nt.number theory – integer ring of a cyclotomic extension of $ mathbb {Q} _p $

Yes. This continues, p. of Proposals 16 and 17 in Serre: Local fields.

In fact, let's leave $ n = p ^ mn & # 39; $, where $ (n & # 39 ;, p) = 1 $. Applying Proposition 17, we see that $ mathbb {Q} _p ( zeta_ {p ^ m}) $ has an integer ring $ mathbb {Z} _p ( zeta_ {p ^ m}) $. Then, applying Proposition 16, we see that $ mathbb {Q} _p ( zeta_ {p ^ m}, zeta_ {n & # 39;}) $ has an integer ring $ mathbb {Z} _p ( zeta_ {p ^ m}, zeta_ {n & # 39;}) $. However, it is simple that $ mathbb {Q} _p ( zeta_ {p ^ m}, zeta_ {n & # 39;}) = mathbb {Q} _p ( zeta_ {n}) $ Y $ mathbb {Z} _p ( zeta_ {p ^ m}, zeta_ {n & # 39;}) = mathbb {Z} _p ( zeta_ {n}) $, so we are done.

Schengen visa extension – Important personal reasons


Do you really have a visa or are you traveling in rule 90/180 as a person without a visa?

Based on the samples given, private The reasons do not seem to meet the condition:

Examples of important personal reasons:
Business reasons or urgent professionals that were not predictable before entry

However, the last part offers the possibility of a reasonable solution.

Assuming that a reservation has not been made for the rest of the family, a clearly stated letter of intent that, on condition that your stepdaughter leaves to stay, extends, that a common vacation will be made for the entire family. Family: It was not part of the original plan.

Along with the Application form, she must request it at the local Foreigners office (you may have to use a form from that local office).

Then it would be up to them to decide to make an exception or not.


This is county specific, so each country can treat this differently. In Germany, an extension can only be requested locally and, if extended, is made immediately. Going to the Portuguese embassy may not be very useful.

Chrome Extension to sign in to the website and then navigate [on hold]

I am looking to create a Chrome extension that navigates to bet365, login and place bets in certain markets (markets driven by a data source), any help greatly appreciated.

magento2.3 – The price slider extension does not work in Magento 2.3

I have installed the free third-party extension for the price slider in Magento 2. After installing the extension, I ran the update, implementation and cache commands, but I receive the following error:

Exception #1 (PDOException): SQLSTATE(42S22): Column not found: 1054 Unknown column 'e.created_in' in 'where clause'

I have also tried to execute the reindex command but there is still an error.

Could someone help me correct this error?

Schengen visa extension? – Exchange of travel packages

I have an existing Schengen visa that I applied for through the German consulate while traveling to Germany, valid until October 31. I applied for this visa using my children's passport, which is a British citizen. And now I bought a ticket to Spain and returned from Spain to the United Kingdom on November 2. I will travel with my British children again. I am trying to apply for another visa. But I have been told that I have to cancel my other Schengen visa and reapply to Schengen in Spain.
1. there is the possibility of extending
2. Can I simply apply for a visa through the German consulate, since I already have a visa and try to continue, if that is the case, how would I do it?
Thanks x

co.combinatorics – Extension of Dinitz conjecture to rectangles

The Dinitz Conjecture, which Galvin later demonstrated in a more general way, stated that given a $ n times n $ matrix, its elements could be filled exactly as a Latin square, where the elements in each row / column are chosen from a set (list) of $ m ge n $ symbols

Is an extension of this possible for partial Latin rectangles? It is given a size rectangle. $ m times n $ and symbols $ ge max (m, n) $Is it possible to fill a maximum of $ min (m, n) $ symbols in each row and / or column so that the symbols in each row, column and diagonal (places $ a_ {ij} $ with $ j = i $, where $ i, j $ denote row and column indexes and $ to $ denotes the symbol) are they different?

javascript: create the Chrome extension to replace div with a specific class

Hi, I want to create a Chrome extension that will automatically replace a div with a specific class to another div. There is an online CAD software called Ondrive and I want to see a modified version of its menu.

Note that the div that will be replaced and the result will contain several more elements inside (therefore, many brands such as divs, svg images, text and links)

There is a good tutorial in the following link to replace the text, but I don't know how to modify it with something so complex

How-to: Make your own text-replacing Chrome extension like ‘Millennials to Snake People’

var elements = document.getElementsByTagName('*');

for (var i = 0; i < elements.length; i++) {
var element = elements(i);

for (var j = 0; j < element.childNodes.length; j++) {
    var node = element.childNodes(j);

    if (node.nodeType === 3) {
        var text = node.nodeValue;
        var replacedText = text.replace(/(word or phrase to replace here)/gi, '(new word or phrase)');

        if (replacedText !== text) {
            element.replaceChild(document.createTextNode(replacedText), node);

magento2 – Adding block to default.xml from the extension

Hi, I create a custom module that allows people who have logged in and have an attribute to show a button. I would like to do everything from the extension without touching the default.xml. I would like to refer to the container and place a block inside it, but it doesn't seem to be working.
Here is the block:

_customer = $customer;
        $this->_customerUrl = $customerUrl;
        $this->httpContext = $httpContext;

        parent::__construct($context, $data);

     * @return string
    public function isLoggedIn()
        if $this->$_customer->create()->addAttributeToSelect('is_allowed',array('eq'=>1)) {
            return $this->httpContext->getValue(MagentoCustomerModelContext::CONTEXT_AUTH);

Here is the design file located in vendor / namespace / view / frontend / layout


For some reason he is not putting it in the container and was wondering if anyone could point me to the right place.

here is the defualt.xml










Any help is appreciated and thanks!

Sync settings or backup of the Chrome extension?

Chrome extensions are easy to sync.

Is there a trick to synchronize or download and back up the Extensions configuration?

Example use case:

  • There are a lot of news websites where I need to disable AdBlock to
    Read them.
  • If I move to a new PC, I currently have to, one by one, disable
    Adblock on each of those sites again.
  • I wish I could have a faster technique to quickly copy the configuration
    from one PC to another.

Representation theory rt – Bruhat orders and does not disappear extension groups

Leave $ P_ {x, w} (q) $ Be the polynomial Kazhdan Lusztig. It is well known that $ P_ {x, w} (q) neq 0 iff x le w $.

For the interpretation of the polynomial Kazhdan Lusztig in terms of extension group, he argues that $ x le w iff mathrm {Ext} _ { mathcal {O}} ^ i (M (w cdot (-2 rho)), L (x cdot (-2 rho))) neq 0 $ for some $ i ge 0 $, where $ M ( eta) $ it's the Verma module, $ L ( eta) $ it's your simple and unique quotient $ rho $ It is the average sum of positive roots.

Leave $ mu $ be an integral antidominant weight, $ Delta $ be the set of simple roots $ Sigma = { alpha in Delta: langle mu + rho, alpha ^ lor rangle = 0 } $, $ W ^ { Sigma} = {w in W: w <ws_ alpha, forall alpha in Sigma_ mu } $ Y $ x, w in W ^ { Sigma} $.

Not hard to show $ mathrm {Ext} _ { mathcal {O}} ^ i (M (w cdot mu), L (x cdot mu)) neq 0 $ for some $ i ge 0 implies x le w $.

I would like to know if the opposite:

$ x le w implies mathrm {Ext} _ { mathcal {O}} ^ i (M (w cdot mu), L (x cdot mu)) neq 0 $ for some $ i ge 0 $

Is it true or not? If it is true, I would like to know why. If not, any counterexample?