In chapter 4, we have seen what are the definitions of an object’s state or of an even process, as well as the types of the processual states which are coming from this kind of definition. Based on these definitions, and on the fact that the assessment of each state type is made against a reference system, and on the fact that the object whose state is assessed may be a complex object, there are also other state classes which can be defined.

When we
have discussed about objects, we saw that their properties are
determined first of all against an internal reference system and in
this case, we are dealing with some *internal
properties.* All the properties of an
object are also determined against a reference which is outside the
object and that is why they are called *external
properties*. Let us remember the
definition 3.1.3 which was given to the notion of object: The object
is a finite and invariant set of qualitative attributes (properties),
with simultaneous, finite and invariant distributions, on the same
finite and invariant support domain, which are determined against a
common internal reference system. If the set of the attributes of an
object is made-up from *m*
properties, each element *x*_{k}
of the common support will be associated with *m*
values of the distributed attributes which are related to that
particular element by means of *m*
assignment relations.

According to the
definition 4.2.1, all the existing (distributed) invariant attributes
on an element *x*_{k}
of the common support, makes-up the abstract *state
*object at the value *x*_{k}
of that particular support. In chapter 2, we saw that the support
element may be a singular value, that is a case when we are dealing
with a primary distribution, or an elementary interval of values
(with an internal reference *x*_{k}),
and in this case we are dealing with a derived distribution (of a
primary distribution). In chapter 4, we saw that the state applicable
to a singular value of the support is a state *S*_{0}
(state of a primary distribution element), and the one which is
related to a support finite interval is a state *S*_{n},
where *n* is
the rank of the finite difference distributed on the elementary
interval
(state
of an element of derived distribution of rank *n*).

Because any of the
above-mentioned states, either *S*_{0}*
*or *S*_{n}
represents a set of properties belonging to a certain element of the
support attribute, all of these will be considered as * local
states* (specific either to the
support element

The evaluation
of the value of the local states attributes can be done, as we have
previously pointed out, against a reference system inside the object,
when we shall be dealing with * internal
*(local)

We were previously
saying that the local states are states *specific*
to a certain distribution element, either primary or derived
distribution which belong to an object. The *m*
distributions which belong to an object *Ob*
with *m*
qualitative properties in set, have a finite number of elements (for
the realizable distributions): the number of normal singular values
corresponding to the primary distributions, or the number of
elementary intervals in which the support is divided, concerning the
derived distributions. In chapter 3, we saw that the elements of a
distribution are elementary objects at the same time, therefore, the
object *Ob *is
an object composed from a set of elementary objects, each with its
own *m*
properties which are provided by means of the assignment relations.
Since all the properties of an elementary object are specific (local)
properties, they all have a common component, aspect which was
presented in chapter 3, the reference value against which these
properties are evaluated, that is a value which belongs to the
internal reference system of the object *Ob*.
We have also noticed in chapter 3 that this reference value valid for
an isolated object has a null value *(absolute
reference*), and for an object which
deploys relations with other external objects, its value shall be
established against an external reference, common to all the objects
which develop mutual relations, and it becomes a *relative
reference*. In this case, the set of
objects which deploy external relations makes-up a complex object,
the composition relations being created between the internal
reference systems of each constitutive object, and as a result of the
existence of such relations, each internal reference shall be
assigned with a non-zero value. But, this means that there is a set
of dependence relations deployed between the values of the internal
references of the constitutive objects and the external reference,
set which will make-up a new distribution, which represents the
complex object.

The total amount of
properties assigned to the internal RS of a complex object against
the external reference makes-up an external state of this RS, and
because that state is common to all the internal elements of the
complex object, it will be a * global
state* of this object.

As a conclusion, an
amount which is placed inside an invariant confined surface may be
characterized from two points of view -
*local* and
*global.*
The local characterization is given by the elements of the spatial
distribution of that amount inside the surface (mostly by their
density), and the global one is given by the integral of this
distribution (the total attribute amount distributed into the inner
volume, that is the attribute *stockpile*),
or by the internal RS of the distribution. As for the distributed
processes, the local characterization is made by SEP (the element of
Euler distribution), and the global one is given by the resultant of
the vectors’ distribution (which is also the result of an
integration).

Copyright © 2006-2011 Aurel Rusu. All rights reserved.