04th Août2022

by carodah

I’ve tried search and removed  »  » + « ? » + space a lot of time, but no successful. A: I’m not 100% sure what your problem is, but if all you are trying to do is drop the spaces into the file, then you can use a loop: for %%x in (« %~1 ») do set « var=%%x » & SET « var=!var: =! » & SET « var=!var: \= » & SET « var=!var: \ « ! » & SET « var=!var: |= » & SET « var=!var: |! » & SET « var=!var: « ` » » The : will switch any spaces that are converted from your original string into \\, which is a escaped backslash. If you want to convert all characters in the string, you can replace the : with a single!. Q: Verification of $[\phi(x):\phi(y)]=e^{K(y-x)}$ Let $\mathbb{F}_p$ be the finite field of $p$ elements and $\phi : \mathbb{F}_p \rightarrow \mathbb{F}_p$ a linear surjective homomorphism with kernel $\langle 0 \rangle$. Let $K=\sum_{n=1}^\infty\frac{1}{p^n}$ and $x,y \in \mathbb{F}_p$. I want to show that $$[\phi(x):\phi(y)]=e^{K(y-x)}.$$ Attempt: Note that $|\ker(\phi)|=p^\ell$ for some $\ell \in \mathbb{Z}$. If $[\phi(x):\phi(y)]=e^{K(y-x)}$, then \begin{align} &[\phi(x):\phi(y)]^K[\phi(x):\phi(y)]=e^{K(y-x)\times K(y-x)}\\ &[\phi(x):\phi(y)]^Ke^{K(y-x)^2}=e^{K^2(y-x)^2}\\ &[\phi(x):