Kaklamani, "Application of bicomplex
(quaternion) algebra to fundamental electromagnetics: a lower order alternative to the Helmholtz equation," IEEE Transactions on Antennas and Propagation, vol.
Xu, "Coherent source localization: Bicomplex
polarimetric smoothing with electromagnetic vector-sensors," IEEE Transactions on Aerospace and Electronic Systems, Vol.
In this case, only the bicomplex case is covered (it is a particular case, but sufficient for most of the applications of the BPL in Kenzo ), but the whole constructive path is included: effective and locally effective objects are worked together, producing an effective homology algorithm.
Rubio, Effective homology of bicomplexes, formalized in Coq, Theoretical Computer Science 412 (11) (2011), 962-970.
A key point is that this ring [S.sup.*.sub.[infinity]] [F,Y] is split into a bigraded variational bicomplex which provides Lagrangian theory in Grassmanngraded (even and odd) variables [1, 2, 9].
A DGR [O.sup.*.sub.[infinity]]Y is split into a variational bicomplex. Its cohomology provides the global first variational formula for Lagrangians and Euler-Lagrange operators of a Lagrangian formalism on a fibre bundle Y [1,16, 24, 25].
Pohjanpelto, "The cohomology of invariant variational bicomplexes
," Acta Applicandae Mathematicae, vol.