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According to the objectual philosophy, a modification occurs in the definition of the elementariness concept (of an object or process), which means that the elementariness as an attribute and abstract object must have the two components, respectively, the qualitative and quantitative component. Qualitatively speaking, the elementariness of an abstract object is provided by means of the existence of a single qualitative property (the set of the distributed attributes contains a single element). Quantitatively, the same elementariness is provided by the existence of an indivisible quantity (non-decomposable) from the elementary qualitative attribute. From the point of view of the distributions, the quantitative elementariness of an assigned attribute is related to the distribution element.
As for the primary distributions, the distribution element is a singular value (virtual or normal) of the distributed attribute, assigned to a singular value (a virtual or normal too) of the support attribute, by means of a local relation. Depending on the distribution class (virtual or realizable), the two values have a non determination interval (null for the virtual distributions and DP-type for the realizable ones.
In case of the derived distributions, the distribution element is made-up as a result of an elementary variation (of a certain rank) of the distributed attribute, assigned to an elementary variation of the support attribute, through a local relation. Here, the processual quantitative elementariness intervenes, which means that a non-decomposable variation is imposed (as magnitude) for the two variations (mostly for the support one) which makes-up the element of the derived distribution, but which also allows the existence of a non-null process. The definition manner of this elementary variation is different for the two distribution types, one currently used by mathematicians, and the other used by the objectual philosophy. As for the classic derived distributions (the ones used in mathematics), the elementary variation is defined as a limit of a process which implies the amount decrease towards zero, whereas in case of the systemic derived distributions, the quantitative elementariness is provided only with the condition that the previous distribution (in terms of rank) of the dependent attribute on the elementary support interval to be considered as linear, so that its density to be evenly distributed.
Due to such a definition of the elementariness, mostly in case of the processes (whose model abstract objects are the derived distributions), it is possible the unified approach of all the vector classes (SEP), including of the position vectors, which according to a classic quantitative approach, do not belong to the class of the elementary processes (their variation being unlimited in terms of magnitude), but which are elementary in terms of quality, due to the fact they have the spatial density (direction) evenly distributed on the support domain.
Copyright © 2006-2011 Aurel Rusu. All rights reserved.
