Results 61 to 70 of about 6,848 (171)

Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations [PDF]

Journal of Sciences, Islamic Republic of Iran, 2006
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i.
doaj  

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

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

Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices.
Hjalmar Rosengren
doaj  

High-Accuracy Spectral-like Legendre–Darboux Method for Initial Value Problems

Mathematics
A high-order single-step implicit method, the Legendre–Darboux Method of order six (LDM6), is introduced for solving both linear and nonlinear initial value problems.
Mohammad W. Alomari
doaj   +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

Detecting and determining preserved measures and integrals of rational maps

, 2020
In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra tools.
Celledoni, Elena, Evripidou, Charalambos, McLaren, David, Owren, Brynjulf, Quispel, Reinout, Tapley, Benjamin   +5 more
core  

Disturbance Dynamics and Its Effects on Carbon in Human‐Impacted Mountain Forests in Northwestern Yunnan, China

Ecology and Evolution, Volume 15, Issue 9, September 2025.
Identifying and quantifying natural and anthropogenic disturbances at fine spatial scales is critical to assess the role of forests in climate change mitigation. Using tree rings, fire scars, satellite imagery, official records, and interviews, we reconstructed historical disturbances and identified fires, logging events, landslides, and icy ...
Zhongqian Cheng, Tuomas Aakala, Chengjun Ji, Markku Larjavaara   +3 more
wiley   +1 more source