@DominicMichaelis I’ve made very little headway on that one. I do know that if $\varphi$ really is principal, the only possible generator is $\{x_f:f\in\mathscr{A}\}$.
I am still thinking about, what property does $\mathbb{Z}$ have to grant us only having a one point filter, right now I guess it is just being countable but maybe we need something else too
@Lord_Farin i'm sorry but you can explain me this :ϕt is automatically a diffeomorphism onto its image for every t, and repeating the argument but reversing the direction of the gradient flow for f shows that ϕb−a:Ma→Mb is onto
Hi! Is it obvious what the matrix $G$ is here? $$ G^T \begin{bmatrix} A & Aa+ b\\ (Aa+b)^T & a^T Aa+Ab+c \end{bmatrix} G = \begin{bmatrix} A & b \\ b^T & c \end{bmatrix} $$
@GitGud oooops, there is $2b^T a$ instead of $Ab$, this matrix corresponds to translation transformation
@GitGud look, the general equation of second-order algebraic hypersurface $$ \begin{bmatrix} x & 1 \end{bmatrix} \begin{bmatrix} A & b \\ b^T &c \end{bmatrix} \begin{bmatrix} x\\ 1 \end{bmatrix} = 0 $$
after transformation $x = y + a$ we obtain matrix from my question
@Charlie, have you and Somaye managed contact on, I don't know, facebook chat or the like? i have her email
@Chris'ssisterandpals, Hi, I actually was Willie as a child, sometimes my oldest sister calls me that. Which is fair, I still think of my brother as Jimmie.
@skullpatrol, sometimes, more when I was younger. I grew up in New York, live in California, so baseball and nfl were part of it. But I began playing soccer frequently after grad school and got surprisingly good. So there is a level of understanding and interest when I watch the best play.
@Charlie, could you please email me, addresses at ams.org/cml search? I suppose you need to be awake at the time. People may email while asleep, but they probably do not do so very well.
@Chris'ssisterandpals Good night. Quite unexpectedly, I have been able to reduce the problem to finding an initial condition to an ODE. This computation however appears to be hard.
@Charlie, good. Because Somaye wrote to me, I was able to faorward her paper to an expert, so that aspect worked out. However, she also wants someone to Skype with, if i understand her request. I don't have that or a webcam, and I'm not particularly fond of Facebook chat either. I like email. So, the email idea was mostly so that i could send you her email address and repeat what I just wrote.
ok... this is a long shot, but I'll try anyway: There's a substitution I've seen quite often that's used for definite integrals. If you're working on $\int_a^bf(x)dx$, the substitution says that you can do something like $x = x+b-a$, and not change the integral. But I can't remember the exact substitution. Anyone know what I'm talking about?
@Charlie, long pause, I will take that as reluctance. A few notes: (A) I think communication off site is a good thing. (B)This began on MO, when I put some people in touch about some math, who wanted to keep their email secret. (C) done the same for amWhy, so you might ask (D) Chris'sister did email me although with no name and a meaningless email address. Other than that info, I guess I will drop it.
@user68610 well you got your independent random variables, $X$ and $Y$. they've got a certain probability distribution over the integers, meaning $X$ has a certain chance of being any integer $n$, and that chance is denoted $p_n$. same for $Y$, its probability distribution is $q$.
so, suppose you wanna know the probability that $X+Y$ is equal to some integer $n$. if $X$ takes the value $k$ for some $k<n$, then in order for $X+Y$ to be equal to $n$, you're going to have to have that $Y$ takes the value $n-k$. so the probability for that is $p_nq_{n-k}$.
@AlexanderGruber What does this have to do with 'probability distribution' Does convolution as in the convolution for Linear time-invariant systems' (image processing and stuff like that) has anything to do with probability?
@user68610 sorry i can only help you understand the mathematics of it - if you need to know how the math relates to programming and stuff you should ask at stackoverflow
