5.7.
[8]
(5.21)
m +1(t), m (t) - m + 1 m ; P (t - τ) - (t - τ); am (τ) - m τ.
, P (t - τ) am (τ) .
(5.7) (5.9). () [4, 8]:
(5.21 )
(5.22)
λ - .
[4, 8]:
(5.23)
(5.24)
λ 0 1 0 - () .
P (t) (5.15) - (5.17).
(). , , - .
, . , .
. . , ( 1). (). λ 1, λ 2.
:
) ( 5.8). S 0 , , S 1 - , , S 2 - , . - ;
|
|
) S 0, S 1, S 2 . . :
dP 0(t) / dt = - λ 1 · P 0(t), (5.25)
dP 1(t) / dt = λ 1· P 0(t) - λ 2· P 1(t), (5.26)
dP 2(t) / dt = λ 2· P 1(t). (5.27)
, , , . dPk / dt = 0 . . P 0(t) = exp(- λ 1· t), :
dP 0(t) / dt = - λ1 · exp(- λ 1 · t); (5.28)
dP 1(t) / dt = λ1 · exp(- λ 1· t) λ 2 · P 1(t). (5.29)
1(t) .
dP 1(t) / dt + λ 2 · P 1(t) = 0. (5.30)
dP 1(t) / P 1(t) = λ 2 dt (5.31)
ln P 1(t) = λ 2 × t +ln C, (5.32)
ln C - .
,
P 1(t) = · exp(- λ 2 · t). (5.33)
(5.29)
P 1(t) = (t) · exp(- λ 2 · t). (5.34)
,
dP 1(t) / dt = (d (t) / dt) · exp(- λ 2 · t) - λ 2· (t) · exp(- λ 2 · t). (5.35)
, P 1(t) dP 1(t) / dt (5.29),
(d (t) / dt) · exp(- λ 2 · t) - λ 2· (t) · exp(- λ 2 · t) + λ 2· (t) · exp(- λ 2 · t) =
= λ 1· exp(- λ 1 · t). (5.36)
(d (t) / dt) = λ 1· exp[(λ 2 - λ 1) · t ]. (5.37)
(5.38)
2- .
(5.29) (t),
(5.39)
, t = 0 0(t) = 0(0) = 1, t = 0 [ 1(0) = 2(0) = 0].
P 1(0) = 0 = [ λ 1 / (λ 2 - λ 1)] + 2. (5.40)
2 = λ 1 / (λ 1 λ 2). (5.41)
(5.39) (5.29)
(5.42)
, (5.41) (5.42) , . . ,
(- λ · t) ≈ 1 λ · t, (5.43)
λ · t . (5.43) (5.42)
(5.44)
) 1(t), (t) (5.43):
(t) = P 0(t) + P 1(t) = exp(- λ 1· t) + λ 1· t = 1- λ 1· t + λ 1· t = 1; (5.45)
|
|
) :
3(t) = 1 (t) = 1 - 1 = 0. (5.46)
, S 0, S 1, S 2, .. , , , .. (- λ · t) , (- λ · t)2, (- λ · t)3, (- λ · t)4 . .
, (5.21), [8]. , , .
.
5.1 [8].
. λ = 0,110-4 l/ . () λ 1 = 0,810-4 l/. t = 1000 , .
.
. , , , . t :
- t ;
- 1 , τ < t, 2 t;
- 2 , τ < t, 1 t.
(t) , ..
(t) = (t) + (t) + (t). (5.47)
, (t) = (t)
(t) = (t) + 2 (t). (5.48)
(t) , t ,
(t) = (-2 λ · t). (5.49)
,
(5.50)
a 1(τ) · dτ - τ (, dτ); a 1(τ) = λ · (- λ ·t) - τ; P 2(τ) = (- λ ·t) - 2 τ, .. ; P 2(t - τ) - 2 τ t. λ 1,
P 2(t - τ) = [- λ 1×(t - τ)]. (5.51)
(5.50) (t) ,
(5.52)
(t) = (t) + 2 (t) =
= (- 2 λ · t) + 2 · λ ·{[- t ×(2 λ - λ 1)] -1}· [(- λ 1× t)] / (λ 1 - 2 λ) =
= λ 1· (-2 λ · t) / (λ 1 - 2 λ) - 2 λ · [(- λ 1 × t)] / (λ 1 - 2 λ). (5.53)
t = 1000 , λ = 0,110-4 l/ λ 1 = 0,810-4 l/, (t) ≈ 0,999.
1 (3.17)
|
|
(5.54)
λ 1 λ, , 1 = 62500 .
, ( ) [8]. n
(5.55)
n(s)
(5.56)
(5.55) (5.56) : λ 0 - ; λ 1 - ; λ 2 - ..; n - ; sk = - λk - k - (5.55); B '(sk) - sk.
λί, .. λ 0 = λ 1 = λ 2 == λn,
(5.57)
(5.55) - (5.57) , ( ) , n - , .. , n . 0, 1,..., n , (), .
1
(5.58)
λί - ί - .
5.2 [8].
, 5.1, .