I am in the process of writing a paper and I have a doubt. I am not sure that this is the best stackexchange site where to post since it is more a terminology problem than a mathematical one. Please point me to the right site if I am wrong.
During my experiments, I am acquiring a set of kinematic variables (angles) which we can call $x_i$ and I have a set of 5 outputs $y_i$. To each variable is associated a time-series.
Therefore, I wanted to denote the variables introduced above in the following way, but I am not sure if it is the best one.
(I need to introduce explicitly the time series because in the paper I talk about the correlation of the two time-series.)
I will write:
We denote with $\mathbf{x}=\{x_1,x_2,\dots,x_{n_x} \}$ (with $n_x=10$) the set of kinematic variables acquired at each time step, and with $\mathbf{y}=\{y_1,y_2,\dots,y_{5} \}$ the outputs. Moreover, we denote with $X_i,Y_i$ the time series respectively associated to the variable $x_i, y_i$.
Thanks for your help.
There is just one choice of notations you made that I find a bit strange, but I am not saying it is compulsory to change it.
One should try not to write redundancies like $x_{n_x}$. If you want to avoid confusions between indexes and bounds (here we have $x_i$ with $i \le n_x$), you should tend to use upper cases letters without any index. So I would rather write : $\mathbf{x}=\{x_1,x_2,\dots,x_{N}\}$.
Otherwise I find your notations perfectly fine.
To write the $j$-th term of the time serie, you have plenty of choices $X_i(j), X_{ij}, X_i^{(j)}$. If the treatment of those times series involves matrix operations, $X_{ij}$ seems like a very good choice.