing invariants of ordinary differential equations is tested using the full Toda lattice model. We show that the standard method of undetermined coefficients and modern symbolic algebra tools together with sufficient computing power allow to compute Darboux invariants without any additional information.
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