# Magnitosphere law spectra 1996 by Milovanov By Milovanov

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As P, ... e. it must be we asserted. Pn to the In particular (3). P P ^} **&gt; are the it P * P ) U ^2 &gt; coefficients Having found all may to )t "i J semi -canonical form, and of their derivatives, of the of the seminvariants We same function of the from (1) by a trans must therefore be equal a function of these quantities the semi-covariants. ) differential equation obtained formation of the form / must be equal It -Pn . -, we proceed to determine confine our attention to semi-co variants 1 th which contain no higher derivatives of y than the n For, if (n+1) a semi -co variant contains yM, y etc.

65) shows that zf(y} In every case, for arbitrary functions y and an exact derivative, s. This property is characteristic of the Lagrange adjoint expression, as such the left member of the Lagrange adjoint equation. we denote if In other words, if, for all possible functions y an exact derivative, where is of the nih order of f(y), i- in 2, cp(/) is &lt;JP(#) mnst where (y, #) is a from (65) we find i/; . /, ^ \) \tS By 0. / subtraction ^)// . the derivative of the right member would be a linear function derivatives of s multiplied into y.

Pn to the In particular (3). P P ^} **&gt; are the it P * P ) U ^2 &gt; coefficients Having found all may to )t "i J semi -canonical form, and of their derivatives, of the of the seminvariants We same function of the from (1) by a trans must therefore be equal a function of these quantities the semi-covariants. ) differential equation obtained formation of the form / must be equal It -Pn . -, we proceed to determine confine our attention to semi-co variants 1 th which contain no higher derivatives of y than the n For, if (n+1) a semi -co variant contains yM, y etc.