Incomplete class template issue - C++
Why can templates only be implemented in the header file?
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$ If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$.  I tried assuming Diophantine Equations for all the relations and representing everything in terms of $a$, but that didn't lead me anywhere. There must be an intuitive and elegant approach right? How to monitor USB power consumption? I'm looking for a way to monitor the power being drawn from the USB ports on my Mac.  System Profiler doesn't appear to display this and I haven't been able to find any applications or tools to do the job either.  Can anyone suggest anything (preferably software based)? A question occurred to me when browsing SE this evening, just curious.  What specifies the inside of a 3D construct? If I have a hollow sphere, what's to say that the world isn't the inside, and the center of the sphere isn't the outside. Picture the Asylum in the Hitchhiker's Guide to the Galaxy series, if you have read that.  Additionally, if the inside of a 3D object is defined as what is smaller than the outside, what happens when there is a a sphere with a volume equivalent to 51% of the universe? Website Visible only to Registered users I watch a lot of old movies, and I've noticed that American actors of the 1930s and 1940s often spoke in a quasi-generic-posh-British accent.  Katherine Hepburn's accent would be the perfect example. It seems exaggerated, and I imagine it was not common off the stage and screen. What was that? Was it just an accent or was it a dialect? Did real people actually speak that way? Why MOSFET source is indicated with arrow ? Do not give the impression that all votes are unanimously in favor of the winning close-reason. I closed for "belongs on superuser," yet SO claims I closed for a completely different reason.  Source: Since Ubuntu 18.04 I can't drag a file e.g. image file to an open application such as Inkscape or  email message window. In Ubuntu 17.10 I was able to select the image file by clicking on it, and while holding down left mouse button I would hit the supper key displaying all open windows where for there I could then drop the file in any open app or folders. This is no longer possible/default behaviour since Ubuntu 18.04. Is there a workaround that would allow me to achieve this or even a way to recreate the same behaviour like in 17.10? Is "tri-quarterly" a real English word meaning 3 times a year? Is "tri-quarterly" a real English word meaning 3 times a year? Are there any other words that mean 3 times a year? Lebesgue measurable but not Borel measurable HTTP webpage is showing "Not Secure" in Chrome I've called GoDaddy a few different times and they said that it looks like it is a problem with my HTML file.  Except, my HTML file is the basic outline of a webpage, nothing fancy at all.    Chrome still says that the webpage is, "Not Secure" with the big red x over it.    I'm not sure what to do to fix it, I don't have any personal information on the site nor am I collecting any information from visitors (it's sort of an information site).  I shouldn't need an SSL certificate because I am not hosting anything privately. A concise definition of a frame of reference in Newtonian mechanics? I've read  on frame of reference and also followed all of the references cited in the text (Salençon, Brillouin, Norton, etc) but I'm struggling to find any concise definition in all of that.   I would like a concise definition for a frame of reference in the context of Newtonian mechanics. This definition should not involve any additional qualifiers such as inertial and must be mature enough as to differentiate a frame of reference and a coordinate system. Is there one such definition? $\mathbb{R}P^4$ and $\mathbb{R}P^6$ do not admit fields of tangent $2$-planes See the related question . This is the second part of question 4-C in Milnor and Stasheff's book on characteristic classes. In the solution to the first part, we rely on the fact that having a field of tangent $1$-planes allows us to split the tangent bundle into a direct sum. It doesn't seem like this should be true for a field of tangent $2$-planes (otherwise the question wouldn't just be asking about $P^4$ and $P^6$), so I'm not sure exactly where to start.  edit: actually, since $P^n$ can be given a Riemannian metric, any subbundle should be a Whitney summand; this doesn't answer the question as to why they only ask for $P^4$ and $P^6$ though, so I'm still confused. The residue at $\infty$ I am stuck on the following problem :      $\,\,\,\,$*Problem*$\quad$The residue of an entire function at $\infty$ is $0$.      Solution: True. This follows from the definition of the residue at $\infty$ together with the Cauchy-Goursat Theorem. Another way to see this is to take the Taylor expansion for $f$ at $0$ $\displaystyle f(z)=\sum_{n=0}^\infty a_nz^n$ and replace $z$ with $1/z$ to get the Laurent expansion for $f(1/z)$ at $0$: $\displaystyle f(z)=\sum_{n=-\infty}^0a_{-n}z^n.$ Then we have that the residue at $\infty$ is given by the negative coefficient of the $1/z$ term of    $$ \dfrac1{z^2}f\left(\dfrac1z\right)=\sum_{n=-\infty}^{-2}a_{-n-2}z^n, $$   which is clearly $0$.   I am having trouble to understand the last few lines (in italic) in the given solution. Can someone give lucid explanation? Thanks and regards to all. How to access a variable from another script in Unity c# We have the matrix: $$\left[\begin{array}{rrr} 0.8&amp;0&amp;0\\ 0&amp;1.2&amp;0\\ 0&amp;0&amp;1\\\end{array}\right]$$ Finding the eigenvalues and eigenvectors are easy. But finding ${\bf M}^n$ when $n \rightarrow \infty$ is the hard part. Any suggestions? How to merge vertices in Blender? I am attempting to create my first 3D character just for practice. Being one of my first 3d models I going through the learning curve needless to say. In doing so I find myself creating many extra vertices. Where we will say 10 vertices on a rounded shape are spaced out on the equator and on the other north pole end of the edges they are very close. The close end could all be one vertex. Is it possible to say merge all points to one point and delete the rest? I messed up my system earlier, I was greeted with a black screen, when booting in to Ubuntu. When I started up my laptop, I selected the recovery option from the grub menu, and chose fallback at root terminal. I saw that I was able to use the add user command, with it, I probably could use to create a privileged user on my machine.   Isn't that a security issue?  One could have stolen my laptop and at startup chose recovery and add another user, I'm fudged then. Including my data.  Come to think of it, even if you somehow remove that entry, one could boot from a live-CD, get a chroot up and running and then add another user, with the right privileges that allows it to see all my data.   If I set the BIOS to boot at my HD only, no USB, CD/DVD, Network startup, and set a BIOS password, it still wouldn't matter, because you'd still have that grub recovery startup entry.  I am fairly certain that someone from China, Russia can't hack my Ubuntu Trusty Tahr, from the network, because it's secure like that. But, if one has physical access to my - your - machine, then, well, that's why I'm asking this question. How can I secure my machine so that hacking through physical access is not possible?    Bug Report: Object Positions Reset On Blender Load So I am attempting to make a modular environment in Blender, so I'm modeling many pieces in one scene to make sure they all match up properly before separating them out.  However, whenever I restart Blender after saving and closing it, many of my grouped objects (and their subobjects) have positions reset NOT to where I placed them.  For example, take a look at this:   Here you can see that the door pieces are in the "open" state, when I left them closed AND the "column" for the wall on the left has been moved from being flush with the wall (on the side) to being inside it.  It appears to be trying to move all of the objects to 0,0,0 which is what is messing this up. I'm not sure if it's an object hierarchy problem, but here is my hierarchy if anyone has ideas there:  Wall_Normal (parent)   Wall_Normal_Column (child)   Empty Axis Object (parent)   Door_Left (child a) Door_Right (child b)   Is there a reason why object positions (and their relative subobjects) aren't being saved? Why is everybody so concerned about etc/passwd?