Recent content by Togli

I suppose "wanting to be the best" itself is the greatest obstacle to be really the best. The best just happens to be...

I usually get it if I verify the derivation by a simulation on the computer. Until then, I can never believe I really did it. And if the simulation verifies, it is orgasmic, I jump from my chair, and once again believe in the power of the formulas, which becomes unbelievable quite soon.

There are various ways of estimating instantaneous amplitude and phase. Hilbert transform might be a good choice for that.

Really! There have been many books, thinkers beyond collective action & intelligence, i.e., http://en.wikipedia.org/wiki/Commons" . They are countless. And there is a book coming out November 2011 by http://michaelnielsen.org/blog/" about "Open Science",titled Reinventing Discovery. He is...

It is not conspiracy a bit. They hold it back, because otherwise they won't be able to publish. It is that simple. And if you don't publish in a high-impact journal, no way to go for Johnny. There would exponential progress, much more ahead. Not everybody has the ability or budget to collect...

I have always had some problems with the current political situation of science where some data are collected and some scientific computer program written, yet they are concealed deliberately. The logic is that you spend some labor on it, so you have the right to "possess it" and "publish it"...

Sure man, I am happy if I was any help. Have a good one.

I would like to simplify this series as much as possible f(m)=\sum_{n=0}^{\infty}\frac{m^n (2n)!}{(n!)^3} Approximates would also be fine. One can easily notice that (2n!) / (n!)^2 > 2^n hence I figured out that f(m) > \sum_{n=0}^{\infty}\frac{(2m)^n}{n!}=\exp(2m) but this is not the best...

You can either keep the matrices in cell arrays : A{1}, A{2}, A{3}... OR you can keep'em in multidimensional matrices A(1,:,:), A(2,:,:) and in the latter case, you got to use command "squeeze" to convert them into 2 dimensional, i.e., B = squeeze(A(1,:,:))

I guess that depends whether your matrices have anything in common: What are their names for example? There should be a relation between them for that.

You can also use a function called "D = horzcat(A,B,C)" for that purpose, though it should be equivalent to "D = [A B C]". I did not exactly understand what you mean by tedious. Could you be more specific?

In fact, the range of m in my problem is : 0 < m < 2*pi And yes, for m ~ 0, the approximation exp(-0.5*m) ~ 1 but for large m ~ 2pi, exp(-0.5*2*pi) = 0.04, hence it substantially deviates from 1. I am not sure whether Taylor's expansion exp(-x)=\sum (-x^n) / n! would work in this case...

Thank you! You are right, it is easy to show that pi/2 * exp(-0.5*m) < f(m) < pi/2 by simply inserting sin(x) for the boundaries. However, these are a bit relaxed bounds, I prefer a real approximation. I did not understand your statement about f'(m); if I take the derivative as you...

It is basically an integration that cannot be properly solved, so I look for an approximation or maximum&minimum bounds of f1(m) and f2(m) such that f1(m) < f(m) < f2(m). Here is the integral: f(m) = Integrate [ exp( -0.5* (sin(x)^2) *m) dx, x=0:pi/2] where m is a variable. When I take sinx ~...