. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. THE ABSOLUTE SYSTEM 19/10 they should form a finite continuous (Lie) group of order one with t as parameter. (1) The system is assumed absolute. Let the initial state of the variables be x°, where the single symbol represents all n, and let time t' elapse so that x° changes to x'. With x' as initial x»—. Figure 19/10/1. state let time t" elapse so that x' changes to x". As the system is absolute, the same line of behaviour will be followed if the system starts at x° and goes on
. Design for a brain. Brain -- Physiology; Central nervous system -- Mathematical models; Neurophysiology. THE ABSOLUTE SYSTEM 19/10 they should form a finite continuous (Lie) group of order one with t as parameter. (1) The system is assumed absolute. Let the initial state of the variables be x°, where the single symbol represents all n, and let time t' elapse so that x° changes to x'. With x' as initial x»—. Figure 19/10/1. state let time t" elapse so that x' changes to x". As the system is absolute, the same line of behaviour will be followed if the system starts at x° and goes on for time f -f- t". So x- = Fi{xi . ., a£; t") = Fi(x°v . .,' x\; t' + t") (i = 1, . n) but Xi Fi{x°l9 ,o . n (* = i, ., n) giving FilF^x"; n • .» Fn(af>; t'); t"} = Fi{x°v . ., xQn; t' + n (i = 1, . ., n) for all values of x°, f and t" over some given region. The equation is known to be one way of defining a one-parameter finite con- tinuous group. (2) The group property is not, however, sufficient to ensure absoluteness. Thus consider x = (1 -f- t)x° ; the times do not combine by addition, which has just been shown to be necessary. Example : The system with lines of behaviour given by Xl = x\ + x\t -f Z21 Xo — Xo -f- "I J is absolute, but the system with lines given by xx = x\ + x\t + V is not. '2 — 2 ~" • 205. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Ashby, William Ross. New York : Wiley
Size: 2447px × 1021px
Photo credit: © Central Historic Books / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookpublishernewyorkwiley, booksubjectneurophys
