Where w _ n ( n = 1, 2, & ) are weight coefficients reflecting the confidence on individual resonance measurements.
2.
Where ? 0 corresponds to the intercept or the probability of a response when M and G are equal to 0 with remaining ? s corresponding to weight coefficients for each independent variable.
3.
If " V " is spanned by monomials in the positive weight coefficients of the fields ( i . e ., finite products of operators " J " a n applied to 1, where " n " is negative ), then we may write the operator product of such a monomial as a normally ordered product of divided power derivatives of fields ( here, normal ordering means polar terms on the left are moved to the right ).
4.
Rods ( bacteria that have the shape of a rod and grow in length, but not in diameter ) are a "'static mixture "'between a V0-and a V1-morph, where the caps act as V0-morphs and the cylinder between the caps as V1-morph . The mixture is called static because the weight coefficients of the contributions of the V0-and V1-morph terms in the shape correction function are constant during growth.
5.
Crusts, such as lichens that grow on a solid substrate, are a "'dynamic mixture "'between a V0-and a V1-morph, where the inner part acts as V0-morph, and the outer annulus as V1-morph . The mixture is called dynamic because the weight coefficients of the contributions of the V0-and V1-morph terms in the shape correction function change during growth . The Dynamic Energy Budget theory explains why the diameter of crusts grow linearly in time at constant substrate availability.
6.
More generally, if one is given a vector space " V " with an endomorphism " T " and vector 1, and one assigns to a set of vectors " J " a a set of fields " J " a ( " z " ) " End ( " V " ) " z " ? that are mutually local, whose positive weight coefficients generate " V ", and that satisfy the identity and translation conditions, then the previous formula describes a vertex algebra structure.
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