2.7 Conclusions

The meaning of the distribution concept used across this paper is not much more different as compared to the dictionary meaning, namely: allotment, division of a property (attribute) to some elements belonging to a set of objects which may own that property (see also the annexes X.2 and X.3). Taking into account the above-mentioned issues, there are few conclusions to retain:

1. A distribution is an abstract object made-up from a set of assignment relations of a property, on the objects of a support set. There is a strict, univocal correspondence between the two sets, each support object (which corresponds to an AAV in case of virtual distributions) must be related to an assignment relation and a value of the distributed attribute (even if this latter value is null).

2. If the assignment relation has the same form (invariant structure) for the entire support domain, that particular relation is the classic continuous function from mathematics field.

3. The distribution inside a distribution element of an allotted property is an elementary distribution (either it is even in case of the realizable primary distributions, or linear, in case of realizable derived distributions). For such an element, a distribution density is defined as a ratio between the variation of the distributed attribute which comes from the assignment relation and the variation (amount) of the support (we shall see in the next chapter that the values implied in the primary distribution element are also variations, but variations against an absolute reference).

4. Any type of uneven distribution is decomposable in elementary distributions, evenly or evenly variable.

5. The virtual distributions (from mathematics) are the asymptotic models (virtual objects toward which the realizable objects tend to) of the realizable distributions. Only for this type of distributions, the infinite, continuous support domains or AAV singular support values are allowed.

Comment 2.7.1: The fact that the distributions have a higher generality level, as compared to the classic mathematical functions, this also provides a higher generality degree to the theoretical papers which are dealing with distributions. According to the current physics and chemistry (based almost entirely on functions), the properties of the studied objects are divided in two categories: extensive and intensive properties. The value of the extensive properties depends on the size of the object which owns the property, and the intensive ones are independent from these sizes. For example, the volume of a body, the number of elements (atoms or molecules) of the body, its total mass and energy are extensive properties, while the mass density, temperature, pressure, are intensive properties. By using the distributions, we may observe that the extensive properties are distributions or stocks of some distributions, while the intensive properties are inner references or densities of some distributions.

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INDEX

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