Subring of Gaussian integers has no greatest common divisor property
Find two elements that don't have a gcd in a subring of Gaussian integers
Continuous Images of $GL_n(\mathbb{R})$ Which of the following is a continuous image of $GL_n(\mathbb{R})$?  The real line $\mathbb{R}$  The subspace $\{(x,\frac1x):x\in \mathbb{R},x \ne 0\}$ of $\mathbb{R}^2$  $\mathbb{R}^2 \setminus \{(x,\frac1x):x\in \mathbb{R},x \ne 0\}$  $\{(x_1,x_2,...,x_n):x_1^2+x_2^2+...+x_n^2 \le 1\}$ of $\mathbb{R}^n$   How do I proceed? $GL_n(\mathbb{R})$ is not compact, not connected, so I cannot rule out some options using topological properties. Looking for a book with parallel universes like pages, possibly with "maze" in title, and a black Jewish female character Looking for a book. A series,  actually.  The main characters were a Jewish man and a black woman who was his wife. There was a running gag when she would tell people her last name and they thought it was unusual that a black woman would have a Jewish name.    They went on adventures in parallel dimensions. I believe that each book had a word repeated in the title, maybe "mirror?" Or "maze?" Or "page..."  it seems they jumped into worlds through a tool like a mirror or a book.   The parallel universes were like pages, and the pages closest to you were most similar but the further you got the further they were from your life.  One page over might be that you had something different for breakfast and so now you have a tummy ache, a few more pages over you might have become a prostitute, too far and it was theorized that humans had evolved differently altogether, I didn't get that far in the series.  For adults, and humorous.  I read them about 15 years ago, so they are not new. I would love to find them again. Is there a software utility to adjust screen gamma/brightness/contrast? When should I use "when" and "while"? But you can't find anything while you're crying.   But you can't find anything when you're crying.   I'll tell you about it while Frank saddles the horse.   I'll tell you about it when Frank saddles the horse.     When should I use when, and when while? Are these sentences correct? Between you and ("me" or "I")? What is necessary and/or sufficient for polynomials to provide isomorphic quotient rings? Windows 8 OEM Reinstalling I know this question is a repetition but I didn't find any solution of my problem from any of the previous questions. Recently I formatted my Laptop HDD and now I want to re install windows 8 I've a Windows 8 OEM license but the problem is I don't have a disc , I downloaded en_windows_8_x64_dvd_915440 from msdn , but when I boot the windows it shows the error that the current version is not suitable with my serial key, so where I can find an OEM Windows 8 and also I've a retail windows 8 disc so if I install that windows 8 in my pc and is there any way to activate it using my OEM key How to remove a filter that is an anonymous object? In my functions.php file I would like to remove the below filter, but I'm not sure how to do it since it's in a class. What should remove_filter() look like?  add_filter('comments_array',array( &amp;$this, 'FbComments' ));   It's on line 88 . Compound literals in MSVC Is there a way to configure pdflatex to make all but the .tex and .pdf files hidden files? I have asked a  about how to manage all the files generated when my LaTeX files are compiled but the approach in the answer I accepted is still unsatisfactory for the many small documents I generate.    I realize the LaTeX  all the files it generates so I can't prevent their creation.    However is there a way to configure pdflatex to make all but the .tex and .pdf files hidden files (i.e., preceded by .)?   (Edit: The two main systems that I use are tex live on Ubuntu Linux and BasicTeX on OS X) Why does my query run fast in Environment A, but slow in Environment B? I have a piece of SQL that seems to run really fast in Environment A, but the exact same query runs really slow in Environment B!  Environments are supposed to be the same, so what should I do and/or where should I look in order to see why the query doesn't perform the same? What is the reasoning behind limiting "recidivists" to post one question per week? currently restricts recreated accounts to "posting only one question per week..."  I would like to understand why this rate was picked, and not, say, once a day or once a month?  The reason why I ask is that some users limited or banned at Stack Overflow . I expect that learning more about the limitation would help me better understand its impact on Programmers. What part of a multi-type damage roll is reduced by a non-type-specific effect? Effects like  (PHB, p. 54) and Spirit Shield (XGtE, p.  10) reduce damage by a roll, irrespective of damage  (PHB 196). However, single damage rolls can have multiple damage types, as confirmed (for wording) by Jeremy Crawford in .   How do you know which part of the damage is reduced?   This could actually make a difference to the amount of damage taken if, for example, the creature taking damage is resistant to one or more of the damage types involved.       Cutting Words: ... When a creature that you can see within 60 feet of you makes an attack roll, an ability check, or a damage roll, you can use your reaction to expend one of your uses of Bardic Inspiration, rolling a Bardic Inspiration die and subtracting the number rolled from the creature's roll.   Using this ability to expand upon the examples found in  and :     Barny, an Ice Devil (MM, p.  75) hits Bobby, rolling 9 slashing damage and 11 cold damage.      Bobby's ally, Vera, is a level 10 bard of the college of Lore, and uses her Cutting Words ability on the attack's damage roll. She rolls a 9, which is subtracted from the Barny's damage roll.      Bobby is wearing his Boots of the Winterlands (DMG, p.  156), giving him resistance to cold.   We know that "resistance and then vulnerability are applied after all other modifiers to damage" (PHB, p.  197) and both slashing damage and cold damage are treated as "one big damage roll" (see the JC tweet), so is all the 9 slashing damage removed by cutting words, and then the cold damage halved for 5 total damage, or is 9 of the cold damage removed by cutting words, leaving 2 to be halved for a total of 1 + 9 = 10 damage taken by Bobby?   Who makes this decision?  When an effect (like cutting words) reduces damage without specifying type from a source containing multiple damage types, what part of the damage is reduced? How to check if $\sum_{n=1}^\infty \frac 1{n!}$ is converging or diverging by direct comparison test? $$\sum_{n=1}^\infty \frac 1{n!}$$   I think we may compare it with $\frac{1}{n^n}$, and say that $\frac{1}{n!}&gt;\frac{1}{n^n}$. But I am not sure of the convergence or divergence of $\frac{1}{n^n}$ itself, so this turns out to be useless.  What other way is there? Is $(B_t^2)$ Markov where $(B_t)$ is Brownian motion? I am pretty sure $(B_{t}^{2})$ not Markov because the squared random walk is not.    I guess I can repeat the method since to be Markov it must satisfy the discrete.  Thanks induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$ I encountered the following induction proof on a practice exam for calculus:  $$\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$$  I have to prove this statement with induction.  Can anyone please help me with this proof? How should I interpret this residual plot? I am unable to interpret this graph. My dependent variable is total number of movie tickets that will be sold for a show. The independent variables are the number of days left before the show, seasonality dummy variables (day of week, month of year, holiday), price, tickets sold till date, movie rating, movie type (thriller, comedy, etc., as dummies). Also, please note that movie hall's capacity is fixed. That is, it can host maximum of x number of people only. I am creating a linear regression solution and it's not fitting my test data. So I thought of starting with regression diagnostics. The data are from a single movie hall for which I want to predict demand.  The is a multivariate dataset. For every date, there are 90 duplicate rows, representing days before the show. So, for 1 Jan 2016 there are 90 records. There is a 'lead_time' variable which gives me number of days before the show. So for 1 Jan 2016, if lead_time has value 5, it means it will have tickets sold until 5 days before the show date. In the dependent variable, total tickets sold, I will have the same value 90 times.  Also, as a side remark, is there any book that explains how to interpret residual plot and improve model afterwards? %AX = (%AH + %AL)  So why not %EAX = (%SOME_REGISTER + %AX) for some register %SOME_REGISTER? How did the house elves start serving wizards? How/Why/When did the house elves start serving wizards? I tried on my own to find the answer but I couldn't find anything relevant to my subject but I am bad at searching. Simulate Multiple Monitors I'm trying to find out if there is a product out there to simulate Multiple Monitors on one large monitor/tv?  So take a screen and turn it into something like below...  -------------------------------- |               |              | |               |              | |               |              | |               |              | -------------------------------- |               |              | |               |              | |               |              | |               |              | --------------------------------   Something like this...even though in reality it's a single screen.  A software solution is perfectly fine as long as it functions like the built in Windows 8 functionality (Start screen only consumes the screen it was started on/etc).  If anyone is curious as to the reason.  I'm looking to get a treadmill desk since I'm a developer and don't like being sedentary all day.  So the two options that I see are having 4 monitors and mirroring them (I don't want to have to worry about forgetting to move the window that I need) or getting a large monitor/tv and putting it on an arm that I can simply swivel into place.  There are dual-monitor swivel mounts, but they are EXTREMELY pricey and the ones I've found don't appear to have the range of motion that I'm anticipating needing.  EDIT:  I found ... but I can't find the answer to the start menu question (I've sent the company a message on facebook).  Hoping I hear good news as this appears to offer many of the features I'm wanting.  So Fingers crossed there.