3.1 .
{T} - , , {T} t {T < t}, , [o, t]. Q(t) = {T < t} {T} . . Q(t) .
. ( )
Q(t) = n(t)/N0 ,
n(t) t.
, Q(t) + P(t) = 1. P(t) = 1 - Q(t). , .
P(t) = (N0 n(t))/N0 = N(t)/N0,
N(t) t.
t0, (0 1) .3.1.
P0 | Q0 |
. 3.1 .
: P0 , Q0 t=t0. P(t) : (0) = 1, P(¥) = 0.
( )
.3.2.
. 3.2. P(t) Q(t).
.
. 3.3 [0, t] Dt.
t
0 Dt t
.3.3
, (0,t + Dt) (0,t) (Dt),
P(t + Dt) = P(t) * P(Dt),
P(t + Dt) P(t) ,
P(Dt) Dt. , t .
P(Dt) = P(t + Dt)/ P(t).
Q(Dt) = 1 - P(Dt) = 1 - P(t + Dt)/ P(t) = (P(t) - P(t + Dt)) / P(t) = (1 - Q(t) 1 + Q(t + Dt))/ P(t) = (Q(t + Dt) - Q(t)) / P(t).
|
|
Q(t + Dt) Q(t) (0, t + Dt) (0, t) .
f(t) . {T} . ,
f(t) = dQ(t)/dt = - dP(t)/dt.
Q(t) f(t) . 3.4.
. 3.4 Q(t) f(t) .
f(t) :
,
f(t) = n(Dt)/(No* Dt),
n(Dt) Dt.
, , . .
,
P(t)* l(t)* Dt = f(t)* Dt.
.
l(t) = f(t)/ P(t).
l(t) = dQ(Dt) / dt = (Q(t + Dt) - Q(t)) / (P(t) * Dt) = (1/ P(t)) * (dQ(t)/dt) = - (1/P(t)) * (dP(t)/dt) = f(t) / P(t).
l(t) = n(Dt) / (N0 * Dt) * (N0/N(t)) = n(Dt) / ((N(t) * Dt).