Recent content by O'Fearraigh

So, I am reading this paper on the physicality of the wave function and I have a question. Here's the passage: "If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus, there will exist...

No, I see what I did originally: I didn't carry the minus sign over. Okay, so now that we have a function for A(a), how do the limits work? We have: (a) lim[a→∞] (b) lim[a→0] I got lim[a→∞] = 0 lim[a→0] = ∞ Is that correct?

I don't know... I just copied that from my first try. Anyway, would the reduced equation be: A(a) = (2a+1)/(2a^2+2a) + ln[(a)/(a+1)] ?

Yes, A(a) = (2a+1)/(2a^2+2a) - ln(a+1) - ln(a) or is it A(a) = (2a+1)/(2a^2+2a) - ln(a+1) + ln(a) ?

Okay... So, when setting up this area equation... would it simply be the the integral of -(x / a^2+a)+(2a+1 / a^2+a) dx - integral of 1/x dx [from x=a to x=a+1]? Okay, doing that, I get that the function for the area between La and f(x) is: A(a) = (2a+1 / 2a^2+2a) - ln(a+1) - ln(a) Is this...

Right, well I know the equation y-y1=m(x-x1). So, I would have: y-(1/a)=(-1 / a^2+a)*(x-a) ---> y=(-x / a^2+a)+(a / a^2+a)+(1/a). Right? Or... y=(-x / a^2+a)+(2a+1 / a(a+1)) Which would imply that: y = (2a+1-x)/(a^2+a) Right?

Consider the curve f(x) = 1/x Consider two points on f(x): Pa and Qa, where the x-coordinate of Pa is a, and the x-coordinate of Qa is a+1. Let La be the line connecting Pa and Qa 1.) Find the equation for La 2.) Find a formula that expresses A(a) = the area between f(x) and La 3.) Determine...

Actually, I was looking at staying away from the mathematical finance realm (since I already did that). I have taken Calculus I and II (both with theory), Calculus III, Mathematical Statistics, Probability (with Calculus), Linear Algebra (proof-based), Mathematical Modeling, and Set Theory. I am...

class. I did a lecture last semester on financial mathematics and stochastic processes. Know of any cool topics that I could lecture on?

It's about GARCH(1,1) processes (mainly it's all statistics and probability). Anyway, there is the section of a book (link below) that is confusing me: Where does "E[ln⁡(β+αz_t^2)]" come from (on page 319, the "second" page)? My other question is why does it say that "ln⁡(β+αz_t^2) holds...