We study the action of Hamiltonian diffeomorphisms a compact symplectic manifold ($X,\omega$) on $C^\infty(X)$ and functions $C^\infty(X)\to \mathbb R$. describe various properties invariant convex $C^\infty(X)$. Among other things we show that continuous R$ are under automatically so called strict rearrangements they in sup norm topology $C^\infty(X)$; but this is not generally true if convexi...

We investigate the effect of Z2 magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental adjoint SU(2) lattice gauge theory. In the limit of complete suppression of the Z2 monopoles, the mixed action for the SU(2) theory in its Villain form is shown to be self-dual under the exchange of the fundamental and adjoint couplings. By further suppress...

Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply...

Abstract: A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem) to the standard action of sy...

Using the scattering transform for n order linear scalar operators, the Poisson bracket found by Gel’fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side. Action-angle variables are then constructed. Using this, complete integrability is demonstrated in the strong sense. Real action-angle variables are constructed in the self-ad...

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the q → 1 scaling limit of the braided adjoint action or R-commutator of q-Minkowski space on itself. We also describe the qdeformed conformal algebra in R-matrix form and its quasi-∗ structure.