An x-ray field at a point P contains 7.5 x 10^8 photons/m^2-sec-keV, uniformly distributed from 10 to 100 keV.
a.) What is the photon flux density at P?
b.) What would be the photon fluence in one hour?
c.) What is the corresponding energy fluence in SI units?
work shown:
a.) 7.5...
Model the arterial tree as a simple branching network in which each junction is composed of a parent vessel and daughter vessels, each having a diameter related to the parent's via the cube law (D_n-1)^3= (D_n*a)^3 + (D_n*b)^3 which is approx. equal to 2*(D_n)^3
a.) Show that D_n/D_0=...
since t>0 and |t|=t and for t< 0 |t|= -t
and since the inverse Fourier transform integral for t>=0 is given .. .u can add the the results for the inverse transform for t<=0 to the result to get Ge(f)
however, how do u integrate the expression for
neg. infinity to zero for integral of...
in that case.. is the solution for X and part b correct?
if that's the integral... it is an imaginary integral so how do u solve that part.. I'm confused?
Suppose that you obtain a one dimension magnetic resonance image from two water-filled cubic shaped containers arranged as shown below. This diagram is a cross-section of the cubic containers in the x-y plane.
figure description:
-one of cube's is 2 cm wide, the other is 1 cm wide, and...
i forgot to include the echo signal info Se(t) info, which can be rep. by
Se(t)= Se(0) exp (i(2pi(f0)(t))* exp (-|t|/T2*) from negative inf. to inf
therefore, since the |t| is the magn. of t,
therefore i assumed the img. part can be ignored which was helpful in my assumption. in my...
The "Free Induction Decay signal" (FID) is a particular type of NMR signal observed in both MRI and MRS. An idealized representation of the signal Sf(t) is given by
Sf(t)= Sf(0) exp (-i2pi(f_0)(t))*exp(-t/T2*) t>=0
Sf(t)= 0
it was proven that Gf(f) corresponding to this signal is given...
since, it asks for the magnitude of X, this is the 'real part of the solution so the imaginary part can be ignored right from my previous expression..
therefore i get
X= e^{(-((T2-i(w-wo)T2^2)/(1+(w-wo)^2*T2^2))*T}
=e^{(-((T2/(1+(w-wo)^2*T2^2))*T}
therefore for part b, it's
X=...
so if it's gnew(w)= g_old(w)(1+X)
isn't X=e^-aT
or based on there expression
X= e^{(-(T2-i(w-wo)T2^2)/(1+(w-wo)^2*T2^2)*T}
for part b.) if T=a*T2
therefore how do u solve, do u simply sub in a*T2 for T into the expression
X= |e^{(-(T2-i(w-wo)T2^2)/(1+(w-wo)^2*T2^2)*(a*T2)}|...
then you would get the expression, S(0){-(e^(a*t))/a} from 0 to T
so you would get: S(0)*-{((e^aT)/a)-(1/a))
how do you determine the expression for X then,
if a= 1/T2 + i(w-w_0)
therefore you get, S(0){-((e^(1/T2 + i(w-w_0)t)/a)) -1/(1/T2+ i(w-w_0)}
what is X in this case?
and...
for the that integral... the expression consists of an imaginary number i with t.. and additionally your integrating the expression from 0 to T for t, therefore u can't integrat the T2 expression right?.. how do u you go about integrating the expression...
i'm confused.. I'm sure it's easier...