In many systems, the tensors used to describe physical properties must acquire their structure from one vector. Knowledge of that fact alone leads to an interesting line of analysis for such systems. The analysis begins with a discussion of the types of dyadics that can be constructed from one vector. Attention is focused on certain exemplary dyadic operators, which, because of their geometrical properties, would appear particularly basic; the algebra of these dyadics is developed in detail. The algebra is then (...) used in a derivation of the expansion of general functions of these dyadics. Several applications of the general expansion are presented: the inverse of a general dyadic operator (when it exists), a general rotation operator that includes strains and reflections, the determinant of a general dyadic operator, and operators, including some new ones, used in constructing Lorentz boosts. Finally, a coordinate-free representation of the Levi-Civita tensor is provided. (shrink)

The coordinate-free methods of the preceding paper are illustrated in three problems. First, the electrodynamics of a homogeneous, isotropic, and gyrotropic medium is investigated; it is shown that such a medium can exhibit optical activity, and the propagation of a plane electromagnetic wave in such a medium is discussed. Then, the electrodynamics of a homogeneous system made anisotropic by a uniform external magnetic field is considered; a description of Faraday rotation is provided, the ionosphere being used in an example. Finally, (...) the reflection and refraction of a plane electromagnetic wave at the interface of two media are described by coordinate-free operators. (shrink)

Stone, J. Thoughts on supposed "Death of law".--Krishna Iyer, V. R. Jurisprudence and jurisconscience.--Sharma, G. S. Law and social change in India.--Sharma, S. D. The concept of justice in Manu.--Chand, H. Legal values for a developing country.--Ramarao, T. S. The new international law relating to the rights and duties of States.--Sinha, B. S. Custom and customary law in Indian jurisprudence.--Mazumdar, D. L. Techno-economic structure of our industrial society.--Subrahamanian, N. Law and social change.