group theory gr. – Relation to the Bruhat cell

Let $ g in mathrm {SL} _n ( mathbb Z) $ such exists $ v∈ mathbb Q ^ n $
such as $ v, gv ,. . . , g ^ {n – 1} v $ is a $ mathbb Q $-base of $ mathbb Q ^ n $ and there is a $ mathbb Z $-based $ w_1 ,. . . w_n $ of $ mathbb Z ^ n $
as for each $ 1 ≤ k ≤ n $,

$ mathrm {span} _ mathbb Q ${$ w_i | 1 ≤ i ≤ k $}$ = mathrm {span} _ mathbb Q ${$ g ^ {i – 1} v | 1 ≤ i ≤ k $}.

Why is it $ g $ conjugate in $ mathrm {SL} _n ( mathbb Z) $ to a matrix that belongs to Bruhat's cell $ B_σ $ corresponding to the permutation $ σ: = (12 … n) $?

ios – iPad as possible cell phone?

Is it theoretically possible that with the existing hardware in a cellular iPad model, the device software can enable it to become a great iPhone (make phone calls + send texts via a cellular system)? or is there a physical limitation that would prevent that? For this question, suppose a GSM operator (ie T-mobile) and an iPad Air with

How to quickly change the text color of a cell in Google Sheets?

How can I quickly, in one or two clicks, assign a color to the text of a cell in Google Sheets?

In order to quickly determine the status of certain data in a worksheet that I manage, I assign a text color to the value of a cell. I do this dozens of times several times a month, and it's very tedious because it depends on an external manual process (for example, looking at the value of a cell, going to do a process manual, return and manually update the color of the text cell).

I have examined the execution of a script or a macro when I double-click on each cell (not currently available), adding a drop-down menu to the cell as well as the value existing cell (impossible, as far as I know), add a check box to the cell with the existing cell value (this does not seem possible), and use text formatting from the context menu ( not available).

Delete cell element if the field is true on a display page

I have a table views page in Drupal 8 that displays the node titles. On the node, there is a checkbox field that, when checked, indicates on the view table page that this title should not display.

I thought about prepocessor_views_view_field To do this, my question is the function of processor views hook below correct?

 * Implements hook_preprocess_views_view_field()
 * @param $variables
function pnc_views_overrides_preprocess_views_view_field(&$variables){

  if ($variables('field')->field === 'field_display') {
    if($variables('field')->getValue($variables('row')) === 1){

SUM column except for cells where there is text in a cell in a separate column but in the same row? Google Sheets

I need a formula but I do not know how to do it and I do not know if it's even possible.

Here is a photo to show what I want. I hope you understand.
visual explanation

reference request – What happens when the head is in the leftmost cell and that an infinite time asks the Turing machine to move the head to the left?

I'm looking for articles with an explicit answer to the following question:

What happens when the head is placed in the leftmost cell and that an infinite time asks the Turing machine to move the head to the left?

The article "Theory of Infinite Time Calculable Models" contains the following succinct note:

The calculation stops only when the stop the state is explicitly obtained and, in this case, the output is the one that is written on the output tape. (If the head falls off the tape, no output is given.)

Does this mean that we can introduce a special program? Fault that occurs if the head falls off the tape, stops the calculation in exactly the same way as stop done but we have to ignore all the programs that reach the Fault State?

The article "The computing forces of Turing machines in infinite time on α-tape" contains the following information:

When the device is prompted to move the head to an undefined location, its default position is $ C_0 $. This occurs when a left move instruction occurs while the head is on a boundary ordinal cell because there is no "next cell left" determined in such cases.

I'm not sure that the notion of limit ordinal cell here includes the leftmost ($ 0-th) cell, but in all cases, the model of $ alpha $The Turing bands described in this document differ from the original model. This document is therefore not entirely relevant.

The first part of my question is: does anyone know of any other documents dealing with the problem? (I remember very well reading a detailed view of the problem in a document a few years ago, but for some strange reason, I can not find this document now.)

The second part of my question is: can we simply replace the instruction "move your head to the left" with the instruction "do not move your head" in such situations? That is, if the head is in the leftmost cell and the current instruction is "move the head to the left and go to the state $ s_i $", The machine does not move the head at all, but goes into state $ s_i $. Does such a solution in any way affect the computing power of Turing machines in infinite time?

How to analyze an iPhone cell, iOS devices with AV?

Regarding iOS, devices and cell phones / watches, iPads, etc.

How can I scan them with an AV?

google sheets – Extract specific phrases from one cell and pass them on to another

The functions you are looking for are REGEXMATCH combined with OR and IF.
So, IF will test three conditions (with OR) and then if OR returns a TRUE boolean, copy the contents of the cell, otherwise do what you want.


Here's a way to do it with one formula


Conditional formatting. How to highlight a cell if its value is a multiple of a given number

I want to apply conditional formatting to any cell in a range containing a multiple value of it.

THIS IS TO SAY: Apply bold font in any column cell A it is a multiple of 4 (4,8,12,16,20,24, …).

Can someone help with that?

How to find two cell column values ​​in another Excel file and how many times it has been found

I have an excel where I want to look up as a 43675 cell and another 2010 cell value.
The two values ​​above must appear in the same row and how many times it has been found in another Excel.
Can any one help me with this vba's