The higher moments of GFF (in the

generalized function sense) are

9 it follows that each

generalized function f [member of] [H'.

By introducing a higher

generalized function to the imaginary part of the response function, causality and the f-sum rule become more tightly linked.

In section 4 we give a mild generalization of this mock theta function and show this

generalized function belongs to the family of [F.

With the help of this function we can define the Laplace transform L of a

generalized function [PHI] [member of] [F's.

Finally, as for the usual Dirac delta as a

generalized function, we show how to express a mean geometric density [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in terms of a suitable approximating sequence of classical functions.

0, m](0, [alpha], q) is the partial

generalized function.

is a n-dimensional

generalized function, v > 0 a real constant, t [member of] [0,[infinity]) the time parameter, x = ([x.

In Section 3 we will study this equation with an initial condition and show that the unique solution is a

generalized function.

The

generalized function is one of the most important branches of mathematics, says Rahman (mathematics, Dalhousie U.

Among the topics are quantifying soil-root interactions, nitrogen management effects of root systems, characterizing root length density distribution in wheat using a

generalized function, modeling Lolium perenne L.

Farassat, Introduction to

generalized functions with applications in aerodynamics and aeroacoustics, NASA Technical Paper 3428, (1996), 1-45.