The mathematical models and methods of analysis of opposing forces, stemming from the original Lanchester equations are summarized in terms of two broad categories: (a) deterministic models, (b) stochastic models. The present limitations of previous methods are used to identify topics that require attention in the future.
Since the original formulation of Lanchester's equations pertaining to the combat of two opposing forces, the theory has been extended, organized and applied by many writers, including R. H. Brown, J. H. Engel, R. N. Snow, and H. K. Weiss. Certain more recent extensions of this theory, which have been developed under Project NUMERICS (Northeastern University Mathematical and Engineering Research in Complex Systems) will be described in this paper. The model considered is limited to only one kind of combat unit on each side, but operational losses, in general different for each of the two sides, are also included. Under these conditions, certain results were obtained in the following problems. (a) the total losses of the victor as a function of varying amounts of forces included, (b) prediction of outcome from initial performance, when the values of the various attrition rates are not known, (c) analog circuits simulating the performance of the model.
Instantaneous indication of the beginnings of individual pitch periods of a voice-sound speech wave is often desirable in speech analysis. With conventional means, such as linear filtering and subsequent waveform shaping, this instantaneous indication is very hard to achieve because of the considerable time delay involved.
In the “instantaneous” pitch-period indicator the problem is solved by using nonlinear techniques and a variable time-gating circuit; a pitch-period beginning is indicated by a marker pulse having a maximum delay of the order of five percent of the pitch-period duration. The application of the device to certain problems of speech analysis is indicated.
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