Geoscience Reference
In-Depth Information
Let us assume that before interaction the systems H and N have certain limited
energy resources (vital
“
substrates
”
) V
a
and V
b
, where V
a
={V
aj
,j=1,
…
, m
a
},
V
b
={V
bi
,i=1,
, m
b
}. These substrates generate working elements in such a way,
that the substrate V
aj
(V
bi
) can generate H
j
(N
i
) a(b)-elements of the j(i)-th type of
values a
j
(b
i
).
The protective and active elements of each system are generated by the working
elements. First of all the protective E
Rm
ð
E
Rm
Þ
and active E
Cm
ð
E
Cm
Þ
substrates are
created which, in their turn, generate R-and C-elements of the m-th type. These
processes are described by the following dependencies:
…
H
m
a
Þ
¼
X
m
a
E
Rm
¼ E
Rm
ð
V
a
;
w
mj
f
jR
ð
V
aj
;
H
1
;
...
;
H
j
Þ;
j¼1
N
m
b
Þ
¼
X
m
b
E
Rm
¼ E
Rm
ð
V
b
;
w
mj
f
jR
ð
V
bj
;
N
1
;
...
;
N
j
Þ;
j¼1
E
Cm
¼ E
Cm
ð
V
a
;
H
1
;
...
;
H
m
a
Þ
¼
X
m
a
w
0
mj
f
jC
ð
V
aj
;
H
j
Þ;
j¼1
N
m
b
Þ
¼
X
m
b
E
Cm
¼ E
Cm
ð
V
b
;
w
mj
f
jC
ð
V
bj
;
N
1
;
...
;
N
j
Þ;
j¼1
w
0
a
ð
b
Þ
where w
a
ð
b
Þ
mj
mj
and f
a
ð
b
Þ
are certain present weights and functions respectively.
We shall assume that as a result of such hierarchical synthesis, elements in the
systems H and N have at the beginning of the interaction (t = 0):
;
(1) m
j
and n
j
working elements of the j-th type with values a
j
and b
j,
respectively,
where
X
X
m
a
m
b
a
j
H
j
¼ M
a
ð
0
Þ;
b
j
N
j
¼ M
b
ð
0
Þ
;
ð
10
:
3
Þ
j¼1
j¼1
(2)
r
a
and r
b
types of protective elements, the m-th type having
α
m
and
β
m
ele-
ments, and:
X
X
r
a
m¼1
a
m
¼
M
R
a
ð
0
Þ;
r
b
m¼1
b
m
¼
M
R
b
ð
0
Þ
;
ð
10
:
4
Þ
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