The Functional Synthesis of Linear Plots

Cover The Functional Synthesis of Linear Plots
The Functional Synthesis of Linear Plots
R F Dressler
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We may thus rewrite (13) as (2-) F = M^^^x^, X2, o.. , x^)exp N^^^(y^, 72^"*>yn^* VJhen we return to the original formulation of the problem in terms of the x's, y's and z's, it follows that the most j5:eneral functional form for F is £iven by (21) P = M^^^x^, X2, . O. , x^) exp N^^^(y-|_, y2*o. Oyp, In z-, In 23, ... , In z^), where M is a general multilinear function of the x's and N a general constant-free multilinear function of the y's and In z's, the coefficients in both being functions o...nly of the u ' s I 3, 5 SOME ELj5Mi:, i^TARY SKaIIPLSS As short illustrations of the general result (21), we now give a few examples where P has linear plots against just three variables. In each case \-ie list the specific form that (21) •'•. VV ' . J 8 assumes and the slopes and intercepts on the appropriate plots. By comparing the behavior of the slopes and intercepts in the various experimentally given families of curves that define the function P with these listed formulas, one can readily determine which coefficients vanish, if any, and thus obtain a specific formula for F in any actual case, Hsre "in" denotes a natural logarithm and "log" a coi.

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