chain complex

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chain complex

[′chān ‚käm‚pleks]
(mathematics)
A sequence {Cn }, -∞ <>n < ∞,="" of="" abelian="" groups="" together="" with="" a="" sequence="" of="" boundary="" homomorphisms="">dn : CnCn-1such that dn-1° dn = 0 for each n.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
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 [10]), 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.