Recent content by grquanti

If I understand, you mean: from ##\partial_t f(x,t) -2a\partial_x f(x,t) = ax\partial_x^2 f(x,t)## I take ##s## such that ##\partial_s f(x,t) = \partial_t f(x,t) -2a\partial_x f(x,t)## This implies ## \frac{d}{ds}t=1## ## \frac{d}{ds}x=-2a## So that ##t(s)=s+c_1## ##x(s)=-2as+c_2## and...

Forgive me, I'm not an expert (actually I don't know nothing about the method of characteristics), can you be a little more explicit? If it's what you mean, my starting point is ##\partial_t f(x,t) = k\partial_x^2 xf(x,t)## with ##k>0## (there is an error in the first post: when putted in...

Hello, I have an equation of the form: ##\partial_t f(x,t)+a\partial_x^2 f(x,t)+g(x)\partial_xf(x,t)=0 ## (In my particular case ##g(x)=kx## with ##k>0## and ##a=2k=2g'(x)##) I'd like to know if there is some general technique that i can use to solve my problem (for example: in the first...

Hello everybody. Consider $$\frac{\partial}{\partial t}f(x) + ax\frac{\partial }{\partial x}f(x) = b x^2\frac{\partial^2}{\partial x^2}f(x)$$ This is the equation (19) of...

In the case of systems with a continuum of states (e.g. a classical gas) the concept of "number of states" is not well defined I think: let A be a state and B a second state, identical to A, but with this difference: ##v_i^A = (v_x,v_y,v_z) → v_i^B = (v_x + ε, v_y,v_z) ## where ##i## is the...

##∑_{i≠j}^{k≠j}T_{ki}P_i = ∑_{i≠j}P_i∑_{k≠j}T_{ki} ≤ ∑_{i≠j}P_i ≤ ∑_i P_i = 1##

Yes, you mean ##∑_{i≠j}^{k≠j} T_{ki}P_i = ∑_{i≠j} P_i ∑_{k≠j}T_{ki} ≤ ∑_{i}P_i = 1 ## Thank you!

Yes, I know that ##∑_i T_{ij}=1 ∀ j## but I have to do (at least, I think I have to do) ##∑_{i≠j}^{k≠j} T_{ki}P_i## For sure, the summation over a single index is not greater than one, but here I have to do the summation over two index...

I think you are suggesting me this: ##P[ X(t) ≠ j | X(t-1) ≠ j ] = ∑_{i≠j}^{k≠j} P_{i→k}P_{i}(t) = ∑_{i≠j}^{k≠j} T_{ki}P_{i}(t)## It seems reasonable to me, but am I ensured that this summation in not greater than 1? I would say ##P( A | B ∪ C ) = \frac{P(A | B )P(B) + P( A | C...

Hello everybody. I have a Markowian homogeneous random walk. Given the transition matrix of the chain, I know that ##P[ X(t) = i | X(t-1) = j ] ≡ P_{j→i}=T_{ij}## where ##T## is the transition matrix and ##X(t)## is the position of the walker...

thanks for all!

Yes, this is the case: I have integer variables. In fact, I found the best way to do the histogram is using a linear binning with unitary bin length until the fluctuations becomes relevant and then smoothing them via the logarithmic binnig. I found this also in the case of a non integer...

As you can see in the log-binned case I have an overstimation of the frequency for small x. The article I posted says something very general, whitout explanations, that is: "data are best left unbinned for small x" I think the behaviour I obtain is due to the fact that when I divide for the bin...

what do you mean with "resample" if then you talk about interpolating them?

I compare with the histogram I obtain when the bins are equally spaced (really equally spaced, not in logscale). The problem is more or less this: when plotting the histogram on a logscale with equally spaced bins, I have a straight line up to a certain value of x. Going over that value the...