In this paper we represent harmonic moments in the language of transfinite functions, that is projective limits of polynomials in infinitely many variables. We obtain also an explicit formula for the Jacobian of a generalized harmonic moment map. Mathematics Subject Classification (2000). 13B35; 30E05; 47A57.

In order to study the ”problem of time”, Rovelli proposed a model of a two harmonic oscillator system where one of the oscillators can be thought of as a ’clock’ for the other oscillator. In this paper we examine a model where the Hamiltonian is a difference between two harmonic oscillators, and we consider one of them which has the minus sign as a ’clock’. Klauder’s projection operator approac...

This is the third part of our project initiated in [LW1] on the study of the weakly convergent sequence of smooth (or certain classes of weak) solutions to the heat equation of harmonic maps or approximated harmonic maps (i.e. the negative gradient ow of the generalized Ginzburg-Landau functionals). The general situation for the heat ow of harmonic maps is as follows. Let un(x; t) : M R+ ! N be...

We present summation identities for generalized harmonic numbers, which generalize reciprocity laws discovered when studying the algorithm quickselect. Furthermore, we demonstrate how the computer algebra system Sigma can be used in order to find/prove such identities. We also discuss alternating harmonic sums, as well as limiting relations.