Recent content by Gwinterz

Awesome, Thanks so much! I think I got it!

Thanks for your answer and patience. I am just wondering about one last thing. When I see essential singularities defined, they are always a subset of isolated singularities. Is it correct to say that essential singularities must be isolated? I'm just a bit confused here because if that's...

My problem is with the details, I think once I understand the idea I can begin to formulate the proof. At the moment I really don't see the relationship between the solutions and the singularity. These questions are really tough for me and I waste so much time trying to figure out what set of...

So because the only analytic function is f(z) = 0, does that mean our f(z) can't be analytic? Then since it isn't analytic, it breaks the definition of an isolated singularity?

It would tell me that the function is not analytic at the point z = 0, as there is more than one zero. Is that right? Does that mean that the singularity is not isolated?

Hey, I have been asked to show that z = 0 is not a removable singularity of: f(z) = z cos(1/z) The catch is, I have to show this by first finding all the solutions to the equation (f(z) = 0) then use them to show that the singularity is not removable. The only relevant theorem I can find is...

Thanks guys that makes sense. Is the integral equal to zero because its a closed path?

Hey, I have been stuck on this question for a while: I have tried to follow the hint, but I am not sure where to go next to get the result. Have I started correctly? I am not sure how to show that the integral is zero. If I can show it is less than zero, I also don't see how that shows it...

Hey, Thanks for your replies, Yea, this is a tough one, there really isn't any more information I can give. I have found that the literature is split, half of the time people do it one way, and the other half another way. What I would think is the correct way is to say that the solution...

For future reference, There is a pretty good review paper which was published in the International Journal of Molecular Sciences. The title is: Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy

Hey, I was hoping to be directed to some literature regarding the van der waals forces between a particle and a surface. I have found lots of models regarding particle-particle forces but no extensions of this. Thanks

Hello, I was just after an explanation of how people get to this conclusion: Say you are looking at the Helmholtz equation in spherical co-ordinates. You use separation of variables, you solve for the polar and azimuthal components. Now you solve for the radial, you will find that...

Hey I just have a kind of broad question, typical derivations of the optical trapping force involve the approximation that the particle is spherical. I'm about to start looking into papers which discuss deviations from this but before I do I just wanted to see if I could reinforce some...

Hey, Thanks for your reply. Sorry I omitted the formal code for the sake of explaining. I found the source of my problem, I didn't include it here because I didn't think it was the problem. The problem was that I was using the If function, e.g. f[a,b,c] = If[a>x,a*g[b,c],100*a*g[b,c]]...

Hey, Say I have a function f[a,b,c] which depends on another function g[b,c] such that: f[a,b,c] = a*g[b,c] If I input, f[a,1,2], mathematica spits out a*g[1,2] rather then actually evaluating what g[1,2] is. Is there a way I can force mathematica to evaluate g[1,2] so instead, e/g if g...