Recent content by Unconscious

Ok, clear, thank you :)

Sorry for my ignorance... what is ##\eta_{(\mu)(\nu)}##?

Suppose we have n vector fields ## Y_{\left(1\right)},\ldots,Y_{\left(n\right)} ## such that at every point of the manifold they form a basis for the tangent space at that point . I have to prove that: $$\frac{\partial Y_\mu^{\left(\sigma\right)}}{\partial x^\nu}-\frac{\partial...

This is clear to me, thank you. What is not clear to me is the pure math, in particular the step highlighted in my last post. So, are you saying to me that if the noise is not white, then I can’t correctly write the equality ##p(x_k|x_{k-1})=\mathcal{N}(f(x_{k-1}),Q)##? In other words, this...

Thank you for the link, but unfortunately I have not found an answer in that pages. Anyway, I try to share with you my doubt more precisely. Let's consider the formulas in Fig. 1 in this article: https://arxiv.org/pdf/1712.01406.pdf These two formulas have been obtained without assumptions on...

In Kalman filter mathematical treatment I have always read that a foundamental hypothesis is represented by the whiteness of the process noise. I have tried to do again the mathematical steps in the Kalman filter derivation but I can't see where such hypothesis is crucial. Could you help me...

I mean pointwise convergence, optionally except on a measure-zero set of ##\mathbb{R}^n##.

I have a sequence of functions ##0\leq f_1\leq f_2\leq ... \leq f_n \leq ...##, each one defined in ##\mathbb{R}^n## with values in ##\mathbb{R}##. I have also that ##f_n\uparrow f##. Every ##f_i## is the limit (almost everywhere) of "step" functions, that is a linear combination of rectangles...

Thank you, I will read again with this in mind. Surely, I will come with other questions.

I have read some documents on the subject, but until now, unfortunately, I still do not have a good understanding of them, most likely due to personal shortcomings that start from physics. In this regard, I would like to try here to expose some doubts that will almost certainly appear very...

I had no intention of being rude, I was just exposing my thoughts trying to argue it as best as possible. I am sorry to have offended you. Thank you for the time you have dedicated to me.

I set up the problem this way because I followed the path my antenna book taught me, but it only set the problem for arrays whose source distributions do not rotate (which would be like I did in post #8). In the last equation there is no change of integration variables. There, it was only used...

Could I ask you where you see logic errors, please? Is there a particular step in my analysis in the first/last message that is wrong?

The linked pdf is an extract of the second chapter of the book 'Conformal array antenna theory and design' of IEEE Press. Yes, it's true, in fact I said that this other equation is not applicable to our case: ##\mathbf{A}(\mathbf{r})=\sum_n\mathbf{A}^{(n)}(\mathbf{r})=\frac{e^{-jkr}}{4\pi...

It is precisely this formula that cannot be applied to my case, because when you write ##(\mathbf{r}'-\Delta\mathbf{r}_n)## you are actually schematizing a generic array where, however, the elements are obtained using only and solely rigid translations of a reference element: this is not the...