Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular, without using $\lambda_1\cdot\ldots\cdot\lambda_n = det(A)$.

I would like to know if there is any proof without using the fact that:  $$\lambda_1\cdot\lambda_2\cdot\ldots\cdot\lambda_{n-1}\cdot\lambda_n = det(A)$$  I managed to prove that if $\lambda = 0$ then, A is singular, by:  $$ det(A-\lambda\cdot I)=0 \Rightarrow det(A-0\cdot I)=0 \Leftrightarrow det(A)=0 $$  However I can't prove that if A is singular then, $\lambda = 0 $.  I talked to my teacher and he told me that maybe I could prove by induction that:  $$ p(\lambda)=a_n\lambda^n+\ldots+a_1\lambda+a_0 $$  where,  $$a_0=det(A)$$  Then:  $$ p(\lambda)=a_n\lambda^n+\ldots+a_1\lambda\Rightarrow p(\lambda)=\lambda(a_n\lambda^{n-1}+\ldots+a_1) $$  which guarantees that $\lambda=0$ is an eigenvalue.  If anyone could help, I would greatly appreciate it.


What are duties for jobs like Professor, Lecturer, Research Scientist, Research Assistant, and Research Fellow in the UK (Oxford)?

In Oxford's job website ( and ), I see positions including Professor, University Lecturer, Departmental Lecturer, Research Scientist, Research Assistant, and Research Fellow. What are the differences between the roles/duties and salary between these?  These job titles are discussed in answers to  but only in terms of career progression,  without much detail as to roles, duties, and salaries.


How to override controller of other modules?

Let's say in /var/www/drupal8/core/modules/search/src/Controller/SearchController.php below is the snippet  class SearchController extends ControllerBase {      ...      ...    public function view(Request $request, SearchPageInterface $entity) {         ...        ...       if (count($results)) {          $build['search_results_title'] = array(         '#markup' => '
' . $this->t('Search results') . '
',        );      }       ...    }  }   So  in the above snippet I want to change the text Search results in line  '#markup' => '
' . $this->t('Search results') . '
',   I want to override above view method extending class SearchController in my custom module.  What are the exact steps to do this?  I am using drupal 8.2.1.


Is there a way to hide all file extensions like in Windows?


There is a standard CW-topology on the finite product $X\times Y$ of CW-complexes $X$ and $Y$. Is there a standard CW-topology on an infinte prodcut $\prod_{n=1}^{\infty}X_{n}$ of CW-complexes? With the usual product topology such spaces are not even locally contractible. If so, what would this structure be explicitly for an infinte product of spheres $\prod_{n=1}^{\infty}S^k$?   Edit: Perhaps this question is more explicit. If $CW$ is the category of CW-complexes does the forgetful functor $CW\to Set $ preserve (at least countably infinite) products? A positive answer would imply that you can identify a CW-structure on $\prod_{n=1}^{\infty}X_{n}$ which would provide a topology finer than the usual product topology.


How can I hide the console window in a PyQt app running on Windows?

Surely this is possible? I have been hunting through PyQt tutorials and documentation but cannot find the answer to it. Probably I just need to phrase my search query differently.  [Edit]  Thanks PEZ for the answer - more details including use of the .pyw extension in


Find all files in the current directory and its subdirectories with the extension .png

In a directory and its subfolders I need to see all the files with the png extension.  For this, I used the command ls -R *.png  I get an error saying that the directory *.png doesn't exist. I am surprised that my regular expression is not recognized.  ls: Cannot read '*.png': the file or the directory doesn't exist


rest app php "Trying to get property of non-object"

I would need some help on my rest app plz. I'm trying to understand the reason of this error message "Trying to get property of non-object" but I'm stuck  I commented the following snippet who's manage a formations create form :  header("Access-Control-Allow-Origin: *"); header("Content-Type: application/json; charset=UTF-8"); header("Access-Control-Allow-Methods: POST"); header("Access-Control-Max-Age: 3600"); header("Access-Control-Allow-Headers: Content-Type, Access-Control-Allow-Headers, Authorization, X-Requested-With");  include_once '../config/database.php';      // Database connection file  include_once '../objects/formation.php';    // Formation class file  $database = new Database(); $db = $database->getConnection();  $formation = new Formation($db);            // class Formation                $data = json_decode(file_get_contents("php://input"));  // Posted datas   $formation->formation = $data->formation;   // This line return an error : Trying to get property of non-object  // var_dump($data)      return an object(stdClass) with a ["formation"] property // var_dump($formation) return an object(Formation) with a ["formation"] property  if($formation->createFormation()){   echo '"Message": "Success"';   }   else {     echo '"Message": "Failed"';   }   I don't understand why the line "$formation->formation = $data->formation;" doesn't work ...  Did I use a wrong syntax ? Any advices ? Thx


What arguments did Maxwell use to add the extra term in Ampère's original law?

I have read in Griffith's Introduction to Electrodynamics that Maxwell's correction on Ampère's original law, $\nabla \times \mathbf{B}=\mu_{0}\mathbf{J}$, fixes the problem that arises from applying $\nabla ·$ to the equation:  $$0=\nabla \cdot(\nabla \times \mathbf{B})=\mu_{0}(\nabla \cdot \mathbf{J})$$  The RHS is not necessarily zero, as it happens in the cases of non-steady currents. So, using the principle of conservation of charge and Gauss's law, it can be found that adding the extra term $\epsilon_0\mu_0\frac{\partial\mathbf{E}}{\partial t}$ overcomes the problem.  However, Griffith says that Maxwell's reasons had not to do with the principle of conservation of charge but with the concept of "ether".   Which were these reasons he followed in order to make the correction?


Is it possible to transfer a domain without a "gap" in Whois privacy protection?

I currently own several domains on which I am using a Whois privacy protection service to hide my personal details. In the near future, I would like to transfer some of these domains to a different registrar.  It has been many years since I last performed domain transfers, so I am no longer knowledgeable about what it involves. However, I have read from several registrars that they ask their customers to disable Whois protection before effecting a domain transfer. Since there are several websites out there that publish archived versions of Whois information (and ask handsome money for the information to be hidden, of course), I would prefer to avoid having such a "gap" in my privacy protection.  I figured that these websites would fetch Whois information mainly when a query is effected through their own website. However, I have found out that at least one of these sites had a copy of the Whois information for a new domain up on their site within hours after I registered it, so they must have some other source (of course I used a Google search to find that out, not their own site). What that tells me is that the time it takes for the domain transfers to go through would be more than enough for these rogue websites to cache my information.  If my new registrar offers privacy protection for domains right from the point of registration as well, is there no way to transfer the domain between the two without reverting to my default Whois information in between?


I've noticed the text of the Hot Meta Posts box is not within its limits. I guess this would happen for any question with a word that's long enough:


Why do i get this error message while trying to run sudo apt-get update

I want to upgrade my python version 2.7 on ubuntu 14.04 to 3.7 If i run sudo apt-get update, a lot of error message will be displayed.  i had tried a lot of of suggestions but none work. Can someone help me out please.   Here are the errors i got:   Failed to fetch http://archive.ubuntu.com/ubuntu/dists/trusty/Release  Unable to find expected entry 'restricted/source/Sources' in Release file (Wrong sources.list entry or malformed file)  E: Some index files failed to download. They have been ignored, or old ones used instead


So I am playing multiplayer four corners farm and I want to know 2 things. 1, the mini rock quarry will become better based on your mining level. In multiplayer, who’s mining level affects it? Same question for monsters on the farm, as they scale with combat level.


I added 3/4 cup of oil instead of water to a quick bread mix. Can it be saved?


Why this character is punished instead of being honoured?

In the final episode of Game of Thrones, a pivoting moment resides in       A gathering where all greatest remaining Lords & Ladies of Westeros are presented Tyrion and Jon Snow by Grey Worm, in order for them to be judged.   I don't understand how the Council made up by the remaining Lords & Ladies was so merciful with Tyrion and so harsh for Jon Snow.  First, it seems that Grey Worm and the Unsullied (which for some reason have not executed the two prisoners the moment they found out they successfully conspired to kill their queen, and waited for a trial gathering Lords of the kingdom to be assembled) hold a lot of authority on the prospects of the prisoners, and almost hold as hostages the Lords & Ladies.   However, as the scene unfolds, it seems they decide to fall in with the Council's authority on its own lands.   As such, they accept to see Tyrion go from allegedly sentenced to death for treason to choosing the future of Westeros and becoming the Hand of the new king, as it's what the new king and the rest of the Council wants.  However, Jon Snow is most severely punished by a life-long exile in the Night's Watch (taking the black being often represented in the series as an ultimate choice with death). But most of the Lords & Ladies at the table are in fact on Jon's side, or, if not exactly, are at least expected to have been horrified by Daenerys's slaughter and wishful for her cruel reign to end. In fact, we're very much in the same situation as with the Mad King prior to Robert's Rebellion. When Jaime Lannister killed this king, judged by most as a tyrant, he was pardoned by the new king and remained a King's Guard knight.  At the gathering, except for Grey Worm which seems to respect the Council's decisions, only Yara Greyjoy seems to be unhappy about Daenarys's death. Though, her opinion is of light importance as, as opposed to a lot of others present in the Council and particularly Jon's allies, she has played a very little role in the Long Night and the attack against Cersei.  How come Jon was punished for killing a queen almost everybody judged as a tyran deserving to die, and not honoured for having accomplished the only move leading to potential peace in Westeros? All the more so when the two persons that can truly decide his fate – the King and his Hand – are his brother and the man that convinced him to kill the queen to save the Realm?  Finally, as discussed in comments for this , Jon is at this moment the true heir to the throne, and an important part of the Council is aware of it. In fact, the plot insists heavily on that Daenerys decided to reign by fear because she was afraid that the people of Westeros would turn to Jon, who they like better and who has a better claim to the throne. But when she is ruled out, this much advertised turn of events strangely doesn't take place.   Edit: I don't believe it's a duplicate of , as my question asks why the judgement for Jon is so harsh, while the other one asks why Tyrion judgement ends up freeing him. Those are two different characters, and I can't see the answer to the other question that would apply to this one.


Why do some logos look dated? How does design age?

What makes a design look old? How subjective is this? Who decides?   Look at this Bell logo:    It's from 1969. And boy, does it look that way. It's simple and minimal, but.. it looks old.  Take a look the this BP logo:    Old. And not too pretty. And yet.. someone thought it's a good idea.   And something I find ridiculously curious: the old Chrome vs the new Chrome logo:    I remember when I first saw the new icon. I thought it was pretty bad. It lacked something. Today, I look at the old one and smile, thinking "aw, that was ugly. In a cute way, though".  This doesn't only apply to logos that have been improved, I think:    Sorry, Nike. I love the brand, but that logo looks like you paid $35 back in '71 for it.  Now let's go for something else, though a bit off the real logo-esque topic:    I'd believe if someone told me this was a 2013 model. I want one, by the way.  Take a look at most cars from the 90s. 80s. 70s. 95% look horrible. 4% are nearly classic, 1% are so ugly they have their own cult.  What drives the way we perceive "new" vs "old" design?  Look at the web. Flat UI is becoming more and more popular, making gradients look old.  Why? Who decides this? How much of this is about taste and how much about trends?  I mean.. you couldn't slap the old, rainbow-colored Apple logo on the back of every MacBook out there and make it look good today, could you?


when parent process is killed by 'kill -9', how to terminate child processes

kill -9 will send SIGKILL signal to parent process. But SIGKILL can not be caught. So How do parent process terminate child processes?


What is the best way to get diamonds in minecraft?

I know the Y11 Strip Mine and the Y11 Strip Mine/Poke Hole methods (mining to Y11 and then mining 5 blocks forward and as far as I can reach to the left, right, up and down), but is there any better way?    I am playing version 1.12.2.


Difference between connection.close and connection.dispose using Asp.net Connection String?

Difference between connection.close and connection.dispose using Asp.net Connection String ? for ex:  Globals.dr.Dispose();  Globals.dr.Close();


Decrypt affine cipher given encryption key

i have a ciphertext C=TLNJG formed using the equation c=(7p+11) mod 27,c equivalent to numerical equivalent character of ciphertext and p the plaintext how do i get the plaintext back? for encryption:c=(7p+11) mod 27 for decryption:p=5(c-11) mod 27 let's say i encrypt the letter B(1) I would get  c=(7+11) mod 27 c=18 mod 27=18 (letter S)  but if I do decryption using the decryption equation of the letter S I will get the letter I instead of B.Why?  p=5(18-11) mod 27 p=35 mod 27=8(letter i)


How do I perform HTML decoding/encoding using Python/Django?

I have a string that is HTML encoded:   '''&lt;img class=&quot;size-medium wp-image-113&quot;\  style=&quot;margin-left: 15px;&quot; title=&quot;su1&quot;\  src=&quot;http://blah.org/wp-content/uploads/2008/10/su1-300x194.jpg&quot;\  alt=&quot;&quot; width=&quot;300&quot; height=&quot;194&quot; /&gt;'''   I want to change that to:  <img class="size-medium wp-image-113" style="margin-left: 15px;"    title="su1" src="http://blah.org/wp-content/uploads/2008/10/su1-300x194.jpg"    alt="" width="300" height="194" />    I want this to register as HTML so that it is rendered as an image by the browser instead of being displayed as text.   The string is stored like that because I am using a web-scraping tool called , it "scans" a web-page and gets certain content from it, then returns the string in that format.  I've found how to do this in C# but not in Python. Can someone help me out?  Related


Null Pointer Exception with initialized variable

I am working on this asteroid game inside of greenfoot and my code keeps spiting out a       java.lang.NullPointerException.    The code is below. Error occurs on line 50:      count = world.numberOfObjects();.    I know there are several posts about this error but the research I've done about this error shows it occurs when you try to use a reference that points to null. However, I have initialized my variable so i'm not sure why this is happening. I'm still fairly new to programming so I'm probably just not understanding this correctly. Any help would be great. Thanks!      public class Rocket extends SmoothMover   { private static final int gunReloadTime = 5;         // The minimum delay between firing the gun. private static final int protonReloadTime = 500;    // The minimum delay between proton wave bursts.  private int reloadDelayCount;               // How long ago we fired the gun the last time. private int protonDelayCount;               // How long ago we fired the proton wave the last time.  private int count = 0; //count the number of asteroids    private GreenfootImage rocket = new GreenfootImage("rocket.png");     private GreenfootImage rocketWithThrust = new GreenfootImage("rocketWithThrust.png");  /**  * Initialise this rocket.  */ public Rocket() {     reloadDelayCount = 5;     protonDelayCount = 500;     addToVelocity(new Vector(13, 0.7));    // initially slowly drifting }  /**  * Do what a rocket's gotta do. (Which is: mostly flying about, and turning,  * accelerating and shooting when the right keys are pressed.)  */ public void act() {     move();     checkKeys();     checkCollision();     reloadDelayCount++;     protonDelayCount++;      Space space = (Space)getWorld(); //call space objects     World world = getWorld(); //call world objects      count = world.numberOfObjects(); //ERROR IS HERE       /**      * Add an asteroid when the starting ones are cleared      */     if(count <=2)     {         space.add();     } }  /**  * Check whether there are any key pressed and react to them.  */ private void checkKeys()  {     ignite(Greenfoot.isKeyDown("up"));      if (Greenfoot.isKeyDown("left"))      {         turn(-5);     }     if (Greenfoot.isKeyDown("right"))      {         turn(5);     }     if (Greenfoot.isKeyDown("space"))      {         fire();     }     if (Greenfoot.isKeyDown("z"))      {         startProtonWave();     } }  /**  * Check whether we are colliding with an asteroid.  */ private void checkCollision()  {     Asteroid a = (Asteroid) getOneIntersectingObject(Asteroid.class);     if (a != null)      {         Space space = (Space) getWorld();         space.addObject(new Explosion(), getX(), getY());         space.removeObject(this);         space.gameOver();     } }  /**  * Should the rocket be ignited?  */ private void ignite(boolean boosterOn)  {     if (boosterOn)      {         setImage(rocketWithThrust);         addToVelocity(new Vector(getRotation(), 0.3));     }     else      {         setImage(rocket);             } }  /**  * Fire a bullet if the gun is ready.  */ private void fire()  {     if (reloadDelayCount >= gunReloadTime)      {         Bullet bullet = new Bullet (getVelocity(), getRotation());         getWorld().addObject (bullet, getX(), getY());         bullet.move ();         reloadDelayCount = 0;     } }  /**  * Release a proton wave (if it is loaded).  */ private void startProtonWave()  {     if (protonDelayCount >= protonReloadTime)      {         ProtonWave wave = new ProtonWave();         getWorld().addObject (wave, getX(), getY());         protonDelayCount = 0;     } }  }


Python csv.reader: How do I return to the top of the file?

When I'm moving through a file with a csv.reader, how do I return to the top of the file.   If I were doing it with a normal file I could just do something like "file.seek(0)".  Is there anything like that for the csv module?  Thanks ahead of time ;)


$100$ prisoners problem - But here they write their guess on paper

A variant of the $100$ prisoners problem.  $100$ prisoners are given each either a white hat or a black hat. They can see each other's hat but not their own and they cannot communicate.   Each prisoner must write(not yell like in the classic one) on a piece of paper his guess for the color of his hat, which can be "black", "white" or "pass" ($3$ options instead of $2$ in the classic one).  If not all prisoners choose "pass" and all those who didn't pass guess correctly, then all prisoners are sent free.  Invent a strategy for the prisoners that will maximize their chance of getting free, assuming the hats are chosen randomly.  My current thoughts: It is possible to find a strategy in which the chances increase with the number of prisoners. For $3$ prisoners a strategy might be to choose "pass" if the colors of the two hats are different, otherwise to choose the opposite of the same color. This gives a $75$% chance of getting free.


Why do external observers see LIGO results if an object falling into a black hole never reaches the event horizon?

If I throw a clock towards a black hole, its time slows down, it is redshifted, and according to many theories it never reaches the event horizon from my point of view. How is it then, that a star can fall into a black hole, and be observed to do so by me (by its emission of gravitational waves)?


How does a simple weighing balance actually work?

I have made a simple sketch of how I think the system looks like. My problem is:   I always thought that the angle the balance makes is a function of the difference between the two masses (or the difference in torques): a small difference in mass will give a small angle, and in the limit the angle will be equal to zero when both masses are equal.  Now I cannot derive that from the picture. As I see it now, the torques will always be different, no matter at which angle the balance is tilted, since both torques scale with the same sine. This leads to a equilibrium only when the balance is completly vertical (or in my figure pressing against the triangle), which is contra-intuitive. Moreover, when the masses are the same, equilibrium would be obtained at every angle as can be seen from my figure (torques are equal independant of the angle of the balance), which would contradict with the working of a balance.  I see that my question kind of overlaps with , but the accepted answer doesn't solve my problem.   (One way to solve my problem, would be to draw a half circle instead of the triangle in my figure, so the lever of the torque becomes a function of the angle. But somehow in my head the schematic drawing of a balance is with a triangle in the middle. Is this perhaps the simple solution I'm looking for?)


Prove that there is not a retraction of the Möbius band to its boundary

I would like a hint to solve the following problem:  Let $X$ be the Möbius band and $A$ its boundary (which is a circumference). Prove that there is not a retraction $r:X \rightarrow A$.   Each try I did gave no solution.   Any hint to solve this problem?  Thanks!


For the case where universe is not flat, has it got an extrinsic curvature towards (an)other spatial dimension(s)?

I got the idea that expansion of the universe is not to somewhere, it is just getting stretched of spacetime since a point of singularity. And I know that universe was calculated as flat (which means sum of angles of a triangle is exactly π ignoring local instrinsic curvatures caused by celestial masses) with a very small error rate. But still universe is possible to be hyperbolical or elliptical. If it is elliptical, when you travel on a straight route, you will eventually arrive at your starting point (we assume expansion of the universe is frozen). So, can we say that in that travel I am actually circumnavigating on the surface of a higher dimensional sphere and that means spacetime has an extrinsic curvature beside its intrinsic curvature.


Mid 2014 Macbook Swollen after High Sierra / What should I do?

This discovery came after my latest question:   I use my macbook on a stand with good airflow, after High Sierra, I noticed unusual high heating along with poor gpu performance, afterwards I noticed screen damage, and now, I discovered that my macbook is physically swollen, 2-3mm's I'm guessing  The issues could be unrelated to High Sierra, yet, it would be too big of a coincidence if it's not the cause, as things were breezy beforehand  Here's a picture of the issue:     The trackpad area is swollen, the trackpad doesn't click any more, the battery reports "Normal" condition (Cycle count: 12), the lid doesn't close any more, but everything luckily works for now  I assume it's the battery that's swollen, but even with the high heating I complain about, the GPU temperatures was 80C at most and enclosure temps weren't extremely high  It's a shocking issue for me, I'm wondering whether there is a solution other than buying a new Macbook, unsure how to approach the issue in general, and since I use the device daily, really don't want to part with it even for repairs or inspection, I'm located in Turkey  Also curious why I experienced these issues with High Sierra and whether anyone else has similar experiences


How does stock exchange affect the company?

People invest in the company initially using an IPO. Now I don't understand how trading the stocks with others (who didn't participate in the IPO) would benefit the company. Also, why do the people invest in stocks in the first place when some companies like Google don't even give dividends (part of their profits) to the shareholders?


Can not understand simplification of equation

Hello,  in the picture there is an equation I can not understand. What I do not understand is how to get to the first step. I have been thinking and thinking but can not find an explanation. Could somebody please explain? Thanks.


I want to create a html based chart like below , not sure how to proceed


How do I disable Wi-Fi roaming? (disable autoconnecting to the strongest AP)

I can't find a way to disable Wi-Fi roaming on my Mac so I can connect to a specific AP and stay associated to it without roaming to the strongest AP. Is there any way I can do that?  My MacOS version is High Sierra 10.13.2.  I have already tried all airport JoinMode settings ( /System/Library/PrivateFrameworks/Apple80211.framework/Versions/Current/Resources/airport prefs JoinMode) and the "airport-bssid" tool that is available on GitHub, and both solutions didn't work.


CR calculation for monsters at low level in D&D 5e

In order to master my first campaign soon, I wish to change/create some monsters (what I love). However, I don't understand the calculating of the CR. So, I tried to calculate the CR of existing monsters to understand… and I don't find the values of the Monster Manual.  I'm using the DMG p. 274-275, calculating the defensive and offensive CR to make an average.    Here are two examples. First, the zombie. It has a CR of 1/4.  Defensive: average 22 hp and AC 8. I look in the table for HP: I have 1/4. Then, according to the book, I drop the CR by 1 for every 2 points of difference between the suggested AC for the CR. The suggested CR is 13 and the zombie has 8. So, I lower the value by 2. Negative CR makes no sense, so I will keep 0. Defensive CR: 0  Offensive: average damage 4 and attack bonus 1. I look in the table for damage: I have 1/4. Then, according to the book, I drop the CR by 1 for every 2 points of difference between the suggested attack bonus for the CR. The suggested attack bonus is 3 and the zombie has 1. So, I lower the value by 1. Negative CR makes no sense, so I will keep 0. Offensive CR: 0  I make the average 0! Great! A zombie has Undead Fortitude, yes, but is it worth a CR of 1/4?    Here is the second example with the bandit. He has no particularity and a CR of 1/8. I'm doing it the same way.  Defensive: average 11 hp and AC 12. I look in the table for HP: I have 1/8. The suggested AC is 13 and I have 12. Only one point of difference, I do nothing. Defensive CR: 1/8  Offensive: average damage 4-5 and attack bonus 1. I look in the table for damage: I have 1/4. Then, according to the book, I drop the CR by 1 for every 2 points of difference between the suggested attack bonus for the CR. The suggested attack bonus is 3 and the bandit has 1. So, I lower the value by 1. Negative CR makes no sense, so I will keep 0. Offensive CR: 0  The average is 1/16... So 0 or 1/8 as I wish.  I'm quite lost. I don't want to be stuck in maths, but I just want to establish monster's XP and difficulty after all. Could someone explain me what I'm missing here? Maybe creating new monsters doesn't work at low levels?


How do I turn off a command that's on repeat on Switch Bedrock?

I put a command block that would teleport "@p" so when i get close it teleports me back to another place, its Always Active and its a Repeat Command Block, I've tried lots of commands but none work, I've been trying for hours


Can anyone help me show that:  $||x|-|y||≤|x-y|$  I am new to proofs and I am not sure how I can show something as trivial as this!


How to find the sum that are not geometric series or telescoping series?

$\sum_{k=0}^\infty \frac{(-1)^k}{2k+1}$  How do I find the sum above, and I am confused that how to find the sums which are not geometric series or telescoping series.  I know Taylor series and Taylor expansion, but is it possible to reverse it from the series?


Is there a difference between modern English and formal English?

In high school I was taught that it is not proper grammar to end a sentence with a preposition. My instructor was very strict about grammar on every paper we wrote. He always said to not end a sentence with a preposition and showed the ways to not do this. Is this different now with modern English as opposed to the English I was taught in high school?


Why is the unit of measure placed before the value for currencies? Are there other measures where the unit precedes value?

$1,000 is pronounced as "one thousand dollars". Reading from left to right, it seems like it would make more sense to write the value as: 1,000$. This way the pronunciation of the value follows the way it's written. Every other numerical value I can think of places the unit after the value:   1 kg 1 L 1 m, etc...   I'm not sure if this question fits in with the rest of the questions on this site. But I'd like to know why currencies are so different from other quantities. Not to mention the need to separate groups of three digits with commas.


I have a function defined as follows: $f(x,y)= \dfrac{x^2-y^2}{\left(x^2+y^2\right)^2}$, if $(x,y)\neq (0, 0)$ and $f(x,y)=0$ if $(x,y)=(0,0)$.  Now, $$\int_0^1\int_0^1 f(x,y)\,\text{d}x~\text{d}y=-\frac{\pi}{4}$$ and $$\int_0^1\int_0^1 f(x,y)\,\text{d}y~\text{d}x=\frac{\pi}{4}.$$   The question I have is this: why does this not contradict Fubini's theorem?    thanks.


How to enlarge Ubuntu system partition to the left?

sda6 is ext4 file system and where my ubuntu is installed, 30GB. sda3 is "ntfs" file system and where my windows is installed, 400GB. sda7 is a 50 GB empty partition with "ext4" file system.   How to move the space of sda7 to sda6 to let sda6 become 50+28=78 GB.    Here's a real case of mine :( I want to add more space into my ubuntu (28.2 GB one) from other emtpy partition space.


Planet full of robots turn out to be all humans pretending to be robots

I'm looking for a classic science fiction story where a man disguised as a robot is send to investigate a robot uprising on a mining/factory planet.   He is found out to be a human and brought before the robotic overlord of the planet who offers a deal, we will not kill you if you pretend to be a robot for the rest of your life. He agrees.  He later finds out that in fact all the robots on the planet are humans that made similar deals. We all think everybody else is a robot, but in fact nobody is.   Possibly from Lem or Asimov.


Does $\langle f(x),x\rangle=\langle g(x),x\rangle$ imply that $f=g$?

Let $V$ be a a Euclidean or unitary vector space and $f,g$ be linear endomorphisms from $V$ such that $\langle f(x),x\rangle=\langle g(x),x\rangle,\,\forall x\in V$ holds. Does $f=g$ hold? Does it hold if $V$ is finite-dimensional?  I thought that this looked like a good application of the polarisation identities since the terms in there look similar to the above terms but I haven't been able to show the validity of the claim above with this or anything else so far (nor have I been able to disprove it).


Suppose $\mathcal{A}_1 \subset \mathcal{A}_2 \subset \ldots$ are $\sigma$-algebras consisting of subsets of a set $X$. Is $\bigcup_{i = 1}^\infty \mathcal{A}_i$ necessarily a $\sigma$-algebra? If not, what is a counterexample?


Prove that $\mathfrak{sl}(3, F)$ modulo $Z(\mathfrak{sl}(3,F)$ is semisimple

Let $L= \mathfrak{sl}(3, F)$, with $charF= 3$. I want to prove that $L/Z(L)$ is semisimple. I already know that $Z(L)$ is the set of scalar matrices in $L$. I think it is sufficient to show that every solvable ideal, or equivalently, the radical lies in $Z(L)$, but I don’t know how to move on from here. Any hints?


How can I fix this error in the ULS logs: ERROR: Failed to OpenThreadToken, LastError=1008?

I'm constantly getting this error since yesterday afternoon on the WFE box. No one was creating a site or anything. I'm running SharePoint 2010 with SP1.   Thanks in advance.


PROBLEM SOLVED...THANKS PGMATH FOR THE HELP.  I'm brand new to using Blender, and I'm trying to teach myself some basics to use in conjunction with 3D printing.  To do that I'm trying to 3D print a plate with a logo on it.  However, I'm having an issue with one single letter in the logo showing up as "negative" space after slicing the model in the 3D print software (Repetier-Host).  I'm lost on why this is happening or where in the process I'm messing up?  The only thing I notice that is strange is that the shadowing for the letter in Blender looks a little different from the surrounding parts (and its more noticeable when input into the print software). In Blender and Repetier-Host that specific letter still looks extruded, even though the shadowing is strange (less shadowing, i guess), and its not until the model gets sliced does it become "negative".  And it's not like each letter in the logo was uploaded separately.  The entire logo was a single PNG file originally and converted to a SVG file through Inkscape. So why this specific letter is behaving differently is very confusing?  And FYI...when making the file Blender file I appended the logo (previously extruded) with a plate part to create the file full part.  Anybody have any thoughts or experiences with something like this?  Thanks.


Finding volume of the intersection of two cylinders

Two horizontal circular cylinders both have radius a, and their axes intersect at right angles. Find the volume of their solid of intersection(where a = 1). Is it clear to you that each horizontal cross section of the solid is a square?  I know that this should be found by using integral.But I cannot find the borders and the function that I should integrate( Please do not ask for my way of solving as I could not solve it)


Why we can not call this function Base::P(int)?  class Base {    protected:     string s = "Base"; public:     void P(int a){ cout << "Base" << endl; } }; class Derived : public Base  public:     using Base::s;       void P(){ cout << "Derived" << endl; } };  int main() {     Derived a;     a.P(2);   // Error, Why we can not use Base::P(int)? }   Why we can not use Base::P(int)?


Let $C$ be a figure $‘‘8"$ in the $xy$ plane and let $S$ be the cylinder surface over $C$; that is, $$S=\{(x,y,z)\in\mathbb{R^3}:(x,y) \in C \}$$ Is the set $S$ a regular surface?  I know that the answer is no and the reason is because this surface have self-intersections in the levels of the intersection point of $‘‘8"$, but how can I prove this more mathematically?


After rendering a very short animation (simple turntable) the nodes for the textures have disappeared. The "use nodes" is active in materials but nothing in the texture node editor window, Did I hide them by accident? Hope you can help. Blender 2.91


How to CONCAT two columns into an email address

I have a university table that consists of prospective student information.  I need to populate the email address column and the format is first_name.last_name@su.edu.    I have been trying to used the CONCAT method but every time I execute the code I run into an error stating that 'invalid number of arguements'.  SELECT CONCAT(first_name, '.', last_name, '@su.edu') AS prospect_email FROM prospect;   The expected output should be first_name.last_name@su.edu.


Which one should should I use? For some reason I have always used "towards", but I see some people saying "toward", like :     A great deal of his work in economic   theory has been directed toward   strengthening the foundations of our   understanding of central banking and   social insurance--indeed, one of my   most advanced macroeconomic classes   was nothing but a set of changes rung   upon a particular model that Peter   Diamond had advanced at...   Is there a difference between the two? When should they be used?


Can supremacist Purebloods (like the Malfoys) be seen wearing Muggle clothes in the books?

First of all I only mean books, not the movies please.  To begin with, here is  - it doesn't reflect Draco's case though. I do not ask what he wears under his robes, I ask if he can be seen walking around dressed like a Muggle somewhere in the books.  So here is what I found on Draco wearing school robes:     He pulled the robes over his head and threw them onto the floor at Madam Malkin's feet... And with that, the pair of them strode out of the shop..   So apparently he was trying his new robes on some causal closes. It would do with a jeans a t-shirt I think, but trying on robes on top of other robes doesn't make much sense. Was Draco doing his shopping on the Diagon Alley in Muggle clothing?!  And later on the train:     To his relief, Malfoy seemed to decide that he had imagined the noise; he pulled on his robes like the others...   He pulled his robes on what? There was Pancy in the compartment and seemed like they changed all together. So were they in Muggle clothes, wearing their robes on those as Ron and Harry apparently do? Or did they have to change their common robes to the school ones?  Now I was thinking - do Pure-blood families arrive to the train station in their wizarding clothes? It seems against the Statute of Wizarding Secrecy, does it mean every year all Pure-bloods have to wear Muggle clothes to take their children to the station? Say, Lucius Malfoy?  We see at the and of The Order of the Phoenix that a whole bunch of adults waiting for Harry at the platform are dressed in Muggle clothing:     There was Mad-Eye Moody, looking quite as sinister with his bowler hat pulled low over his magical eye as he would have done without it, his gnarled hands clutching a long staff, his body wrapped in a voluminous travelling cloak. Tonks stood just behind him, her bright bubble-gum-pink hair gleaming in the sunlight filtering through the dirty glass of the station ceiling, wearing heavily patched jeans and a bright purple T-shirt bearing the legend The Weird Sisters. Next to Tonks was Lupin, his face pale, his hair greying, a long and threadbare overcoat covering a shabby jumper and trousers. At the front of the group stood Mr and Mrs Weasley, dressed in their Muggle best, and Fred and George, who were both wearing brand-new jackets in some lurid green, scaly material.   Though it could be they did it only this time because they intended to talk to the Dursleys. Or not? When Harry first meets the Weasleys on the platform he never notices their clothes, only their talk about Muggles and their owl.     Harry swung round. The speaker was a plump woman who was talking to four boys, all with flaming red hair. each of them was pushing a trunk like Harry's in front of him - and they had an owl. Heart hammering, Harry pushed his cart after them.   Does it mean all wizards obliged to dress as a Muggle when going to the platform and the Malfoys every year appear there in Muggle clothes?   Or Muggle wear is not a big deal for the new generation and Draco does occasionally wear Muggle clothing (like, in Diagon Alley) without considering it to be beneath him?


Starting multiple Chrome full screen instances on multiple monitors from (batch) script

My goal is to show different web content full screen on multiple monitors automatically after booting from a single computer. The browser I would like to use is Chrome. If Chrome does not support this and Firefox does that would be fine.  The OS I would prefer is Windows, if it turns out that Linux is possible that would be fine.  On Windows it is possible to set the position of the Chrome browser window (--window-position=) and make Chrome start in full screen mode (--kiosk). Using these options combined you can start Chrome full screen on any of the desktops/screens that you have connected to your computer. I have managed to get this working.  However, if I then try to do the same thing a second time to have Chrome full screen on a second screen the second Chrome window will open over the first window, no matter the coordinates I use for the --window-position parameter.  I have tried using Chrome profiles and copying the Chrome directory and starting the second chrome.exe. All these things result in the same behaviour.


NPC casting Suggestion on PC: who decides it's reasonable?

A simple scenario:  The DM wishes to break a cleric's concentration on their  spell, and a foe uses  to tell the cleric to cast  on an enemy spellcaster.  The rationale is that this would prevent enemy AoE spells from affecting frontliners.  The PC rejects this, saying "No, my PC thinks that's unreasonable and continues to concentrate on bless instead."      In such a case, who gets the say whether the suggestion is or is not reasonable? Or should it be determined by a Persuasion roll? How can the DM give a fair ruling that doesn't take away the player's agency, but at the same time does not allow the player to freely deny the effects of suggestion?  The rationale is assumed to be "50-50".  This question is different from , as this is specifically asking for guidance on how to give a fair ruling that the suggestion will fail/succeed when the spell is cast on a PC, which may result in agency being taken away from the player.


What does "soft" in "soft symmetry breaking" mean?

For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained.


How do I create a vertical bar in text mode, which is a bit thicker and taller than the | character?  I used to know how to do this with boxes, but googling no longer turns up any useful resources.  I'm specifically using xelatex.


the output of sudo apt-get update command are below:  Hit:9 http://ppa.launchpad.net/ubuntu-mozilla-daily/ppa/ubuntu xenial InRelease Get:11 http://archive.ubuntu.com/ubuntu xenial-backports InRelease [102 kB]     Hit:12 http://ppa.launchpad.net/ubuntu-wine/ppa/ubuntu xenial InRelease         Hit:13 http://ppa.launchpad.net/webupd8team/brackets/ubuntu xenial InRelease    Err:14 http://dell.archive.canonical.com/updates xenial-dell InRelease            Could not connect to dell.archive.canonical.com:80 (91.189.89.6), connection timed out Fetched 306 kB in 2min 0s (2,551 B/s)                       Reading package lists... Done W: Failed to fetch http://dell.archive.canonical.com/updates/dists/xenial-dell/InRelease  Could not connect to dell.archive.canonical.com:80 (91.189.89.6), connection timed out W: Some index files failed to download. They have been ignored, or old ones used instead.


Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?

How to show  that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal? Is it possible to find the cardinality of $\mathbb{Z}[i]/I$ as well?  I know how to show that it is an integral domain, because that follows very quickly.


What is the point in using API such as Open GL or DirectX when there are game engines?

I was wondering why  today programmers place so much emphasis on API like DirectX, and even OpenGl. As far as I know, you'd need thousands of lines of code to make a simple 3D game using one of the aforementioned. But with game engines like Unity, the process is simplified and you can pretty much drag around shapes to create the graphics in lieu of programming it. So what I wanted to know: why is knowing APIs DirectX more preferable than being knowledgeable in Unity, other than the fact that with an API you can code it to be portable on other systems. To me it's like choosing Assembly over a high level language like C. Sure, with assembly I'll really understand what's happening at machine level, but it's take a lot longer to write programs using it and it would be a lot harder to debug.


What exactly is the Box-Jenkins method for ARIMA processes?

The  page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call proc ARIMA, supply the parameters $p,d,q$ and SAS will give me AR and MA coefficients. Now, I can try different combinations of $p,d,q$ and SAS will give me a set of coefficients in each case. I select the set with the lowest Akaike information criterion.  My question is: where in the above procedure did I use Box-Jenkins? Am I supposed to use Box-Jenkins to come up with initial estimates of $p,d,q$? Or did SAS use it internally somehow?


Current waveform in an inductor with AC source

If we connect an AC source with a pure inductor when AC source is going through 0 volts we get the following graph of the voltage and current.  There are few things in the graph about which i am confused.  In the first graph/diagram "A" of the picture which shows the voltage when it starts to flow and the corresponding current, the current doesnt seem to be lagging behind the voltage by 90 degrees. What is the reason behind that? Is the statement "current lags behind the voltage in an inductor BY 90 degree" is valid just for the steady state voltage shown in graph "B"?  Second confusion is that for the first half cycle of the voltage in graph "A", current is rising both for increasing and decreasing voltage. How is this possible that current is rising in the inductor for both increasing and decreasing voltage?


prime and irreducible elements $\equiv 1$ modulo $4$

Consider the set $L= n \in \mathbb{N}$, such that $n \equiv 1$ modulo $4$.  1) What is the set of prime or irreducible elements in $L$?  2) Is prime and irreducible the same (in $L$)?  3) Is there a unique factorization of irreducible elements $\forall n \in L$?  I know that a prime number in $\mathbb{N}$ has to be prime in $L$, too. But are there any more?  I think you can find irreducible elements which are not prime, but didn't manage to do so, yet.  Could you please help me with this problem? I'm stuck..


passing filename with spaces to a shell script

The shellscript is very simple:  retroarch $* -c /tmp/retroarch/Data/retroarch/gambatte.cfg   ("retroarch" is another shellscript)  If the filename passed contains spaces it fails:  RetroArch [ERROR] :: Could not read ROM file.


Generators of $\text{GL}_{2}(\mathbb{Z})$ group, good reference book?

Does anyone know, where I can find a reference (preferably a book) which says that the general linear group $\text{GL}_{2}(\mathbb{Z})$ is generated by the set  $$\left\{\begin{bmatrix} 1&0\\0&-1\end{bmatrix}, \begin{bmatrix} 0&1\\1&0\end{bmatrix}, \begin{bmatrix} 1&1\\0&1\end{bmatrix}\right\}$$  Thank you in advance.


Python Regular Expression check if contains specific characters

I'm trying to create a program where it checks the validation of an email seeing if it starts with a lowercase letter, contains an "@" sign, and a ".com" or a ".co.uk". How would I do this.  My internet is being funny therefore I am not able to check the expressions online.  This is what I have so far :   def valid_email():     email_address = input("Enter your email: ")     valid = re.match("[a-z]",email_address)     if valid:         print("That looks OK")     else:         print("Invalid, must be lowercase and contain an '@' sign")         valid_email() valid_email()


How can I take product shots of a flat (but not absolutely flat) reflective surface?

I need to make a photo of an iPhone case. The picture I've got with my rig used for other (non reflective) cases gave me the following result:    Which I don't like as it don't shows the reflective surface.  I tried to reflect articulated softbox in the front surface. But I get the following:    Don't look at the bad angle and uneven background - it's preproduction shot, my main concerns are:   the roughness of the light glare accuracy needed to set the position of the subject   As you can see the glare is unpleasant. At least I'm far from being satisfied with both these images.  I'd be happy to get something like this:    But in my case the surface is not so flat on a macro (it is a rubber or something like that so it has some curvature) and micro (it has some grains) levels.  Can you suggest anything to make the shots better? My only thought is to draw the glare in Photoshop, but I have tons of those cases to take a shot so I'd better make a rig and save my time with postproduction.  UPD: I decided to make the glare in Photoshop. Of course it is a time consuming job, but I think that the natural glare will be also tricky to obtain and the quality will be probably not as expected. My current result is the following:


Understanding the minimization of mean squared error function

I try to minimize mean squared error function defined as:  $E\left[Y - f(X)\right]^2$  I summarized the minimization procedure from different online sources (e.g.,  (p. 4),  (p. 8)) in the following lines.  First add and subtract $E[Y | X]$:  $E\left[\left\lbrace(Y - E[Y | X]) - (f(X) - E[Y|X])\right\rbrace^2\right]$  Expanding the quadratic yield:  $E\left[\left(Y - E[Y|X]\right)^2 + \left(f(X) - E[Y|X]\right)^2 - 2 \left(Y - E[Y|X]\right)\left(f(X) - E[Y|X]\right)\right]$  First term is not affected by the choice of $f(X)$; third term is $0$, so the whole expression is minimized if $f(X) = E(Y|X)$.  Question 1: I wonder what is the motivation to add and subtract $E[Y | X]$ in the first step of the procedure?  Question 2: How to explain in plain English why third term in quadratic is $0$?


When exactly does Stack Exchange make a new version of what you edit?

As you know, when you edit a post in SE communities (like SO), sometimes your edition will be a new version, and sometimes else the current post will be just updated.  According to some tests, I figured it out:   when there is a comment under the post after the last version, it will create a new version if you edit the post. When 10 minutes passed since the last edition, then it will create a new version if you edit the post.   Anything else?


How do I set the Windows network timeout for physically disconnected mapped drive?

When a network drive () is physically disconnected, Windows Explorer (and other programs) keeps trying to enumerate and/or use it for maybe 60 seconds.  Is there some way to reduce this timeout to maybe 5 seconds?  Just to clarify, I'm not asking about network drives that are automatically disconnected by Windows after a certain period of time, or about automatic reconnections during login.  The question is about this:  Connect a network drive to another computer. Then turn that other computer off. Then try to reconnect the network drive, e.g. by double-clicking in Windows Explorer → very long timeout. How do I reduce this timeout?


Will a 7mm SSD fit in a 9.5mm laptop HDD slot?

I'm planning to purchase a Crucial M4 256G SSD.  There are 2 versions though, 7mm and 9.5mm, at the same price on Newegg.com  My current laptop is 9.5mm SATA II. However, I plan to purchase a new laptop as soon as Ivy Bridge quad-core laptops (the 35W i7-3612QM interests me most) are available, which will certainly have SATA III (and I plan to use a legacy HDD in optical bay). However, I'm not sure if it will come with a 7mm or 9.5mm slot.  My question is, will a 7mm SSD fit in a 9.5 mm slot? Is there any disadvantage?  (BTW, comments are welcome if you feel Crucial M4 is not a good choice. I chose this after I read rumors about SandForce. I also do not see any reason to switch to Intel 320 Series as Crucial seems to have good reliability as well.)


I want to make a schematic of this board. Can anyone tell me how?


How to create a squiggle arrow with some text on it in TikZ?

I need to define a new command to create a squiggle arrow with some text on it. Something similar to what \xrightarrow command produces but with wiggly arrows as in \rightsquigarrow. The length of the arrow should automatically be adjusted to fit the text above it and I do not know how to handle this part in TikZ. Any ideas would be much appreciated.


Virtualbox guest additions installation fails for shared folder support!

I am trying to setup Ubuntu guest OS on a Windows host system.After creating the new virtual machine, I am trying to install the guest additions and I am running sudo sh VBoxLinuxAdditions.run but running that I am getting the following error,    The headers for the current running kernel were not found. If the following module compilation fails then this could be the reason.    Building the shsared folder support module ... fail!    Warning: Unknown version of the X window ystem installed. Not installing X Window system drivers.   Virtual box version : 4.3.4-91027  Host system : Windows 7 64 bit  Guest OS : Ubuntu 12.04 32 bit.  UPDATE  On newer version `4.3.26` it works fine, But I need to make it work on `4.3.4-91027`.   Thanks in advance.


Does MariaDB or MySQL implement the VALUES (expression) table value constructor?

I am just wondering if MariaDB or MySQL implements the <table value constructor> in the SQL Spec. In  and ?  SELECT * FROM ( VALUES (1) ) AS t(x);  x  ---  1 (1 row)   (syntax from ).


How do I programmatically create a new content type?

I'm building a module (my_module) in Drupal 7. It has some functionality and also will create a new content type. In my_module.install, I implemented hook_install() (my_module_install()).    Can I use more hook_install() to create a new content type (my_module_install()) in this module? If the answer is yes, how should I do this? Otherwise, should I do this in another module?


How do I spawn a baby villager using commands?

I am trying to spawn a baby villager using the following command: /summon villager ~ ~ ~ {Age:-2000000000}  But it isn’t working. What is my error?


ESTA approved on the same day as B-1/B-2 visa refused

I am writing because I have a question regarding my ESTA application and because I could not find a similar case online that would help me at this stage. I have never been to the U.S. so this would be my first visit.    I am a German citizen, hence eligible for the Waiver Program. I applied for an ESTA in June 2014 and got approved. After further research on the Internet I learned that the passport should be valid until 6 months after the planned return date. My passport was due to run out in Feb 2015 - which still should have been fine but because I didn't want to take chances I applied for a new passport which was issued August 2014 and is now valid until August 2024. My passport number has been changed also.    After I received my new passport I was advised by a friend to apply for a B-1/B-2 visa as it would allow me to extend my stay and it seemed like a good idea at first. On the day of my interview I also applied for a new ESTA with my new passport number (just in case) which again was granted.   Unfortunately for me the interview for the B-1/B-2 visa was unsuccessful and I got rejected. I was not aware then that after a rejected interview one could not travel with ESTA, otherwise I would have never risked it!  Now I am very concerned, can I still use my ESTA and enter the U.S.? as I read everywhere that once you get rejected the chances of getting through are very slim and any visa rejection will result in not being able to use the waiver program.  It might be important to note that both the B-1/B-2 interview and the waiver application were on the same day, 21st of August 2014, so depending on how one might look at it that might present a problem too I suppose.  I guess the frustration lies in the fact that I did not need to apply for a B-1/B-2 visa to begin with, and had I not I would now not have these problems. I would like to know how likely it is that I can still travel under the waiver program, if at all, and what my options are at this point.


Is there a nice way of expanding multinomials of the form $(1+x+\cdots+x^l)^n$?

I have found an expression for the probability generating function of a random variable:  $G_Y(s)=\frac{1}{(6-k+1)^3}[s^k+\cdots+s^6]^3$  (where $k\in\lbrace1,..,6\rbrace$) and I don't know how to use the multinomial theorem to expand this into something usable.   Essentially I am looking for a formula for the coefficient of $x^i$ in:  $(1+x+\cdots+x^l)^n$  with an explanation being even better. Thanks


Why is geo-redundant DNS necessary for small sites?

This is a  about DNS geo-redundancy.   It's extremely common knowledge that geo-redundant DNS servers located at separate physical locations are highly desirable when providing resilient web services. This is covered in-depth by document , but some of the most frequently mentioned reasons include:   Protection against datacenter disasters. Earthquakes happen. Fires happen in racks and take out nearby servers and network equipment. Multiple DNS servers won't do you much good if physical problems at the datacenter knock out both DNS servers at once, even if they're not in the same row. Protection against upstream peer problems. Multiple DNS servers won't prevent problems if a shared upstream network peer takes a dirt nap. Whether the upstream problem completely takes you offline, or simply isolates all of your DNS servers from a fraction of your userbase, the end result is that people can't access your domain even if the services themselves are located in a completely different datacenter.   That's all well and good, but are redundant DNS servers really necessary if I'm running all of my services off of the same IP address? I can't see how having a second DNS server would provide me any benefit if no one can get to anything provided by my domain anyway.  I understand that this is considered a best practice, but this really seems pointless!


Differentiability of a non-continuous function

So the question that comes to my mind is  does differentiability require continuity? I have read it many a times but what I think of it like this, lets say a piecewise function as below is defined $$f(x) =\begin{cases} x^2 & x \leq 0 \\[2ex]\ x^2-1 & x \gt \mathbb 0 \end{cases}$$ Now as $x\rightarrow0$ the right hand derivative approaches zero and so does the left hand derivative. So apparently the derivative should exit at all points, even though it isn't continuous. Am I somehow wrong here? I recently completed my school so an answer at that level would be really helpful.


Names not appearing in Messages on Watch

On Watch, I suddenly see no names for people in Messages. Instead I see the address (e-mail or phone number) they are sending from, even though the senders are in my Contacts and have the addresses associated with their entries.  This was not the case before a recent update (I'm not sure which one).  How do I get contact names to appear in Watch Messages?


Can a Horizon Walker ranger use the Distant Strike feature to teleport out of the Forcecage spell?

is a  feature which states (XGtE, p. 43):     At 11th level, you gain the ability to pass between the planes in a   blink of an eye. When you use the Attack action, you can teleport up   to 10 feet before each attack to an unoccupied space you can see.   The  spell description states, in part:     A prison in the shape of a box can be up to 10 feet on a side,   creating a solid barrier that prevents any matter from passing through   it and blocking any spells cast into or out from the area.      When you cast the spell, any creature that is completely inside the   cage’s area is trapped. Creatures only partially within the area, or   those too large to fit inside the area, are pushed away from the   center of the area until they are completely outside the area.      A creature inside the cage can’t leave it by nonmagical means. If the   creature tries to use teleportation or interplanar travel to leave the   cage, it must first make a Charisma saving throw. On a success, the   creature can use that magic to exit the cage. On a failure, the   creature can’t exit the cage and wastes the use of the spell or   effect. The cage also extends into the Ethereal Plane, blocking   ethereal travel.   Can the ranger attack a location and thus teleport 10 feet outside the forcecage?


Real valued analytic function defined on a connected set is constant

Let $G$ be a connected set and $f : G \rightarrow \mathbb{C}$ a real valued analytic function. Prove that $f$ is constant.    My idea to prove the result is to prove a subset $A \neq \varnothing$ of the connected set $G$ is both open and closed. So $G=A$ Take $f(w) = a$ $$A = \{z\colon z \in G, f(z) = a\}$$ Now I want to show that $A$ is infinite. How to do it? After that it is easy to prove $A=G$.


Till now I rendered my images and took them to Photoshop and did some color corrections there. Made aware of Color Management options in Blender by Rick's answer on  I am now diving somewhat deeper in Color Management in Blender.   I don't want this post to be a dupe, I just want some basic understanding of color management in Blender. How monitor profiles, color spaces and Blender act together. Like I have some basic understanding how working spaces, monitor profiles act together in Photoshop.


How can I find out when a specific comprehensive rule was introduced?

I wrote , and I feel like it would benefit (slightly - it's not exactly a crucial part of the answer) from knowing when rule 706.4 was introduced. I feel that if I can find out when a rule was introduced, I can more easily research why it was introduced, and then I can write a better answer.  In general, how can I determine when a comprehensive rule was introduced?


How to know which package installs a given command?

I see that llvm-objdump-9 instead of llvm-objdump are installed. What is the command to figure out which package installs it? How to remove the suffix -9? Thanks. EDIT: Please reopen the post. The second question is not answered. To get llvm-objdump in my $PATH, do I need to add /usr/lib/llvm-9/bin in my $PATH? $ dpkg -S llvm-objdump llvm-9: /usr/share/man/man1/llvm-objdump-9.1.gz llvm-9: /usr/lib/llvm-9/bin/llvm-objdump llvm-9: /usr/bin/llvm-objdump-9


Let $f, g \colon \mathbb C \to \mathbb C$ be two nonconstant polynomial functions such that $$f(x) = 1 \iff g(x)=1$$ and $$f(x) = 0 \iff g(x)=0.$$  Does it imply that $f \equiv g$, that is, they come from the same polynomial? This is certainly not true for real polynomials, as an example of $g(x) = f(x)^3 = x^3$ shows.  If possible, I would like to know about generalisations to fields other than $\mathbb C$ - I couldn't find any reference in literature.


I know that a tag wiki "is an editable page that briefly summarizes the topic of the tag and that may provide links to existing questions that are often useful to many people."   How can we find the tag wiki content? Is there a data dump available for downloading the tag wiki content?


I have been trying to remove characters from a string without using extra memory and soing it in place. I just tried removing character 'a' from a given input string but my code gives a segmentation fault .   Input- abca  Output-bc Debugger says the segmentation error is in line "str[j]=str[i]". Please help me out :) Thanks  Here is the code   #include<stdio.h> #include<string.h>  void removest(char *str)  {   int i,j=0;   int len=strlen(str);   for(i=0;i<len;i++)     {        if(str[i]=='a')     {       i=i+1;     }       str[j]=str[i];       j++;     }   str[j]='\0';   printf("%s \n",str); }  int main() {   char *str="abca";   removest(str); }


We see in Harry Potter and the Order of the Phoenix that McGonagall has her Transfiguration students practice the Vanishing Charm () on mice (and has previously had them do snails):  “As  I  was  saying,  the  Vanishing  Spell  becomes  more  difficult  with  the complexity of the animal to be vanished. The snail, as an invertebrate, does not present much of a challenge; the mouse, as a mammal, offers a much greater one. This is not, therefore, magic you can accomplish with your mind on your dinner. So — you know the incantation, let me see what you can do. . . .” Harry Potter and the Order of the Phoenix  ...and Ron manages to vanish most of his mouse:  “Well,  it’s  a  start,”  said  Ron,  holding  up  a  long,  wriggling  mouse  tail and dropping it back into the box Lavender was passing around. Harry Potter and the Order of the Phoenix  This raises the question of is it possible to Vanish humans? We've seen that mammals (such as our friendly, little mouse) are not exempt from being Vanished. Does this hold true for humans?


Python: How to select a collection in the Outliner?

I would like to set an active collection via python and have it selected in the Outliner.  Example: There are two collections A and B.   step 1: Manually select collection A in the Outliner.  step 2: Run   bpy.context.view_layer.active_layer_collection = bpy.context.view_layer.layer_collection.children["B"]  step 3: Observe that collection A is still selected in the Outliner, but I would like to have collection B to be selected.


Which is correct, me and Robyn are going to the bar, or Robyn and I are going to the bar?


How to convert every pixel of raster picture to square objects in Illustrator?

For example I have 10×10px icon. I want to produce 100 squares with correspondent color and location each. Actually, the question is how to make exact pixel mosaic out of raster image.  I tried Live Trace but it added some distortions to squares.


How to reduce the size of shapefiles when features are deleted?

This tiny little script deletes all small features in all layers. This works fine but the size of .shp files are not reduced. Please tell me why...  canvas = iface.mapCanvas() expr = QgsExpression("$length<100") for l in canvas.layers():     l.startEditing()     it = l.getFeatures(QgsFeatureRequest(expr))     for ft in it:         l.deleteFeature(ft.id())     l.commitChanges()


How to setup Squid Proxy (for localhost services and Tor and I2P)

So, here's my dilemma. I had this bright idea that I could use DNS to create my own TLD for my computer. I wanted all services to run on localhost as I will be creating sites that can modify my computer. All these sites will run under the .senor TLD. I currently got this TLD to work with my jekyll server on .  The problem comes in trying to get domains such as .onion.senor and .i2p.senor to work with their respective proxies. Obviously I had oversight when plannning for proxying data from my proxy to Tors or I2Ps proxy as that wasn't in my original plan when creating the .senor TLD. My current setup is dnsmasq on 127.0.0.1:53 which redirects any domain not listed in /etc/dnsmasq.hosts file to dnscrypt which is hosted on 127.0.0.1:52.  I tried searching for answers on how to setup squid like this as the configuration confuses me (I will keep searching) and even found questions such as  that asks to do the same as what I want to do, but nobody's answered it since it was asked 2 years ago, so I am still stuck. Any help or pointing in the right direction will be greatly appreciated!


I found a mysterious folder named e849ad3686d570a415 in the root of a hard disk. It contains a subfolder i386 which is inaccessible.  Do I have malware on my PC? How can I delete this folder?


Prove or disprove: For every integer $n$, the quotient group of $\Bbb Z/n\Bbb Z$ modulo any subgroup is cyclic.

My attempt:  If we take $n$ to be finite, since $\mathbb Z/n\mathbb Z$ is cyclic, there is a distinct subgroup of order $d$ for each divisor $d$ of $n$.   Any subgroup of a cyclic group is cyclic. Any subgroup of order $d$ is isomorphic to $\mathbb Z/d\mathbb Z$, as it is a cyclic group of order $d$.  Cyclic groups are abelian, and $gh=hg$ leads to $gH = Hg$, so all subgroups are normal.  Thus we can view $\mathbb Z/d\mathbb Z$ as the kernel of some homomorphism from $\mathbb Z/n\mathbb Z$ to a group $H$. By the first isomorphism theorem, we have $(\mathbb Z/n\mathbb Z)/(\mathbb Z/d\mathbb Z)$ is isomorphic to the image of that homomorphism.  It is at this point I've become stuck, as I'm not sure what I can say about the image of this homomorphism. I feel like it should be $\mathbb Z/k\mathbb Z$, where $k$ is the integer such that $kd = n$, and this would prove the quotient group is cyclic, as it is isomorphic to a cyclic group. However, I am not sure if this is right or how to justify this?  Any direction is greatly appreciated!


How to change screen resolution in the linux zoom tool

I have an Asus laptop running Linux, and I let one of my younger siblings go on it. He went into the settings and turned on the zoom tool, but increased the screen brightness so it's completely white. Now I can't see anything on my screen and have no way to change it. How can I fix this?


Keyboard shortcut for restoring applications from the Mac OS X Dock?

Is there a keyboard shortcut to restore a minimised application window from the Dock?  Almost all Apple Mac OS X applications respond to the Apple + M command which minimises the current application window to the Dock, which is fine.  I can then use Command + Tab to cycle through my running applications - including the minimised application, but selecting the application with the minimised window neither restores the minimised window, nor sets focus to the minimised application window in the Dock so I can restore it without having to reach for the Mouse.  Update: Thanks for the answers, however the consensus seems to be to use the 'Hide' feature (Apple + H) instead of minimising, as it's easier to get the window back using Command + Tab.


Why my zsh script doesn't echo anything?

script: #!/bin/zsh  IFS=$'\n' arr=($(alias | grep 'git' | grep "^[g|\'g]" | sed 's/=.*//' | sed "s/'//"))  echo $arr  These two lines work in the normal command line: ~/test ·····································································································································  test-Cj2sK_tx ❮ IFS=$'\n' arr=($(alias | grep 'git' | grep "^[g|\'g]" | sed 's/=.*//' | sed "s/'//"))  ~/test ·····································································································································  test-Cj2sK_tx ❯ echo $arr g ga gaa gam gama gamc gams gamscp gap gapa gapt gau gav gb gbD gba gbd gbda gbl gbnm gbr gbs gbsb gbsg gbsr gbss gc gc!' gca gca!' gcam gcan!' gcans!' gcas gcasm gcb gcd gcf gcl gclean gcm gcmsg gcn!' gco gcount gcp gcpa gcpc gcs gcsm gd gdca gdct gdcw gds gdt gdw gf gfa gfg gfo gg gga ggpull ggpush ggsup ghh gignore gignored git-svn-dcommit-push gk gke gl glg glgg glgga glgm glgp glo glod glods glog gloga glol glola glols glp glum gm gma gmom gmt gmtvim gmum gp gpd gpf gpf!' gpoat gpristine gpsup gpu gpv gr gra grb grba grbc grbd grbi grbm grbo grbs grev grh grhh grm grmc grmv groh grrm grs grset grss grst grt gru grup grv gsb gsd gsh gsi gsps gsr gss gst gsta gstaa gstall gstc gstd gstl gstp gsts gsu gsw gswc gtl gts gtv gunignore gunwip gup gupa gupav gupv gwch gwip  However, it doesn't work when these two commands are in the script file... ~/test ·····································································································································  test-Cj2sK_tx ❯ /bin/zsh ./d-alias.sh # nothing here...  Thank you for any help. Many thanks.


Variance of log($X_{\lambda}$) where $X_{\lambda}$ is a exponential function?

Let $X_{\lambda}$ has exponential density $\lambda e^{-\lambda x}$. Then what is the nature of Var log($X_{\lambda}$) w.r.t $\lambda$ i.e. is it increasing, decreasin, etc on $\lambda$.   My approach: Without going into calucaltion, I evaluate log($X_{\lambda}$) which then has a term of the form $-\lambda$ log($\lambda$) which I know is decreasing and hence the answer is decreasing which matches up with the correct answer.  But when I want to explicitly evaluate the term of E$[X]$, I am running into problem because it's of the form $\lambda log(\lambda)\int_{0}^{\infty}- x dx$. This integral would give me $\infty$ and same problem occurs with E$[X^2]$. So can anyone help?


How do I prove the fact that for any valuation ring $V$ the ideals are totally ordered under inclusion?


How to Bind REST API data into Html dropdown

I had written the below code to bind a values of List column into html drop-down. Can any one help in knowing what's wrong in my below code.         <link rel="stylesheet" href="//code.jquery.com/ui/1.11.4/themes/smoothness/jquery-ui.css">      <link rel="stylesheet" href="/resources/demos/style.css">

  Months:	          <select id="drbfunction" class="select">        <option selected="selected">Select</option>        </select>

Programes:
        <select id="drbprogrames" class="select">        <option selected="selected">Select</option>


The significance of the pressure term within the momentum-energy tensor

EDIT: this question is based around my notion regarding the  possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$,   The answer below resolves the question and I have deleted my incorrect reasoning originally contained within the question. As the post contains an answer,  I cannot delete it, which I would normally do. END EDIT.  I am confused as to where potential energy is contained within T$_{\mu\nu}$, or if it is included in the first place.  If this question is rubbish, then how do we allow for the P.E, associated with the other forces within T$_{\mu\nu}$, or do we need to?    If my question is so wrong that you can answer by simply directing me to page X of a particular textbook that provides the correct derivation of p in T$_{\mu\nu}$, that's fine and will be  appreciated.


Set up https/SSL certificate for private Gitlab instance without custom domain

I set up my private Gitlab server. It works fine and when I enter my IP I can access it. I do not have a custom domain and I also do not want one since I don't want to make the server accessible from the outside.   Most of the guides only show how to set up https with Let's Encrypt for which - as far as I can tell - I need to be in control of a domain and configure an A record for it. That's not really an option.   Some rare other guides show me how to create my self signed certificates to use it with GL (using Open ssl). My problem with that is that browsers will still tell me that the connection is insecure and treat self-signed certs as http and not https. So whtat's the sense of doing it in the first place.   So that leaves me with my question: Is there a way to set up https without a custom domain but with a real certificate (best without buying it). Or is that not even possible? If it is possible how could I start to configure my GL intance?  I was thinking maybe using cloudflare could help? I am not sure though.  Thanks very much in advance for help, hints and tipps. Very much appreciated.


How can I have an RPG character redirect / glance off stationary objects and keep going?

I am attempting to create an effect in a game that is identical to the effect I've shown in the attached gifs. Essentially, the character, when they are running or walking and hit an object that is stationary, if it's possible, (meaning there is a valid path for continuation) they should glance off the side of said object and keep going.  In this first GIF I am only holding the UP directional key, notice how the character glances to their right:      In this second GIF I am only holding the DOWN directional key, notice how the character glances to their left:      In this third GIF I am only holding the UP directional key, notice how the character glance first to their left and then to their right:      Could someone describe the process that I would need to follow in order to do this type of collision detection into redirection?


Recently, I asked a  how to sort pairs of lines, and one of the answers suggested concatenating lines with sed, like this:  cat file.txt | sed -n 'N;s/\n//;p' | sort -t";" -k43,43n | perl -F';' -ane '$,=";";print @F[0..13],"\n";print @F[14..$#F]'   which worked brilliantly, but now my problem generalized to sorting n-tupels of lines, which I can't figure out how to do with sed.   Everything I found was either for 2 lines or ALL lines, but I need n lines (where n is 5 at the moment, but a general way would be great).  Bonus points for a nice way of rewriting the perl part to accomodate n lines, but the problem is really about the sed part.  I am also not hung on sed specifically, so if you have a nice solution using a different command line tool, please post it.  Update: Example input (n == 3)  a1;b1;c1;  n1;m1;l1;  d1;e1;f1;g1 n2;m2;l2; a2;b2;c2; d2;e2;f2;g2


I have studied deep copies over the day but I still don't quite get it.  Here's what I want.  static class MyList  List<MenuData> Menu1 = MenuList.Menus.ToList(); List<MenuData> Menu2 = MenuList.Menus.ToList();   I use Menu2 on remove method. However, Menu1 was also deleted. I realize that Menu1 and Menu2 were deleted together because of Swallow Copy.  They also referred to samples of other people, but failed.  static class MenuList {     public class MenuData     {         public string ID { get; set; }         public string Text { get; set; }         public string Image { get; set; }         public Boolean Expanded { get; set; }     }      public static List<MenuData> Menus = new List<MenuData>()     {         new MenuData {             ID = "1",             Text = "Service",             Image = "file_path.png",             Expanded = false         },     };      public static T Clone<T>(T obj)     {         using (var ms = new MemoryStream())         {             var formatter = new BinaryFormatter();             formatter.Serialize(ms, obj);             ms.Position = 0;             return (T)formatter.Deserialize(ms);         }     }      public static List<MenuData> CopyMenus = MenuList.Clone(MenuList.Menus); }   ErrMessage : The format 'Models.MenuData' is not marked serializable.  It was asked to reduce further waste of time.


I consider  badly shaped, so I flagged it to kindly ask for delete.  It was declined with reason None of the answers are upvoted, you can delete it yourself. However, I can't: a red box appears saying Sorry, this question has answers and cannot be deleted; flag it for moderator attention instead.  So I flagged it again, but it is still active since 15.2. I'd like to have it deleted, but it's no big deal: I'm just curious when can I delete my question.


Can a PHP generated main page be indexed by Google?

I generate an index.html file in a PHP script to avoid PHP code within HTML and to show content that is delivered by another script hourly. (Like next flights within an hour.)  This script overwrites the file each time the content is ready (I plan to do this with a cron job).  Then, will my index.html be indexed by Google or it will be punished for being generated content?


I set up an administrator account for myself when I set up a new Ubuntu system. Somewhere along the line I did something wrong, and my account is now a standard account. I no longer have sudo privileges; when I try to use sudo, it asks for the root password rather than my password. I never set up a root password. Is there a default setting for that password? I can't fix anything without that password, because I need root access to make the fix.  My best guess is that what went wrong may have been due to the following sequence of events: I used addgroup to create a group named family. I used adduser to add an account for my wife, and usermod to put her in the family group. I then used usermod to put myself in the family group. Might I have accidentally removed myself from the sudoers list that way?  I needed two additional pieces of information to solve my problem:   By booting in recovery mode, and selecting "root" from the menu, I could operate as root without knowing root's password, even if logging in as root has been disabled by not giving it a password.   When booting in recovery mode, the root partition defaults to read-only mode. I needed to use mount -rw -o remount / in order to make it writable, before I could make any changes.


I am having trouble with using beamer's \onslide in TikZ and pgfplots. The issue I have encountered is that if I use \onslide then the specific parts of the picture I want to appear on a specific slide appear on all the slides in the frame.  Using \only works (I do not obtain the same error). However, I want to use \onslide because then the figure takes up the same space all the time.  The following example demonstrates my problem. It should run as follows: There is a curve and an x-axis (slide 1). Then a second curve is added (slide 2). Then the y-axis is added (slide 3). Then some text is added (slide 4). However, the picture on slide 1 when I run this is how it should look at slide 3. Having given this a lot of thought and google-powered effort, I have no idea what the issue could possibly be! ( tex.SE question is relevant, but does not really resolve the issue, or tell me the underlying issue (which I would be interested to know).)  \documentclass{beamer}   \usepackage{tikz} \usepackage{pgfplots}  %%%  \begin{document}  \begin{frame} \frametitle{A frame}  \begin{figure} \centering \begin{tikzpicture} \begin{axis}[         every axis plot post/.append style={mark=none,domain=-3:3,samples=50,smooth},         clip=false,         axis y line=none,         axis x line*=bottom,         ymin=0,         xtick=\empty, ] \onslide<1->{%on all slides. Note: Changing this to \onslide<2-> does not change anything - all parts of the image occur on all slides.     \addplot {x^2}; } \onslide<2->{%on the 2nd slide and those coming after     \addplot {x^2+1}; } \onslide<3->{%on the 3rd slide and those coming after     \draw (axis description cs:0.5,0) -- (axis description cs:0.5,1); } \end{axis} \end{tikzpicture}\end{figure}  \onslide<4->{%on the 4th slide and those coming after Slide 4. } % \end{frame} % \end{document}   Note: In reality, I want to do this in a minipage. So if you provide an alternative method then you might want to bear this in mind. Or not.  Thanks in advance!


How to setattr to instance such that self is passed?

class C():     def print_once(self):         print(self)  def print_twice(self):     print(self, self)  c = C() setattr(c, 'print_twice', print_twice) c.print_once() c.print_twice()  >>> <__main__.C object at 0x0000028116795108> >>> TypeError: print_twice() missing 1 required positional argument: 'self'  I'm aware setattr(C, ..) does the trick, but this affects future and concurrent instances of C and is undesired. Can print_twice be set only to c, such that self is passed automatically just like to print_once?


Using razer Core X with amd 5700 XT on Mac

Hi I'm on the verge of getting an eGPU Razer Core X and an AMD 5700 XT on macbook pro 15" 2.6 GHz Intel Core i7 32 G RAM for archviz but I need to make sure it's compatible with Blender


No sound from bluetooth headset, but it's detected

I have an bluetooth headset connected to my computer, the buttons play/pause/volume are working fine, but I have no sound in the headset, but in the speaker of the computer.   In fact, I played with the sound settings of my headset in the sound settings of Ubuntu, and after choosing "switch off", the headset did "disappear" from the settings.   My question is: how can I make it appear there again, to be able to hear the sound via the headset? Thank you all for your help!


Induction and Recursion Proof using Catalan Numbers

Note that a product   may be parenthesized in two different ways:   and . Similarly, there are several different ways to parenthesize . Two such ways are  and . Let  be the number of different ways to parenthesize the product . Show that if , then      for all integers .  Keep in mind that the sequence  is the same as the sequence of Catalan numbers.   I am entirely lost. Please can someone offer some hint or direction of where to begin? I humbly thank you so very much.


why does vim has different escape character for newline between searching and replacing

When searching:  \n is newline, \r is CR (carriage return = Ctrl-M = ^M)   When replacing:  \r is newline, \n is a null byte (0x00).   Why designed in such inconsistent way?


Auto-dismiss "welcome back" message if you upvote

When I go back to a site I haven't been to in a long while (e.g. ServerFault), there is a "welcome back" banner that displays at the top and reminds me to upvote the questions/answers if I find them useful.  I don't need the reminder, but that's okay—I have no objection to its existence.  However, I noticed today after I upvoted the question and answer I was reading, the banner was still there.  Could we please have the "welcome back!" banner auto-dismiss if the user upvotes a question and/or answer?


Can fresh pasta sheets be used to assemble a lasagne, then left in the fridge overnight before baking?

Or will this make them mushy or otherwise degrade them?  I have recently gotten into making fresh pasta, and I want to prep a lasagne the night before. I have done this before with store-bough dried noodles, but I'm not sure if doing this will have a negative effect on fresh, more delicate pasta.


How to find next birthday date from list of date from date now?

I'm struggling with this question? How can I find next birthday Date from my list of date ?  I got  const myArray = [           {             name: 'Joe Blow',             date: 'Wednesday, November 25, 1992'           },           {             name: 'Sam lol',             date: 'Thursday, April 16, 1992'           },           {             name: 'Eva lol',             date: 'Thursday, February 26, 1991'           }         ];         myArray.sort(function compare(a, b) {           const dateA = new Date(a.date);           const dateB = new Date(b.date);           return dateA.getUTCDate() - dateB.getUTCDate();         });         // console.log(this.usersBirthdayDate);         console.log(myArray);   but I got Sam first cause he got 1992.. But I would like to display Thursday, February 26, 1991 first  Updated my solution :      sortByDateNoYear(adate, bdate) {         let results;         const lhdate = moment(adate.birthdayDate);         const rhdate = moment(bdate.birthdayDate);         results =           lhdate.month() > rhdate.month()             ? 1             : lhdate.month() < rhdate.month()             ? -1             : 0;         if (results === 0) {           results =             lhdate.date() > rhdate.date()               ? 1               : lhdate.date() < rhdate.date()               ? -1               : 0;         }         return results;       }  [array].sort(this.sortByDateNoYear);


Long-term visa expiration + Count towards Schengen tourist days?

I am an American citizen living in Poland for 6 months.  I arrived in Poland on February 1, 2016 without a Visa. The count toward my Schengen days began. I received my Work Visa for Poland on April 7, 2016.  The work visa expires on July 7th. I intend to stay in Poland until July 30, 2016 (which is 180 days after I entered on February 1)  My question is, do the days that I am on a Work Visa count toward my "90 days within a 180 day period" as a tourist?  And when my work visa expires on July 7th, will I be able to remain in Poland until July 30?  February 1 -> April 7 = 66 days July 7 -> July 30 = 23 days Total days as a tourist = 89 days


How to determine the Galois Group of a polynomial with "ugly" roots?

This is related to my .  Suppose I have the polynomial $p(x) = x^2 - 2 \in \Bbb Q[x]$. This is irreducible over $\Bbb Q$ so we need to move up to the extension field $K/\Bbb Q = \Bbb Q(\sqrt{2})$. Now $p$ splits over $K$ into $(x - \sqrt{2})(x+\sqrt{2})$ and it can be shown that the Galois Group $\operatorname{Gal}(K/\Bbb Q) \cong \Bbb Z/2\Bbb Z$ since it contains only the identity automorphism and one involution that sends $\sqrt 2$ to its conjugate $-\sqrt 2$.   My question is this; what if I have a polynomial with ugly roots? Say, for instance,  $$p(x) = x^5 - x^3 - 2x^2 - 2x - 1$$  This was shown in my previous question to be irreducible over $\Bbb Q$ so the splitting field of $p$ is simply $\Bbb Q$ adjoin the roots of $p$. These roots are, however,   $$\alpha \approx 1.73469\ \ \ \beta \approx 0.79645e^{0.49411\pi i}\ \ \ \gamma \approx 0.9533e^{5.6494\pi i}$$  and the conjugates $\overline \beta, \overline \gamma$ (do we get the conjugates for free when we adjoin complex roots or do we explicitly have to adjoin them?).  Then the splitting field $F$ of $p$ is $\Bbb Q(\alpha, \beta, \gamma)$ and their conjugates (depending on the answer to the question just asked).  At this point I'm not sure where to go; I've been trying to list automorphisms that fix $\Bbb Q$, obviously the identity is included, it seems also that the autmorphisms  $$\varphi_1 : \begin{cases} \beta \to \overline \beta \\ \gamma \to \gamma \end{cases}\ \ \ \text{and}\ \ \ \varphi_2 : \begin{cases} \beta \to \beta\\ \gamma \to \overline \gamma \end{cases}$$  are in the galois group. Also, $\varphi_2 \circ \varphi_1 = \psi$ should be in the group and this sends both $\beta$ and $\gamma$ to their conjugates. Any composition of $\psi$ with either of the others I've listed gives the other. I'm stuck for finding more now though. Since conjugation is an involution automorphism these are self inverse.   I'm not sure where to go from here! Is what I've done thus far even correct or have I totally misunderstood the concepts I'm trying to understand here?


I am looking for a way to trigger a piece of code when a console application is manually closed (users closes window). Been trying with:  AppDomain.CurrentDomain.ProcessExit +=     new EventHandler(CurrentDomain_ProcessExit);   but the above doesn't work if manually closed.  Is there any ways to use a .Net call for this or do I need to import the Kernel dll and do it that way?


Is it dangerous to do a lens change with power on?

I have just accidentally changed my lens over with the power on. In the manual it lists this as something you shouldn't do as a 'caution' . Can this cause damage? If so, what and how will I tell?  (I have an Olympus OM-D.)


I know I cannot do:  var elements = this.template.querySelectorAll('[id^="fieldName"]')[0]; elements[0].getElementsByTagName('lightning-formatted-text')[0].setAttribute("style:", "myCSSAttribute:myCSSValue");   Does this mean then, that, I would also not be able to do something like   var elements = this.template.querySelectorAll('[id^="fieldName"]')[0];  elements.$(lightning-formatted-text')[0].setAttribute("style:", "styleattribute:value");   If that makes sense? I've been trying to see if I'm doing this syntactically wrong or if there is another way to achieve the same result??  Here is my template markup  <template>     <lightning-record-view-form record-id={recordId} object-api-name={objectApiName}>         <template for:each={fieldsArray} for:item='field'>
<lightning-output-field id={field} field-name={field}></lightning-output-field>
         </template>     </lightning-record-view-form>     {dataStyleRulesList}
testidcontent
 </template>   And, I've loaded Jquery as a module like so:  import { LightningElement, api, wire } from 'lwc'; import { loadScript } from 'lightning/platformResourceLoader'; import getDataStyleRules from '@salesforce/apex/CustomMetaDataService.getDataStyleRulesForFields'; import jQuery from '@salesforce/resourceUrl/jquery';   ...   callAfterRenderAll() { $("#testid").attr("style", "background-color:green");$("#testid").attr("style", "background-color:green"); }


Is it possible that a person with myopia will see a blurry picture as normal?

I am trying to process an image in good quality to appear blurred to a normal person and good to a person suffering from myopia as seen in this .  Is it possible that a picture that is blurry will appear normal to a person suffering from myopia (farsightedness)?


Finding the maximum value of a product given certain values for x,y and z

Find the maximum value of $$(1-x)(2-y)(3-z)(x+\frac y2+\frac z3)$$ where $$x<1,y<2,z<3,x+\frac y2+\frac z3>0$$  I tried several cases to find a certain product. I tried 7 such cases. Three of them yield negative values while 4 gave postive fractional values. I chose the highest value which is 5/3. I already gave up and looked at the answer at the back of the questionnaire. The answer is $$\frac {243}{128}$$  Can anyone help me in answering this question?


"Add friend" has appeared on Facebook after a long time without it. Why?

I sent a friend request on Facebook about a year ago that was denied and the Add Friend Button no longer showed next to their name. Recently the Add Friend option appeared again next to their name. Does it appear on its own after a certain amount of time or does the user have to allow it to appear?


Why don't Muggle-born wizards use Muggle technology to fight Death Eaters?

We know that wizards in the Harry Potter universe are subject to regular physical harm (e.g. witness injuries from being hit by Bludgers or just colliding with things when playing Quidditch).  Therefore, it's almost a certainty that an average wizard would be vulnerable to, say, a bunch of bullets.   There may likely be spell(s) to protect from projectiles - witness Dumbledore's  deployed when Voldemort sent a bunch of glass at him during the  at the end of Harry Potter and the Order of the Phoenix (according to , possibly an unusually powerful Protego or the Silver shield).   But:   those spells obviously take effort/energy/time to cast (not everyone's Dumbledore) AND more likely than not most Death Eaters wouldn't recognize a Muggle gun for a threat (or realize what kind of threat) till too late.   So, the guns should at best allow an over-matched OotP member (e.g. Harry or Hermione) to greatly equalize the power between any regular Death Eaters and themselves, and even perhaps help against Voldemort (who can't be killed with a bullet, but, at best, would need to expend magical energy and time into conjuring a shield, and, at worst, be stopped/interrupted/driven off).  So I'm looking for an explanation - ideally in-universe, but possibly just some statement by JKR - of why the Muggle-born OotP - who are likely very much at ease AND familiar with Muggle technology and live in the late 20th century - do not use guns. Or, for that matter, ANY Muggle technology of the late 20th century? Cue Arthur C. Clarke's "indistinguishable from magic" meme.  Even if they are on some kind of idiotic moral crusade to never kill their opponents (even the Jedi aren't this dumb), given the time-frame, non-lethal weapons would have already existed, such as rubber bullets and tasers.  NOTE: Please don't offer the "if they do it, Death Eaters would start using guns as well" theory. First, Death Eaters would have used the guns if they knew how to, anyway. Second, the guns, like any "secret weapon", could be reserved for strategic battles, say the defense of Hogwarts in Deathly Hallows.    The origin of the question stems from two things.  First, Harry's fascination with all things that are different in the magical world (e.g. moving photographs), based on his knowledge of the Muggle material world, as well as the somewhat amusing cluelessness of the "Muggle artifacts" expert, Mr. Weasley, regarding Muggle items and how they work.   Basically, from the books, it's clear that the Wizarding world wouldn't know details about guns or what they are for or how they work.  The second thing is it's clear, at least initially, that wizards are afraid of Muggles finding out about them. Hence all the efforts to cloak their society (basically, do you REALLY want every Muggle gunning for you, even with Magic)? The idea of how control over the Muggle world seems to be more indirect, by Death Eaters asserting mind-control over the government. This means there's an implicit understanding by Death Eaters that they don't stand a chance against armed Muggles even given the magical disparity.  Considering Harry and Hermione's overall adaptability and inventiveness (and brains in the latter case), it's mind-boggling that the idea of fighting Death Eaters with modern technology completely slipped their mind. I mean, it's a basic part of human myth (see Steel vs. Magic themes in Conan books, or Beowulf, or heck, A Yankee in King Arthur's Court). So it's not like the idea of using technology against magic would be impossible to come up with. The question begs itself - why not? Considering the fact that Rowling generally tried to be logical and consistent in building the HP universe, I feel like there must be some in-universe explanation for this that I just didn't notice.   (in-universe answers only unless there are some authoritative out-of-universe statements that are part of canon).


Upgrading 13.10 to 14.04 alongside a windows 7 installation

I have dual boot on my laptop: - Windows 7 with Ubuntu 13.10 installed alongside.  How do I upgrade my ubuntu installation to 14.04 without affecting the Windows installation?


I tried to install Ubuntu over a year ago and was almost able to get it right, aside from my ATI graphics card. Well, 4 months ago I bought a new Nvidia graphics card and thought I'd give Ubuntu another try. Unfortunately, Ubuntu has it out for me.  I've used both CD and USB flash drive, and I had the same issue with both. Once I restart and prepare to install Ubuntu it takes me to an orange and yellow gradient screen and then, shortly after it takes me to a black screen with a blinking underline character at the very top.   I left the computer for over 4 hours last night and came back to find that it was STILL STUCK on this black screen. I'm currently running two hard drives: one has 1TB and the other is 177GB.  My specs are as follows:       Intel i5 2500k 3.3Ghz Quad Core   EVGA NVIDIA GTX 750TI 2GB VRAM   8GB dual channel RAM   Biostar H61MH       Any help in fixing this issue is most appreciated.


Why am I getting 500 error while trying to send emails to some domains?

Recently I've been seeing the following error while trying to send emails to some domains:  Final-Recipient: name@example.com Original-Recipient: name@example.com Action: failed Status: 5.0.0 Remote-MTA: dns; mail.example.com Diagnostic-Code: smtp; 550 "The mail server detected your message as spam and     has prevented delivery."   Neither my IP address nor my domain is blacklisted. The email is a simple test email without attachments or links.  What can I do or where can I get more information about this issue?  Thank you


My problem is with the print composer: it shows a huge red cross. I thought it is because of a wrong image format, because there was a smaller cross on one of the images. So I deleted it, then deleted all of the images I have used, but it is still there.  Can someone help me how to remove it?