I have a document with colored hyperlinks, using the options of the hyperref package.  I also have lots of tikz-figures that use various shades of gray and occasionally some colors.  The way my document is right now looks very nice on screen but not so great when I print it on a monochrome printer. I tried using xcolor's \selectcolormodel{gray} but then all the colors are printed as shades of grey. This is ok for figures but not acceptable for the text.  Is there a way to change the color of the text (and only that) to black when printing the document? The figures should stay as they are (colored/shaded).  If this is not possible, is there a way to turn all the figures in grayscale and all the text to black?  Are things like these possible or do I have to maintain 2 diferrent versions of my document (i.e. one for on-screen reading and the other one for printing)?  I am using XeLaTeX if it is of any importance.  some text    and a figure with shades of grey
I like having my hyperref hyperlinks a different colour, so it's obvious that they are links. But when I print a copy of the PDF, I don't want the links to be coloured, because you can't click them, so it doesn't matter and it's distracting.  Other than just having a separate "for printing" version of the PDF where I turn off the hyperlinks, is there a way to have the printed version come out without the coloured links?
Efficient online linear regression I'm having difficulty with exercise 1.43 of Lang's Algebra. The question states     Let $H$ be a subgroup of a finite abelian group $G$. Show that $G$ has a subgroup that is isomorphic to $G/H$.   Thinking about this for a bit, the only reasonable approach I could think of was to construct some surjective homomorphism $\phi\colon G\to K$ for $K\leq G$, and $\ker\phi=H$, and then just use the isomorphism theorems to get the result.  After a while of trying, I've failed to come up with a good map, since $H$ seems so arbitrary. I'm curious, how can one construct the desired homomorphism? This is just the approach I thought of, if there's a better one, I wouldn't mind seeing that either/instead. Thank you. Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$ Theorem: There are infinitely many primes congruent to $3 \mod 4$. Proof: Assume that $p_1 = 3, . . . , p_n$ are primes of the form $p_j ≡ 3 \mod 4$. We will construct a new one by looking at $N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work).  There is more to this proof but the rest of it I understand, what I don't get is where it says &quot;$N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work)&quot;. I do not understand why we are writing $4p_1 · · · p_n − 1$. Is there a more clear way to prove this theorem? Automatically put PGFPlots xtick scale label in x axis label Why is my ASCII art all wonky? Nothing looks right in the ASCII art.  It looks wrong and nothing is proportional, how do I fix this? I have tried fiddling with my font size, but nothing still looks right! Why does the /winsxs folder grow so large, and can it be made smaller? A Vista virtual machine I use only has a 10 GB virtual hard disk -- and I'm worried about it running out of space over time. I used  to check for the culprits..  And the primary culprit is that /winsxs or &quot;Windows Side-By-Side&quot; folder.  What is the Windows Side By Side folder? Well, that's .  All of the components in the operating system are found in the WinSxS folder – in fact we call this location the component store.  Each component has a unique name that includes the version, language, and processor architecture that it was built for.  The WinSxS folder is the only location that the component is found on the system, all other instances of the files that you see on the system are “projected” by hard linking from the component store.  Let me repeat that last point – there is only one instance (or full data copy) of each version of each file in the OS, and that instance is located in the WinSxS folder.   So looked at from that perspective, the WinSxS folder is really the entirety of the whole OS, referred to as a &quot;flat&quot; in down-level operating systems.  This also accounts for why you will no longer be prompted for media when running operations such as System File Checker (SFC), or when installing additional features and roles. That explains why the folder starts off big, but not why it gets larger over time – the answer to that question is servicing.   In previous versions of Windows the atomic unit of servicing was the file, in Windows Vista it’s the component.  When we update a particular binary we release a new version of the whole component, and that new version is stored alongside the original one in the component store.  The higher version of the component is projected onto the system, but the older version in the store isn’t touched.  The reason for that is the third part of why the component store gets so large.  Lots of other people :  A coworker recently received his every two year work laptop refresh and was in the middle of loading his new laptop with Vista. For some reason, his hard drive C: was partitioned to only 25GB and the rest of the space reserved for a much larger drive D:. Anyway, after loading many Windows Updates, he was left with hardly any drive space left on C:, and for some reason, the WinSxS directory had ballooned to over 8GB. While I knew what the WinSxS (Windows Side-by-Side) directory was for, I wasn't quite sure why that directory would explode in size so fast with normal operating system updates.  I don't really care about having all these duplicate files for safety, but I do care about the VM exploding due to an out of disk space error. So.. can /winsxs be safely pared down in any way? ..  Administrators should not, for any reason, take it upon themselves to clean out the /winsxs directory - doing so may prevent Windows Update and MSI from functioning properly afterwards.  Preventing accidental deletion from the directory is accomplished by putting a strong security descriptor on the directory that inherits to its children.  If this /winsxs folder gets any larger, I'm going to have to re-image this virtual machine.. which I really don't want to do! SQL Server: Examples of PIVOTing String data Trying to find some simple SQL Server PIVOT examples.  Most of the examples that I have found involve counting or summing up numbers.  I just want to pivot some string data.  For example, I have a query returning the following.  Action1 VIEW   Action1 EDIT   Action2 VIEW   Action3 VIEW   Action3 EDIT     I would like to use PIVOT (if even possible) to make the results like so:  Action1 VIEW EDIT   Action2 VIEW NULL   Action3 VIEW EDIT     Is this even possible with the PIVOT functionality? I was working on a userscript today, which had a goal of displaying chat pings immediately at the main site. This would allow me to respond more quicker-like to chat pings.  However, I was met by this fearsome warrior:     Can we please set some decent header things? I want to be able to do this really bad. Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge? Does the following series converge or diverge? $$ \sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}} $$ The methods I have at my disposal are geometric and harmonic series, comparison test, limit comparison test, and the ratio test. Solving $\sqrt{x+5} = x - 1$ I'm currently learning about radicals and simplifying them, and I came across this problem on the internet and tried to solve it:  $$\sqrt{x+5} = x - 1$$  So I used this logic:  $$ \begin{align} \sqrt{x+5} &amp;= x - 1 \\ x + 5 &amp;= (x-1)^2 \\ x + 5 &amp;= (x-1)(x-1) \\ x + 5 &amp;= x^2 - 2x + 1 \\ 0 &amp;= x^2 - 3x - 4 \\ 0 &amp;= (x-4)(x+1) \\ \end{align} $$  Therefore, $x = -1$ and $x = 4$ satisfy the equation $0 = (x-4)(x+1)$.  But then I tried to plug them in the original problem $\sqrt{x+5}=x-1$:  $$ \begin{align} \sqrt{4 + 5} &amp;= 4 - 1 \\ \sqrt{9} &amp;= 3 \\ 3 &amp;= 3 \end{align} $$  So using 4 works as expected, but when using $-1$:  $$ \begin{align} \sqrt{-1 + 5} &amp;= -1 - 1 \\ \sqrt{4} &amp;= -2 \\ 2 &amp;\ne -2 \end{align} $$  At what stage am I going wrong?  And according the , the solution is $x = 4$. Find $x$ in   $$ \Large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$$   A trick to solve this is to see that $$\large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}} \quad\implies\quad 2 = x^{\Big(x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}\Big)} = x^2 \quad\implies\quad x = \pm \sqrt{2} $$  Are these solutions correct? If not, why? If yes, are there other solutions?    PS: An extension of this discussion can be found in Why do you need to know who I know on Google? I just created a SE account using my Google account. It said that it needs to "Know who you are on Google" (I guess my connections). As far as I know, SE is not a social network. I can't even follow other people (seeing when they post questions and answers).  What is the reason you need to know my Google connections?  This was on code review. Actually I have an account there, but for some reason it asked me to reconnect. This is the same on MSO; one sees this explained as "This app is requesting permission to associate you with your public Google profile": I am using gdal_rasterize to create a raster of a huge file containing polygons. I managed to generate the raster file with the right color and with the minimum size to tile it after with the gdal2tile.  gdal_rasterize -of GTiff -co COMPRESS=DEFLATE  -b 1 -b 2 -b 3 -burn 136-burn 46 -burn 17 -co PREDICTOR=2  -co ZLEVEL=9 -ot Byte  -a_nodata 255  -a Niveau  -ts 500000 500000  -l layer W:/layer.shp W:/layer.tif   Tile will be used to overlay Google Maps so the polygon must be transparent.  Has anybody experimented with this usage of gdal_rasterize and succeeded in setting the opacity of the output raster? if $a,b,c$ are non zero positive reals prove $$\sum_{cyc}\frac{1}{a^3+b^3+abc} \le \frac{1}{abc}$$ I have used A.M  G.M  inequality as follows:  $$a^3+b^3+c^3 \ge 3abc$$ adding $abc$ both sides we get  $$a^3+b^3+abc \ge 4abc-c^3=c(4ab-c^2)$$ so  $$\frac{1}{a^3+b^3+abc} \le \frac{1}{c(4ab-c^2)}$$ But since $a,b,c$ are positive reals  $$4abc-c^3 &lt; 4abc$$ so  $$\frac{1}{4abc-c^3} \gt \frac{1}{4abc}$$  but i am unable to proceed here Long-distance Mind Trick In the Star Wars universe, could a Jedi Mind Trick be performed over the telephone?   For instance, could Yoda have called up the Imperial embassy on Dagobah and mind tricked whoever answered into getting him in touch with Palpatine? (I know there's no embassy or telephones on Dagobah, but serious question nonetheless.)   To clarify, are long distance mind tricks not only possible but would being in communication with another person, through telecommunication, allow a force user to better perform the action? I know that who is used when asking about a subject (Who is at the door?) and whom is used when asking about an object (By whom was the door opened?). How do you determine which one to use when the object becomes the subject of another clause?   For example, take the sentence:      I gave the prize to ____ deserved it most.   Would it be whomever because it's the object of "gave," or would it be whoever because it's the subject of "deserved"? Is their a hard-and-fast rule to rely on in situations like this? Prove by induction. How do I prove $\sum\limits_{i=0}^n2^i=2^{n+1}-1$ with induction? Port forwarding with UFW I realize UFW is mainly just for enabling/disabling access on particular ports, but I'm trying to forward one port to another. I want any connection to port 1724 to be forwarded to 1723.   The file /etc/default/ufw already has DEFAULT_FORWARD_POLICY="ACCEPT". And I believe I need to uncomment net/ipv4/ip_forward=1 in /etc/ufw/sysctl.conf. Finally I need to edit /etc/ufw/before.rules to add an iptables rule.   And here is where I get lost because I can't find any documentation for this file. Where do I add the rule? And how exactly?  In particular:   On exactly which line do I add the rule? Do I put anything before or after it? Sci-fi series: humans are immune to telepathy, become soldiers for an alien group fighting against invertebrate telepaths The series involves two groups of aliens who have been fighting an interstellar war for many years before the first book.  The war is started by a race of jellyfish-like telepaths who have used their powers to control several species which they use as soldiers.  The jellyfish aliens have declared a holy war against all sapient vertebrates.  The only species on their side that aren't being actively controlled through their telepathy are invertebrate species who have joined the holy war.  In this series, humans are immune to telepathy--what's more, a completely unconscious reflex tends to destroy the mind of anything even attempting to affect their minds.  One of the central themes of the series is how well suited humanity is to warfare, and all the sacrifices forced on humanity as they become nothing but soldiers fighting against the jellyfish, losing almost all culture not in some way related to being soldiers, as the other races in their alliance take over the other roles.  Other species I recall include a bird race that is gifted at linguistics but can be sent into shock by even seeing a low quality recording of a human walking around a room.  They just cannot handle the hide or flee reflexes triggered by seeing such an obvious predator.  Another race is a crab like group that is so antisocial they all keep suicide buttons at hand when working with other races, and only work to help the human alliance's side because the jellyfish won't leave them alone.  There is a race that bears a faint resemblance to large rats who were previously the best soldiers on their side, and another renowned for their intellect. An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$ Prove that for any positive integer $n$,       $$n^{1/n}  &lt; 1 + \sqrt{\frac{2}{n}}.$$   This due to Victor Linis, Eureka, Vol. 2, No. 2, February 1976, p. 29.   Hint:      Use the binomial theorem.