Showing $\frac{3}{2}\leq \frac{a}{b+c} +\frac{b}{a+c} + \frac{c}{a+b}< 2$, where $a$, $b$, $c$ are the sides of a triangle
Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
Is there a way to change the process group of a running process? Is there a way to change PID, PPID, SID of a running process? It would make sense for the answer to be no, but I'd like to make sure. I'm using an old iBook G4 (PowerPC) running Tiger to serve iTunes to the house. For the past week or so, the mac boots fine, and then sometime during the day starts generating   An unexpected error occurred (error code -50).   errors when iTunes attempts to save its library file.  Checking reveals that the boot drive (main drive, in the laptop) behaves as if it is write-protected - I get the same error code when I attempt to create a folder on the desktop, for instance. If I attempt to create files via the terminal, e.g. via     ls > foo.txt I get an "invalid argument" error.   I've set the iBook to run in Target Disk Mode and run Disk Utility to repair the disk (from a Macbook running Snow Leopard) and get "The volume appears to be ok".   I don't have the option in Disk Utility to Repair Permissions in Target Disk Mode. When I ran Repair Permissions on the iBook itself, it came back with no errors, no permissions corrected, but did not in fact fix the problem.  Rebooting always solve the problem - for the next 5-10 hours or so.   Would Disk Warrior help, or some other software fix, or is it time to buy a new drive? (And, in any case, what's going wrong?) How do I escape a single quote in SQL Server? What's the NB30 or MM-TD in an iPhone description in GSX? What's the NB30 or  MM-TD in an iPhone description? I always see these nomenclatures Non block, etc, what does it mean? Right identity and Right inverse implies a group Let $(G, *)$ be a semi-group. Suppose   $ \exists e \in G$ such that $\forall a \in G,\  ae = a$;  $\forall a \in G, \exists a^{-1} \in G$ such that $aa^{-1} = e$.    How can we prove that $(G,*)$ is a group? Is there a way to conveniently define a C-like structure in Python? I'm tired of writing stuff like:  class MyStruct():     def __init__(self, field1, field2, field3):         self.field1 = field1         self.field2 = field2         self.field3 = field3 Evaluate forecasting ability of GARCH models with RMSE and MAE This question isn't so much about how to achieve the effect of making a scene look like it's modelled in miniature, but why tilting the focal plane creates the effect. What is it about photographing miniatures that makes them look like miniatures, and how is this replicated by tilting the focal plane?  I can understand how when photographing a model of a scene, you have a much higher magnification, which leads to a shallower depth of field compared to when capturing the real-sized scene, but how does tilting the focal plane help? Is it just that you have the focal plane tilted relative to the plane that most of your subject is on, so that you can achieve a narrower depth of field for the focal length and aperture, or is there more to it than that? Horizontal scroll bar occludes text I've been running into this lately.  The scroll-bar gets stuck and makes it difficult to read the text.  I'm running Chrome Version 56.0.2924.87 (64-bit) on macos. Why is $\mathbb{Z}[\sqrt{-n}], n\ge 3$ not a UFD? I just graduated, and I'm starting a new job soon. My employer has pretty good policy for matching 401(k) contributions, so I want to invest as much as possible, especially during this first year.  My question is: should I invest in a traditional 401(k), a Roth 401(k), or some combination of the two? On the one hand, tax rates may be much higher when I retire, and I might be in a higher tax bracket, so a Roth 401(k) would be good. On the other hand, I might be in a lower tax bracket when I retire, so a traditional 401(k) might be better. It's hard to know where I will stand in 30 years.  Is this the same trade-off as with a traditional / Roth IRA, or is there any other tax difference I should know about? How to install NVIDIA driver in Ubuntu I'm running Ubuntu 13.04 on DELL XPS L501 - Nvidia GeForce GT 420M. I'm using kernel 3.9.0-030900-generic.  All kernel-headers are installed in the system.  and  I've tried the following.   Use apt-get to install nvidia-current (which download 304) &amp;&amp; load using modprobe Use apt-get to install nvidia-310 &amp;&amp; load using modprobe Download nvidia 64-bit driver nvidia-319.23 for 400M series and install Use swat-x repo to install nvidia driver   All of these failed. And I tested it everytime like this   After the module is loaded (checked from lsmod),  restarted lightdm tested from get.webgl.org  (Google-Chrome webgl support is enabled)    Problem faced with nvidia-xconfig   after running nvidia-xconfig (which writes to /etc/X11/xorg.conf), and restarting lightdm, my display res changes to 640x480. and had to remove this file to revert back to old setting Have also tried commenting out those two lines which adjusts Horizontal and Vertical Setting in xorg.conf. That just rectified the resolution. But still I wasn't able to use the graphics card (webgl).   EDIT 1: (nouveau)   Tried rebooting after each installation Removed (purge) all of nouveau* before starting.  Removed one more package (dont remember the exact name though) - xorg-xserver-blah-blah.   EDIT 2: (bitlbee)   I had bitlbee installed before. Removed that too before starting installation. When bitlbee was present, NVIDIA-3.9-x86.run (downloaded from nvidia) was not able to recognize graphics card. But it did when I removed bitlbee. (So I'm assuming here that it should work if graphics driver was installed properly)   EDIT 3: (software-properties-gtk)   sudo software-properties-gtk the Additional drivers tab is always NIL. (before and after installation) (even if the installation was successful)   Have been trying this the whole day, and done it quite a few times. None of them worked.  Need help! Is it the problem with kernel-3.9, that there are no updates for this ? How to get back a declined Outlook invitation I accidentally clicked "decline" on an Outlook invitation and now I can't reverse it -- the event has completely disappeared from my calendar!  How can I get back the event invitation and change my "Decline" to "Accept" or "tentative"? 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? How do I breed Pokemon for their Hidden Abilities? I want to legitimately breed a competitive team, but I don't know how to breed for hidden abilities unless I just breed two Pokemon who have their normal ability(s) together until I breed one with a hidden ability. Does someone know a useful trick or item I could use? Expected time to roll all 1 through 6 on a die Finding the maximum likelihood estimators for this shifted exponential PDF? In the LoTR movies (not sure if the books are the same) but when Gollum lost the ring to Bilbo decades ago in The Hobbit, he appeared to look the same and even move the same in The Fellowship of the Ring. Bilbo on the other hand, seemed to have aged very rapidly when he passed the ring to Frodo. When Frodo met up with Bilbo in Rivendell shortly after his quest began, Bilbo appeared much older and even more much slower.  I realize that Gollum had the ring for much longer than Bilbo, but wouldn't him losing the ring have the same effect as it had on Bilbo? This is tricky. I would like to install Ubuntu on a machine that is intended to work as server, and for some reason I do not have an option to connect a screen to it.  I expect this may be similar to remote installation. However, there is currently no OS on that machine, so I will have to set up everything from scratch.  On the other hand, I do have a physical access to that machine. Therefore I can get it to boot from a CD/USB. But that's not enough.  Is there a way to do such installation remotely? Is there a version of Ubuntu image that comes with a SSH server preinstalled, and starts it once booted, so that I can boot the machine with such image, connect to it via SSH and process the installation from a different computer?  If not, what other options do I have? Why is an untranslated string not showing up? In my module I have some custom strings. I use these in the t() function. When I go to admin/config/regional/translate/translate and filter the untranslated strings my custom strings do not show here.  What could be going wrong?