.


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:

































 

 

 

 


,





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) · - τ (, ); 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, .





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