4.9 Conclusions

The processes are distributions of the attribute variations of some objects, on different support ranges (temporal, spatial, frequencial etc.), which means that they are derived distributions.
Any process may be decomposed into specific processes, which in their turn, are made-up from concatenated SEP series.
SEP consist of a finite variation of a single attribute, distributed on an elementary support interval, which means that it is an element of derived distribution of that attribute.
The finite difference rank of the attribute variation (and of the derived distribution as well) is also a SEP rank.
The invariant density of the distribution of a SEP of rank n on its support interval is an abstract object from class S_n (n=1, 2,…), but also other invariant attributes of P_nprocess existing on the same support interval may belong to the state S_n (such as the direction for translation, or the axis and the plane of the trajectory for revolution motion).
SEP, regardless of their rank are represented by means of vectors.
The processes with an invariant internal temporal distribution, concatenated into series against a common external temporal reference make-up the class of periodical processes (cyclical, repetitive).
The motion processes may be either translation or rotation movements (inner and outer). An elementary revolution motion (in case of a simplified 2D space included into the revolution plane) may be decomposed into two elementary translations which are perpendicular one another (the common and specific component of the current SEP against the previous SEP).
The sets of SEP which have a common external reference and which mutually deploy dependent invariant relations (which make-up a compound abstract object), may have common and specific components against this common component.

Comment 4.9.1: In the following chapters, we shall see that the statement from the point 9 is a very important one. If we are dealing with a set of spatially distributed motion-type SEP, that is a vector field, this field is able or not, to have a common vectorial component; in this way, we could determine if that field has or does not have a global motion (overall motion). If there is an overall motion, the vectorial common component shall be non-null; if this component is null, the field is motionless (see annex X.17).

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