Recent content by jakey

so are you saying that this is simply a definition? I'm sorry but I still can't seem to understand it...so the average power based on this definition, then, is merely an approximation of the "real mean"?

I am slightly confused by the definition of average power if the power function $p(t)$ is sinusoidal. Why is it that only one period is considered? I mean I know that it simplifies calculations but if we assume that the period of $p(t)$ is $T$ and I compute the average power over...

Hi hallsofivy, sorry I didnt quite understand your reply. And oh, it's 5/27 not 5/9. Perhaps a better way of explaining it to me would be how to identify the coefficients a_k such that \frac{5}{27} = \sum \frac{a_k}{3^k} ?

Hi guys, I'd like to ask about ternary expansions. they seem easy but I'm having a hard time doing this as well as searching for tips online, specifically for x \in [0,1]. I know that ternary expansions are similar to decimal expansions but for example, how do you find the ternary expansion of...

hi mathman, thanks btw! so there's no rigorous proof for this?

Hi guys, I was reading about random walks and i encountered one step of a proof which i don't know how to derive in a mathematically rigorous way. the problem is in the attached file and S is a random walk with X_i as increments, X_i = {-1,+1} I know that intuitively we can switch the...

Oh by the way, J here refers to the jacobian.

Hi guys, let's say I have a transformation T from (p,q) to (u,v). The inverse transformation would be T^{-1} from (u,v) to (p,q) Now, J(T) = u_{p}v_{q} - u_{q}v_{p}. On the other hand, J(T^{-1})= p_{u}q_v - p_{v}q_{u}. But |J(T)J(T^{-1})| = 0 and not equal to 1. I know it's supposed to be 1...

Hi hallsofivy, thanks for the reply. but it seems that substituting x=t and y = t\sqrt{\frac{a^2-1}{a^2+1}} doesn't satisfy the curve above...

Hi guys, can anyone help me with evaluating this: \int^{}_C |y| \,ds where C is the curve (x^2+y^2)^2=r^2(x^2-y^2) any hints with the parametrization?

it can't be. btw, it's ∫_C |y| ds where C is the curve I gave above. I need to parametrize it so I could use ds = ||r'(t)|| dt.

Hmm, this is the hint given: "Parametrize the curve first using polar coordinates. Next, find the period which is to be done in Cartersian coordinates." you see, the equation i gave above is the curve for the line integral of \int |y| ds.

WOW, really?? But I couldn't find a period for this...? Or, is it t \in (-\infty, \infty)?

hi tiny-tim, I'm stuck. for one, r can't be 0 as the formula I'm dealing with has r=22. i just typed it as r as a generalization. well,for cos 2\theta = 1, a solution, for example would be theta = 0 or theta = \pi. that would just be a line in the polar axis.

Well, r = 0 or cos (2\theta) = 1. how is this going to help, tiny-tim?