The non-linear relation imposed by gauge invariance on the thermal self-energy of gluons, has been recently discussed by Weldon in an interesting paper [1]. He proved that in QCD, the Slavnov-Taylor identities [2,3] require a non-linear constraint among the structure functions which occur at finite temperature. In this brief report, we show that a similar behavior occurs in the gauge theory of ...

We point out a set of operator identities that relate the operators corresponding to the oblique corrections to operators that modify fermion couplings to the gauge bosons as well as operators that modify triple gauge boson couplings. Such identities are simple consequences of the equations of motion. Therefore the contributions from new physics to the oblique parameters can be disguised as mod...

Torsion free connections and a notion of curvature are introduced on the in-nite dimensional nonlinear connguration space ? of a Riemannian manifold M under a Poisson measure. This allows to state identities of Weitzenbb ock type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a non-trivial geometry, a de Rham-Hodge-Kod...

By means of a Picone’s type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.

Perfect reconstruction (PR) filter banks have found numerous applications, and have received much attention in the literature. For linear filter banks, necessary and sufficient conditions for PR have been established for most practical situations. Recently, nonlinear filter banks have been proposed for image coding applications. These filters are generally simple, and produce better results tha...

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...

Based on two higher-dimensional extensions of Lie algebras, three kinds of specific Lie algebras are introduced. Upon constructing proper loop algebras, six isospectral matrix spectral problems are presented and they yield nonlinear integrable couplings of the AblowitzKaup-Newell-Segur hierarchy, the Broer-Kaup hierarchy and the Kaup-Newell hierarchy. Especially, the reduced cases of the result...

We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the spectral transform (in general nonlinear and with non-analytic dispersion relations). The main theorem is that the compatiblity conditions gives always a tru...