Anyone got links for any websites that were used to show miners signaling support for segwit? or screenshots?

Also wanted to confirm if my assumptions are correct about the whole thing:

  1. Initially BIP 9 was supposed to activate segwit but there was lot of controversy
  2. BIP 91 was proposed but again controversy
  3. BIP 148 was proposed and everyone agreed to activate BIP 91
  4. Finally BIP 141 was used to activate segwit

Anyone got links for a website that was used to show miners signaling support for segwit? or screenshots?

Also wanted to confirm if my assumptions are correct about the whole thing:

  1. Initially BIP 9 was supposed to activate segwit but there was lot of controversy
  2. BIP 91 was proposed but again controversy
  3. BIP 148 was proposed and everyone agreed to activate BIP 91
  4. Finally BIP 141 was used to activate segwit

dynamical systems – Show that the hyperbolic toral automorphism on $R^2$ is expansive.

I cannot seem to figure this problem out.

I know that the hyperbolic toral automorphisms $A$ is just an integer hyperbolic matrix with determinant $pm 1$ that has eigenvalues $0<|mu|<1<|lambda|$. I know that we can find a basis of $R^2$ in terms of two eigenvectors corresponding to each eigenvalue say $v_1,v_2$. I also know that is $x=a_1 v_1+ a_2 v_2$ then $A^n(x)=a_1 lambda^n v_1+ a_2 mu^n v_2$ and we can estimate its Euclidean norm using the norm $||x||=max{|a_1|,|a_2|}$. I feel like this is most of the puzzle pieces but I am not sure how to put this all together to show $A$ mod 1 is expansive. Any help would be appreciated.

In case there is many definitions out there a map is expansive if $exists$ a $delta$ s.t for any $x,y$ there $exists$ $n$ for which $d(A^n(x),A^n(y))>delta$

magento2 – How to show customer data ( name, surname, address ) on my custom checkout step after shipping step?

I have created custom checkout step after shopping step.
Now i need to show there customer’s information from shipping step (first name, last name, address, city, country, phone number, etc ) and his orders ( name of order and quantity ).
I don’t know how to do it, please give any advices.

probability – Show 2 integrals are equal

I have two i.i.d continues random variables $X_0, X_1$, with PDF $f$, where the support $subset$ $(0,infty)$.

I need to calculate $P(X_0 geq X_1)$. I know the answer is $frac{1}{2}$ due to symmetry. However, I want to directly prove it using integrals.

My try:

We know that $f(x,y) = f(x)f(y)$.
So need to show:

$int_{0}^{infty} int_{0}^{x_0}f(x_1)f(x_0),dx_1,dx_0 = frac{1}{2}$

Since $f(x,y) = f(x)f(y)$ is a PDF we have:

$1 = int_{0}^{infty} int_{0}^{infty}f(x_1)f(x_0) ,dx_1,dx_0 = int_{0}^{infty} int_{0}^{x_0}f(x_1)f(x_0) ,dx_1,dx_0 + int_{0}^{infty} int_{x_0}^{infty}f(x_1)f(x_0) ,dx_1,dx_0 $

So it is enough to show that:
$int_{0}^{x_0}f(x_1)f(x_0) ,dx_1,dx_0 = int_{0}^{infty} int_{x_0}^{infty}f(x_1)f(x_0) ,dx_1,dx_0 $

To conclude. I tried manipulating the integral, but I wasn’t able to show it. I think I need to use Fubini, but I am not sure.

Thanks for the help!

abstract algebra – Show the order of the Kernel of a morphism between groups

Consider $G_n={ overline{x}inmathbb{Z}/nmathbb{Z}; gcd(x,n)=1 }$, and $q$ an odd prime number.

For all $xin mathbb{Z}$, $overline{x}$ represents, in this question, the class of $x$ modulo $q^alpha$, and let’s use the notation $dot{x}$ for the class of $x$ modulo $q$ and consider the morphism of groups
begin{align*}
Psi : G_{q^alpha} &rightarrow G_q \
overline{x}&mapsto dot{x}
end{align*}

Prove that $|KerPsi|=q^{alpha-1}$ (with $|KerPsi|$ the notation for order).

This question is a step by step to prove that $G_{q^alpha}$ is cyclic, but I can’t solve this part.

sdl – SDL2 – show a tooltip at the cursor that displays RGB of the pixel under the cursor?

I’m writing an SDL2 program, in which I create a SDL_CreateWindow and get its SDL_GetWindowSurface, then I prepare some pixel updates on a separate SDL_CreateRGBSurface and SDL_BlitSurface the result to the window surface before I SDL_UpdateWindowSurface it to the screen.

I would like to have a mouse tooltip feature that would display a dynamic tooltip at the cursor position with some information (such as RGB info of the pixel under the mouse). But the tooltip display should be separate from the pixels of the window surface, not blended into it. Is it possible to do that with SDL2? If so, how would a minimal working example look like? (I googled around but did not see any examples.)