A synchronization is

generalized function projective synchronization, which is a more general definition of chaotic synchronization, it encompasses function projective synchronization.

qualifies as a representative for a random

generalized function.

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.

In higher dimensions we need to define it as a random

generalized function.

The gamma, generalized gamma, Weibull and another type of gamma incomplete distribution are obtained as particular cases of the density

generalized function.

A method based on the theory of the

generalized function of the Fourier transformation is used for solving the matrix equation (2) [1]:

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.

In many instances, the levels of the model include functional purpose (a description of system purposes), abstract function (a description of first principles and priorities),

generalized function (a description of processes), physical function (a description of equipment capabilities), and physical form (a description of physical characteristics such as size, shape, color, and location).