Results 61 to 70 of about 8,235 (175)

On Finite Exceptional Orthogonal Polynomial Sequences Composed of Rational Darboux Transforms of Romanovski-Jacobi Polynomials

Axioms
The paper presents the united analysis of the finite exceptional orthogonal polynomial (EOP) sequences composed of rational Darboux transforms of Romanovski-Jacobi polynomials.
Gregory Natanson
doaj   +1 more source

Christoffel–Darboux Type Identities for the Independence Polynomial [PDF]

Combinatorics, Probability and Computing, 2018
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 Chudnovsky and Seymour, which states that the independence polynomial of a claw-free graph has only real roots. Another application is related to a conjecture of Merrifield and Simmons.
openaire   +2 more sources

Numerical and Analytical Investigation of the Ablowitz–Ladik and Salerno Models: Closeness to Cubic and Cubic‐Quintic Discrete Nonlinear Schrödinger Lattices

Studies in Applied Mathematics, Volume 155, Issue 6, December 2025.
ABSTRACT We study the closeness between the Ablowitz–Ladik, Salerno, and discrete nonlinear Schrödinger lattices in regimes of small coupling ε$\varepsilon$ and small energy norm ρ$\rho$. Two approaches are compared: direct estimates in physical variables and a transformation to canonical symplectic coordinates via Darboux variables.
Marco Calabrese, Tiziano Penati, Simone Paleari   +2 more
wiley   +1 more source

Polynomial and rational integrability of polynomial Hamiltonian systems

Electronic Journal of Differential Equations, 2012
Within the class of canonical polynomial Hamiltonian systems anti-symmetric under phase-space involutions, we generalize some results on the existence of Darboux polynomial and rational first integrals for "kinetic plus potential" systems to general ...
Jaume Llibre, Cristina Stoica, Claudia Valls   +2 more
doaj  

Darboux transformations for multivariate orthogonal polynomials

, 2015
In this version we have not only added two more bibliographic references but also performed major changes in Section 3 on poised sets. This was motivated by our recent finding that full column rank of the Vandermonde matrix is not only necessary but sufficient.
Ariznabarreta, Gerardo, Mañas, Manuel
openaire   +2 more sources

Floer theory for the variation operator of an isolated singularity

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae, Cheol‐Hyun Cho, Dongwook Choa, Wonbo Jeong   +3 more
wiley   +1 more source

Existence and orthogonality of stable envelopes for bow varieties

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3249-3306, November 2025.
Abstract Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. They are part of a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self‐contained introduction to cohomological stable envelopes of type A$A$
Catharina Stroppel, Till Wehrhan
wiley   +1 more source

Darboux Integrability Of the Biological System

Al-Rafidain Journal of Computer Sciences and Mathematics
In the given paper, we investigate the integrability of a mathematical model of a 3D biological system. Our results show that the system admits a polynomial first integrals for some parameters, an invariant algebraic surface with an exponential factor ...
Zakariya Hashem Ali, Ahmad Muhamad Husien   +1 more
doaj   +1 more source

On the integrability and dynamics of the Hide, Skeldon and Acheson differential system

Electronic Journal of Qualitative Theory of Differential Equations
The family of systems \begin{equation*} \dot{x}= x(y-1)-\beta z,\quad \dot{y}= \alpha (1-x^2)-\kappa y, \quad \dot{z}= x-\lambda z, \end{equation*} where $(x,y,z) \in \mathbb{R}^3$ and $\alpha$, $\beta$, $\kappa$, $\lambda$ are real parameters, was ...
Érika Diz-Pita, Jaume Llibre, M. Victoria Otero-Espinar, Claudia Valls   +3 more
doaj   +1 more source

Bispectral operators of prime order

, 2002
The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators.
Horozov, Emil
core   +2 more sources