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[
]
=
[
]
()
()
()
m
l
()
Æ+
l
(
)
()
St
S t
DF
t
St
.
(12)
i
i
i
In this equation the function F relates the states
S
i
(m) in
e
i
that produce a
transition in
e
j
from
S
i
(l) to
S
i
(l¢). Consequently, F can be written in terms
of superscripts only:
(
)
l
¢=
F
ij
l m
,
.
(13)
In other words F relates the subsequent state of
e
j
to its present state and
to the present state of the acting element
e
i
. Take, for instance,
s
1
=
s
2
= 3;
a hypothetical transition matrix may read as follows:
m
l¢ = F (l, m) 123
1
132
l 2
123
3
112
The associated transition diagram is given in fig. 7, where the nodes repre-
sent the states of the reacting element, the arrows the transitions, and the
labels on the arrows the states of the acting element which causes the cor-
responding transition. Inspection of the transition matrix of an element
e
j
will tell us at once whether or not another element, say
e
i
, is actively con-
nected to
e
j
, because if there is not a single state in
e
i
that produces a state
change in
e
j
we must conclude that
e
i
does not have any effect on
e
j
. Again
for
s
1
=
s
2
= 3, the “transition” matrix for such an ineffective connection
looks as follows
m
l¢ = F (l, m) 123
1
111
l 2
222
3
333
FIGURE 7. State transition diagram.
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