CONSTANCY AND INDEPENDENCE 24/19 



passes Hurwitz' test. Whatever the probability may be, it is 

 clearly equal to the probability of stability given by a system of 

 k similar full-functions. 



Conventions and symbols 



24/19. The relations between the various entities defined in this 

 chapter are here summarised for convenience of reference. 



(1) (In these four statements take the upper relation in the 

 braces in all, or the lower in all). 



(a) xA^ not independent of Xj 



(b) F k {. . . , x] + A4 . . . ; ojljlW • • ' X °P • • ' ' ') ; 



a 



(d) The integral matrix has i -^ j> at the {kj)-th position 

 (2) The (hi)-th position is in the h-th row and ^-th column : 



en) (12) (is) . . r 



(21) (22) (23) . . . 



(c)— F k {x° v . . ., x° n ; 0| + 



(3) The differential matrix has <^ j> at (pq) as df p /dx q { i ^0 



„ integral „ „ ,, „ ,, „ dF p /dx q ,, „ 



(4) The following correspond : 



(a) In the diagram of immediate effects : x r — ► x s ; 



(b) In the canonical equations : f 8 (. . . , av, . . .) ; 



(c) In the differential matrix : an J? at the (sr)-th position. 



(5) If sets A and B include all the variables, and if deletion 

 from the integral matrix of : 



columns A and rows B leaves all zeros, and 

 columns B and rows A leaves not all zeros, 

 then A dominates B. 



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