Как выбрать гостиницу для кошек
14 декабря, 2021
a " — ST "n
Equation (3-4) can be |
written as |
|
— |
‘ 00 |
|
V2(t) |
■ E |
(v t 2 v2(aAt) |
a = 0 |
U_ai |
|
00 |
00 . |
|
* E |
23 77 L 77 t v(aAt) v(bAt) |
|
a = 0 |
b = 0 Sf ‘ a m ‘ b |
a* b |
by separating the terms in which a = b from those in which а ф b, and the expected value of V (t). is
■ 00 ‘
<v2(t)> = <(vt f > y2<aAt>
a = о V Ж ‘ а/
‘ 00 00
+ <7? t 7) t >v(aAt) v(bAt), (3-5)
a = о b = о Ж " a Ж ‘ b а Ф b
since the expectation of the sum of a number of random variables is equal to the sum of their expectations.
If the average flux of neutrons is Ф and the counting efficiency of the detector is k,
then the probability of detecting a neutron during the ntb time interval is кФДі, the probability
th
of detecting no neutron during the n time interval is l-кФді, and the expected values of the Tj combinations are
< h7t 2> = [l2 x k<I>At] + [o2 x (l-k^At)]
Ы — a]
= кФді,
<rjt 77 t > = [l2x (кФдО2] + [l x k$At x 0 x (1-кФдо]
+ [o x (l-k$At) x 1 x кФді] + [о2 х (1-кФд02]
= (кФді) ,
У ] кФді v2(aAt) + ^ ^ * (кФдІ)2 v(aAt) v(bAt), |
so
We have postulated a d-c removing component, such as a series capacitor or a shunt inductor, in the linear part of the circuit and it is easy to show that under this condition
which becomes, as Д1—*0, |
.oo. ‘■ . ‘ • .
v(x) dx = 0. (3-11)
’o.
So the expected value of V^(t) is
(3-13)
Also, the output of the integrating circuit, т, satisfies the differential equations
dS(t) + S(t) = AV^(t)
dt t
d<S(t)> + <S(t) > = <AVz(t)> dt t t
and since <AV^(t)> is constant in time, then
If there are two different types of particles present, arguments similar to the above will
yield
(3-15)
where the subscripts 1 and 2 refer to the two types of particles. Because of Equation (3-11); this becomes