Math Is Fun Forum

I've been fighting with these over the last weeks and cannot solve it yet    Can somebody please give a hand? This is the problem, I have these equations

where t>0 is the time,
n is in Z (the integers),

then apply to (4) and (5) the inverse quantum fourier transform defined by

(note that there is a minus sign in the exponential function of the quantum inverse transform)

and obtain equation (6) and (7)

My problem is that I cannot write equation (4,5) in the form of (6,7). I've sent an email to the author and he replied

"The equations (6,7) follow from (4,5) by making the substitution k' = \pi - k in the second term, and noticing that the integrand is periodic with period 2\pi"

I trying this but its not working, can someone give me a hand with this??

Thanks!!!

I have the following problem for which I cannot find an answer. I posted this same problem in "physicsforums" and "mathhelpforum" and still nobody was able to give me an anwser. I looked everywhere in the internet (journal, books, etc) and also found nothing. Maybe some of you guys can give me some hints.

Given the following contour integral

where C is a contour, f and g are analytic functions defined over C. What is the asymptotic approximation of the closed-form solution when t->infinity?

In general you cannot use the classical methods from complex analysis like steepest descent or saddle point methods because these methods require

I found that there are solutions for general f when t is multiplying f, i.e.,

this is the general steepest descent. There are also solutions when

Working with f, you'll find out that you can't cheat, e.g.,

So, for general f it seems that there is no general solution. What do you think?

For a good reading on asymptotics, you can look at these books from google books

http://books.google.es/books?id=_tnwmvHmVwMC&printsec=frontcover#v=onepage&q=&f=false

http://books.google.es/books?id=xooq99A9anMC&printsec=frontcover#v=onepage&q=&f=false

http://books.google.es/books?id=KQHPHPZs8k4C&printsec=frontcover#v=onepage&q=&f=false

Hi, I have the following problem

given a function f(k) defined on the reals and a complex constant z0, what is the maximum of following function?

The maximum of the module is clearly the value k such that

right? because when you take the module, the squares of the real and imaginary parts are maximum and hence the module is maximum.

But what happens when you cannot factorize the complex constants? e.g., given the following fuction

where k is only real, and z1 and z2 are complex constants. Can we still derivate g, make it equal to 0 and still say we can find a critical point? i.e., does solving

thanks in advance for the help 

Hi, althoug I've signed up as a user of this forum around 2 years ago, I don't normally post topics nor comments. I always prefered to just read and entertain myself with all the fun problems that other people post here. But latetly I have notice that it is really important to do networking in every sense of the word (talking with people that shares similar tastes in conferences, virtual forums, etc), and found it to be even more fun that way.

One of the reasons that kept me away from posting seems to be that my interests are in computability and automata theory. It is really hard to find a good forum on theoretical computing subjects, and the computer sciences forums you can find are mainly related to programming, databases, etc., not math.

I really like this forum because I can see that people here really enjoys doing math (as I do), and problems are so cool, and allowed me to learn a lot of stuffs that I never see before. I have a background in computer sciences and always liked mathematics, and when I discover computability, automata and complexity, I just simply felled in love of these subjects, and I knew that I had to learn more mathematics, and this site allowed me to do that. And at the same time, I learned to love mathematics in general.

The main subject of theoretical computing that I like the most is computability and complexity issues of computing paradigms (quantum computing, molecular computing, etc). All these paradigms have their own abstract model with so many questions still to answer. Right now, as a graduate student I studying these subjects, from a strictly mathematical point of view, and I now that this is what I want to do for the rest of my life.

Well, I just wanna to write this and see what other people think about theoretical computing in general. Does somebody knows about these topics? As mathematicians (future or present) what are your thoughts about the field? Is there somebody working/studying  one/some/several of these topics right now?