ag.algebraic geometry – understand the Hasse-Weil boundary

I recently came across the Hasse-Weil boundary while studying number theory, but I know almost nothing about algebraic geometry, so I don't think I fully understood it.
Does this statement have the same meaning as the Hasse-Weil border?

: For an integer coefficient polynomial $ P (x, y) $, the number of solutions $ N $ to the $ P (x, y) = 0 $ in the $ mathbb {F} _p $ satisfied $ | N-q | le 2g sqrt q $
(I don't know what a genus is; I just saw it as constantly irrelevant $ p $ )

Sudo – understand what it does

I just want & # 39; sudo & # 39; understand better.

I'm on my Ubuntu 18.04LTS computer as & # 39; alan & # 39; logged in, who is a normal user and is a member of the & # 39; sudo & # 39; group.

First I did that (I entered my password correctly):

sudo touch /lost+found/test.file

I get this:

$ ls /lost+found/
ls: cannot open directory '/lost+found/': Permission denied


$ sudo ls /lost+found/

That is exactly what I would expect. However, I don't understand why I get this:

$ sudo -u alan ls /lost+found/
ls: cannot open directory '/lost+found/': Permission denied

Why can't I run a & # 39; admin & # 39; command with my own user?

How do I understand the C / S structure of the "host-based vulnerability scanner"?

We know that the Vulnerability Scanner has three types Host-based Scanner, Network Scanner, Database Scanner.

The Host-based Vulnerability Scanner to use C/S Structure, and the host will run an agent.

How do I understand the C / S structure? is the Client is Agent and Server is the host's operating system?

Trying to understand the com.facebook.orca

I have read some sources about recovering deleted messages in Messenger etc. I know you should be able to see the messages if you can access the Android> Data> com.facebook.orca> Cache> fb_temp folder on your Android phone. But you have to "root" the phone, as another question said earlier.

I had another question. Suppose you deleted messages, then deleted the entire Messenger app from your phone, then reinstalled the app, and then wrote (and possibly deleted) some new messages in the app if the original messages were deleted before the entire app deleted was deleted still be in this folder?

Python – Understand how the IM / Chat part of the app is structured

I've read a lot about XMPP and I'm still not sure if I fully understand how XMPP works and how I would create the instant messaging part of my Python app.

Am I right when I think I need to use something like sleekxmpp or aioxmpp to route the messages to a server like IoT Broker / ejabberd / open fire (recommendations for a good free one would be great) that I need to install on my computer ?

Don't I need a better server than my computer when the number of user messages increases? Is it possible to use a cloud server and how would this work with IoT Broker or ejabberd ….. or did I misunderstand this bit?

I also plan to save the chat history in a MySQL database. I can imagine that this has to be hosted on a server (AWS or something?).

Javascript – I can't understand why CSS Transition doesn't work on keydown

I'm trying to create an animation to move the block right and left. But I can't understand why it doesn't work. For example, it works well for on-click events. Here is my codepen.
Thank you very much

.box {
  background-color: gray;
  height: 100px;
  width: 100px;
  transition: margin-left 0.5s cubic-bezier(0, .7, 0, 1);
  transition: margin-top 0.5s cubic-bezier(0, .7, 0, 1);

.move-right {
  margin-left: 400px;

.move-left {
  margin-left: 0px;
const box = document.getElementsByClassName('box')(0);

document.addEventListener('keydown', function({keyCode, which}) {
  const keycode = keyCode ? keyCode : which;
  switch(keycode) {

Set theory – how do you understand the interface between consistency strength hierarchy, reverse mathematics and proof-theoretical order analysis?

I am aware of three important "hierarchies" of mathematical theories, but I do not know how to relate these hierarchies. Here are the hierarchies I'm thinking of:

  1. Strength of consistency. My understanding is that you are looking at (theories recursively?) Theories $ T $ arithmetic (or which interprets the language of first-order arithmetic) of sufficient strength to establish a scheme for the syntax of first-order languages. You arrange these theories (in part) by saying that $ T> T & # 39; $ if $ T $ proves the consistency of $ T & # 39; $ (when $ T & # 39; $ is encoded according to the syntactic scheme mentioned above).

  2. Reverse math. My understanding is that you are looking at theories here $ T $ second-order arithmetic (or those interpreting the language of second-order arithmetic) and (partly) orders them directly according to their implications.

  3. Evidence-theoretical order analysis. My understanding is that you are looking at theories here $ T $ arithmetic (or which interpret the language of first order arithmetic) and orders them according to theirs proving theoretical atomic numberthe highest of all (countable) ordinal numbers $ alpha $ so that there is a relationship $ R subseteq mathbb N times mathbb N $ definable in $ T $ so that $ T $ prove it $ R $ is a good order (although the sense in which $ T $ can even express The $ R $ is a good order, though $ T $ is first order is something I don't quite understand), and $ R $ is (externally) isomorphic to $ alpha $.


  1. Where do the areas of application of these hierarchies overlap?

For example, the "strongest" theories (such as ZFC + large cardinals) usually seem to be examined for consistency, as opposed to reverse math or proof theory. I have the impression that proof-theoretical ordinal numbers are most often used for relatively weak theories, and that the reverse math is somewhere in the middle. But I'm not even sure where to look for overlaps in these areas, also because the types of theories that are considered in each hierarchy are slightly different.

  1. How are these hierarchies related when domains overlap?

In general, I imagine that there are no direct implications saying that one of these sub-orders refines one of the others (even if their areas of application coincide). But I imagine there are some general tendencies – a stronger theory in one hierarchy should probably be stronger in another hierarchy as well.

  1. Should I really see these three hierarchies as "comparable" in the sense that they convey an idea of ​​the "strength" of a theory? And are there other hierarchies that I should also consider in this regard?

Refusal of entry – Can I book a return flight with a visa that expires before the return flight? (I understand that I need to extend the visa there.)

Can I book a return flight with a visa that expires before the return flight? (I understand that I need to renew the visa there.) The visa has too much time to check, and the U.S. Embassy here is currently not accepting new applications at COVID-19. I want to return one month after my current visa expires. Can I enter and fly?