Abstract
It is shown that in using the Laplace transform one has to start with the condition that imposes f(0-) = 0 in order to avoid errors in the derivative and integral operations. In that case the matrix representation of the circuits using the Laplace transform becomes possible and the resolution of integral-differential equations is straightforward. Nevertheless, it is possible to use the Laplace transform with signals that have no null initial conditions, keeping the mathematical coherence, by choosing between two ways: (1) shifting the origin of time domains to the left to obtain the null initial conditions, and (2) using the superposition theorem to obtain one partial signal with null initial conditions.

Abstract
A scheme to frequency multiplex a group of sensors based on all-fiber Michelson interferometers is presented. Lead insensitivity is obtained by using the two fiber leads of the configuration as an extra Michelson interferometer whose differential phase is kept constant by active compensation. Topics concerning the system design, sensor sensitivity, and crosstalk between sensors are investigated. Experimental and numerical computational results are presented.

Abstract
The aim of this paper is to illustrate primarily the suitability and secondly the ability of both PHM and ‘two-sample’ tests in answering problems in the reliability field. The findings stress the fact that ‘two-sample’ tests should be preferred for comparison purposes and PHM for modelling the behaviour of the equipment in the presence of various factors. Copyright © 1991 John Wiley & Sons, Ltd.

Abstract
An online recursive algorithm for power system state estimation is presented which is based on the use of the Kalman filtering theory. The recursive form of the algorithm is advantageous in two ways: it permits the inversion of smaller-dimensioned matrices, which results in simpler algorithms, and it provides the opportunity to obtain a partially updated estimate in case the computer is heavily loaded in a given period and there is not enough time to perform a single batch processing of the measurement vector as a whole.

Abstract
A frequency domain analytic study of laser nonlinear distortion is presented, based on the Volterra nonlinear functional series. This analysis is shown to predict all the intermodulation products up to third order, of particular relevance to the design of subcarrier multiplexed systems, when the laser is modulated by an arbitrary number of channels. Illustrative analytic and simulation results are presented for two and three input subcarriers and are shown to match very closely.

Abstract
The theory of nonlinear systems based on frequency domain analysis using Volterra series is shown to provide an appropriate means of assessing laser distortion which includes the effects of laser resonance. Hence, it is an appropriate and tractable means of assessing the performance of optical subcarrier multiplexed (SCM) systems. Based on this analysis the performance of SCM systems is examined, with calculation of the carrier-to-intermodulation ratio for an eight-channel SCM system providing an illustrative example.