Virtualbox Freezes Entire Computer when starting any Virtual Machine
VirtualBox 5.0.40 crashes the whole host since update to kernel 4.13.0-26-generic
Prior to doing some benchmarking work how would one free up the memory (RAM) that the Linux Kernel is consuming for its buffers and cache?    Note that this is mostly useful for benchmarking. Emptying the buffers and cache reduces performance! If you're here because you thought that freeing buffers and cache was a positive thing, go and read . The short story: free memory is unused memory is wasted memory. Prove that $||x|-|y||\le |x-y|$ Lower bound for $\phi(n)$: Is $n/5  1$? Is it true that :  $\frac {n}{5} &lt; \phi (n) &lt; n$ for all $n &gt; 1$ where $\phi (n)$ is  .  Since $\phi(n)$ has maximum value when $n$ is a prime it follows that maximum value of $\phi(n)$ in term of $n$ is $n-1$ , therefore $\phi(n)&lt; n$ for all $n$. What is the best lower bound for $\phi(n)$? I want to make a long shadow just like in this image.  I can create this shadow with shapes and by deleting the unwanted shadows after rasterizing the layer. But it's not very reusable. I can't resize the layer after rasterizing it.  Is there any easy way to make a long shadow like in the image below? Comment hint not disappearing when I start to type comment If I click "add comment", the comment hint (placeholder; "Request clarification or add information.") is not a hint, but editable text. If I delete the text and click outside of the comment then the hint appears as it should and when I click back into the comment box the hint disappears as it should.   I am on Internet Explorer 10.0.7.  Am I just oblivious and this is how it has always been (having to delete the comment hint), or is this a bug? Why are American-style options worth more than European-style options? Why are American-style options worth more than European-style options?   I realize I can exercise American-style options anytime before the  expire, but I can only exercise European-style options during their  "exercise period" (usually right when they expire, but no earlier).   So it makes sense that an American option is worth at least as much as  a European option.   But why is it worth more? If I exercise my American option early, I  may make more money than waiting until expiration, but I also may make  less. Mathematically, there's no advantage, since I'm equally likely  to make as much money by waiting for expiration.   Mathematically speaking, is there ever a good reason to exercise an  American option early?   I realize people don't always behave logically, but even the formulas  that valuate options show that American options are worth more.   EDIT (answering comments):    Many of the comments people made would apply to lookback options  (), but not to American  options.  American options can do everything European options can and more. I  understand that, and that means American options can't be worth any  LESS than European options, but I'm still not clear on how you would  mathematically calculate this extra value.  @Aaronaught: "The difference between an American and European  option is the difference between getting N chances to get it right (N  being the number of days 'til expiration) and getting just one  chance. It should be easy to see why you're more likely to profit  with the former, even if you can't accurately predict price  movement."    REPLY: I don't think you really get N chances. Once you exercise the  option, that's it, no more chances. And, if you decide not to exercise  the option today, and the underlying's price falls, you can't go back  in time and exercise it yesterday.    @jdsweet: Think of it this way, if you traveled back through time  one month - with perfect knowledge of AAPL's stock price over that  period - which happens to peak viciously then return to its old price  at the end of the period - wouldn't you pay more for an American  option?    REPLY: Well, no. I'd simply buy a cheaper European option that expires  right at the spike. Or, I'd buy a European option that expires later,  and sell it when the spike occurs. American options don't give you  precognition, so you're still guessing as to when to sell/exercise.    @jdsweet: "one of the more common reasons people exercise (as  opposed to sell) an American option before expiration is if an  unexpected dividend (larger than remaining time value of the option)  was just announced that's going to be paid before the option contract  expires"    REPLY: This makes sense. I'm actually trading FOREX options, so there  is no dividend. In that scenario, are European and American options  worth the same? I have a registered StackOverflow account which I normally log into using OpenID.  Recently I logged out in order to post a question anonymously (supplying a fake name and of my secondary email addresses).  The problem now is that I'm logged in to StackOverflow as this "dummy" user, unable to see a way to log out.  The top menu normally has a "logout" link, but when you aren't fully registered this link is replaced with "register".  There is no "logout" link for me. :(  So..   When logged out there is a "login" link. When logged in there is a "logout" link. When "logged in" with an unregistered account, there is only a "register" link (no "logout"). Why is torque not measured in Joules? Recently, I was doing my homework and I found out that Torque can be calculated using $\tau = rF$. This means the units of torque are Newton meters. Work &amp; Energy are also measured in Newton meters which are Joules.  However, torque isn't a measure of energy. I am really confused as why it isn't measured in Joules. I'm experiencing a bug where when the machine comes back from standby a monitor connected via displayport (MST) does not come back on, however the windows are still in the area it cover if it did come on.  The only way to recover from this short of a restart is to disable and reenable the display now I can do that via the command line just fine but when the display is disabled all the windows get rearranged onto the remaining screen.  Is there a way to persist the window positions and restore them so my script could do this sequence:-   enumerate windows, store positions display off (messing up positions) display on (making the display work again, yay!)  restore position of the windows   I can do step 2 and 3 just fine but I'm lost for step 1 and 4  I know I can force a position per app but that's not what I want as I could be doing different things and have the same apps in different positions, I also have multiple terminals open, I need the current positions storing somehow and restoring.  Any help would be appreciated! using underscore's “difference” method on arrays of objects Show that the following series of function defines a continuous differentiable function function in $\mathbb R$. $$\sum_{n=1}^{\infty}\frac{\sin (nx^2)}{1+n^3}.$$  We have , $|f_n(x)|=\left|\frac{\sin (nx^2)}{1+n^3}\right|\le \frac{1}{1+n^3}\le \frac{1}{n^3}=M_n \text{ (say) }$  As, $\sum M_n$ is convergent so, the given series is uniformly convergent. Also , each $f_n(x)$ is a continuous function in $\mathbb R$. So, the given series converges to a continuous function , say $f(x)$.  But how we can show that $f(x)$ is differentiable function ?  Please help... CSS3's border-radius property and border-collapse:collapse don't mix. How can I use border-radius to create a collapsed table with rounded corners? Here's a fragment from Jack London's Star Rover:     Wordsworth knew. He was neither seer nor prophet, but just ordinary man like you or any man. What he knew you know, any man knows. But he most aptly stated it in his passage that begins "Not in utter nakedness, not in entire forgetfulness.   To the best of my — admittedly sketchy — knowledge of grammar, the second sentence should read neither a seer nor (a) prophet, but just an ordinary man. Even if we accept the seer and the prophet as "poetic entities" ("father and son," "robber and robbed," "man to man," or whatever), logic would still dictate that ordinary man should be preceded by an an.  It is a well-known fact that Jack London's usage wasn't always up to par; his grammar, on the other hand, was always top-notch.  Logically, the sentence is grammatically incorrect (correct me if I'm wrong: no pun intended).  Illogically, it reads smoothly: intuitively, a native speaker understands that there's nothing wrong here.  However, those to whom English is not the first language cannot be expected to be intuitive in this case and would want an explanation. Any suggestions? When having a number of files opened in Texmaker, at the top of editor pane, there is a drop down panel with the names of open documents in it. I prefer to have tabs of open documents at the top of editor pane, similar to Texstudio and Winedt. Is there a way that I can change this setting? I'm trying to merge two directory trees that have many common elements but also each have elements that are only present in one of the two trees. The main issue I am having is that when mv encounters two sub-directories with the same relative paths it either keeps the source (with -f) or the destination (with -n) but I can't make it take the union of both sub-directories. I could of course use rsync with --remove-source-files but this will actually copy the data and then delete the old files as opposed to a true move. The two directory trees contain several hundred GB of data and are both on same partition so I would love to do a true move if possible for the sake of time.   Right now I have find * -type file -exec mv -n {} /destination/{} but this only moves  files from the source to the destination when the target directory already exists. I can preface this command with something like mv -n * /destination/ but this only brings over the top level directories. Is there any way to do this in a single line? I could  always write a script to check if the directory exists before copying the file but this seems like such a basic task, it seems like there should be an easier way. How to create or recover Windows Bootloader after deleting Ubuntu boot drive I have a computer that dual-boots (or tri-boots) Windows 8 Release Preview, Windows 7, and Ubuntu 12.04. Grub boots between Windows 8 and Ubuntu; for which I use primarily. Recently, I decided to remove Ubuntu, as I hardly used it. I deleted the Ubuntu partition accidentally before replacing the Grub bootloader. Now, whenever I want to boot the machine, it gives me the "grub-rescue" prompt -- I am unable to boot into either Windows (8 nor 7), nor Ubuntu (except via USB, of course). I do not have any Windows 7/8 recovery media, so that isn't an option. Please note that after I deleted the Ubuntu partition, I put the PC into hibernate, and then turned it on. This means the C:\ [Windows 8] drive cannot be mounted. I don't know if that is bad, but it definitely doesn't make things better.  I am currently booting Ubuntu via USB, in an effort to restore the Windows bootloader. I have looked into using boot-repair to solve the problem using the instructions , although after attempting to apply the changes, it gave the error: "Please install the [mbr] packages. Then try again." I don't know why I'm getting this error; is there a way to install the 'mbr packages?' I honestly don't know what exactly they are, nor how to install them. Are there any other options I have not yet exhausted to be able to boot back into Windows, in the case that there is a better way? I want to set the bootloader to boot into Windows 8, but booting into either Windows 7 or 8 is fine (I can use EasyBCD from there). Is there a simple solution to this? I've checked BIOS, and I haven't been able to find a way to boot into Windows. Big tilde in math mode To post an image in a question/answer an user requires at least 10 rep points (see ). To be able to upload an image in the chat, the rep requirements is instead 100 rep point (see ).  Is there any reason to that? I am asking because IF the rationale is to provide more protection inside the chat, the protection is easily circumvented by uploading the image via the question editor, and then copying the link to the chat. Basically, the more restrictive requirement fail to reach its goal - assuming that blocking uploads from new users was indeed the target.  I am not proposing to change that (it doesn't seem worthy the effort) but I was curios to know if this is just a refuse caused by successive changes to the system or if there is actually a different rationale to this that I am missing.  [note: I will remove the double Discussion/Support tag as soon as I can focus if the question has a staff answer - support or will prompt a discussion] Simple animation in WinForms Imagine you want to animate some object on a WinForm. You setup a timer to update the state or model, and override the paint event of the Form. But from there, what's the best way to continually repaint the Form for the animation?   Invalidate the Form as soon as you are done drawing? Setup a second timer and invalidate the form on a regular interval? Perhaps there is a common pattern for this thing? Are there any useful .NET classes to help out?   Each time I need to do this I discover a new method with a new drawback. What are the experiences and recommendations from the SO community? Not enough space in /var/cache/apt/archives/