The higher arithmetic (5th ed.), by H. Davenport. Pp 189. £12 hard covers, £5 paperback. 1982. ISBN 0 521 24422 6/28678 6 (Cambridge University Press)

Degree of polarization and the principal idempotents of the coherency matrix

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.

n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

Exponential versions of the Jones and Mueller–Jones matrices are derived by use of the theory of semigroup transformations in conjunction with Kronecker products of matrices.

Exponential versions of the Jones and Mueller–Jones polarization matrices

Transient processes important to understanding technical change are modeled using a time-varying version of the Sequential Interindustry Model, SIM. A simple process of technical change is explored, where a new production technique replaces an old one for one of an industry's production processes. Using several measures internal and external to the industry the model can help in understanding the complex processes of technical change, point to difficulties in their analysis, and suggest guidance to further examinations.



An earlier version of this paper was presented at the Eighth International Conference on Input-Output Techniques, Sapporo, Japan, July 1986.

Herbert L. Fox

Papers

Trace orthogonal hermitian basis matrices of arbitrary dimension

Dynamics of structural change