By Norbert Wiener
A chain of lectures at the position of nonlinear strategies in physics, arithmetic, electric engineering, body structure, and verbal exchange theory.From the preface:"For a while i've been drawn to a bunch of phenomena based upon random methods. One the single hand, i've got recorded the random shot impression as a appropriate enter for checking out nonlinear circuits. nonetheless, for a few of the paintings that Professor W. A. Rosenblith and i've been doing in regards to the nature of the electroencephalogram, and specifically of the alpha rhythm, it has happened to me to exploit the version of a approach of random nonlinear oscillators considering a random input.... before everything we had reflected a chain of merely 4 or 5 lectures. My principles built pari passu with the path, and by way of the tip of the time period we stumbled on ourselves with a suite of fifteen lectures. the previous couple of of those have been dedicated to the applying of my principles to difficulties within the statistical mechanics of gases. This paintings is either new and tentative, and that i came upon that I needed to complement my direction via the writing over of those with assistance from Professer Y. W. Lee. "
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Additional resources for Nonlinear Problems in Random Theory (Technology Press Research Monographs)
Conceivably sequence stratigraphic data from many localities, used to create a continuous record of regional or global sea-level ﬂuctuations and assigned a time scale, would be amenable to analysis. However, the problem with such an approach has always been obtaining meaningful estimates of the amplitude of sea-level change, free of local tectonic factors, in tandem with a sufﬁciently reliable time scale. 2 Condition 2 – Unambiguous variable The variable recorded must have had an unambiguous relationship with some changing aspect of the environment.
As just explained, the rather ‘spiky’ nature of the time series, which results from this method of sampling, cannot be assumed to be free of aliasing (Fig. 8). 4 Sampling 37 Fig. 9 For most of the Belemnite Marls time series, each oscillation is deﬁned by many points. 3 m level both records take on a rather ‘spiky’ character suggesting that aliasing has occurred (cf. Fig. 8). irregularly spaced data. 3) to produce regularly spaced values, but interpolation of very ‘spiky’ data is unlikely to be successful.
The AM beat signal can only be preserved stratigraphically if there is at least partial rectiﬁcation of the carrier wave. For example, consider smoothing the AM signal shown in the middle panel. Ultimately increased smoothing would result in a straight line at the zero level. Hence smoothing of sediment composition, due to processes such as bioturbation, destroys the potential evidence for the annual cycle carrier wave. However, if there are processes causing rectiﬁcation (Fig. 3) then there can remain a record of the amplitude modulation (beat) frequency even after smoothing has destroyed the evidence for the annual cycle.