The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal-helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that, while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the ajoint SU(N(c)) matter it survives the conformal symmetry...

Applied researchers often work with demand systems that do not depend on income, with the implicit assumption that preferences are quasi-linear and income sufficiently large. The classic approach to the integrability of demand does not readily apply in this case. Adopting a much simpler approach that is based on Poincaré’s Lemma and duality, we provide necessary and sufficient conditions for th...

We investigate how the integrability conditions for conformal anomalies constrain the form of the effective action in even-dimensional quantum geometry. We show that the effective action of four-dimensional quantum geometry (4DQG) satisfying integrability has a manifestly diffeomorphism invariant and regularization scheme-independent form. We then generalize the arguments to six dimensions and ...

Abstract: In this paper we investigate the complete integrability of the system of six coupled nonlinear ODEs, which arises in the ODE reduction of rotating stratified Boussinesq equations. We use Painlevé test to investigate the complete integrability of the system. And we conclude that the system is completely integrable only if the Rayleigh number Ra = 0. The singular solution of the system ...

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is shown that if the perturbed harmonic oscillator with a homogeneous cubic-polynomial potential and the perturbed harmonic oscillator with a hom...