Managing permission for multiuser manual installation in /opt Similar questions have been asked but I can't seem to find a proper answer.  Basically, I am installing several application manually e.g eclipse, android-sdk, android-adt, arduino etc. and have decided that /opt will be a good place to keep them  By default /opt is root:root with 755  I don't want to run my application as root.Currently I have a single user but I would like the installed applications to be accessible to any user (with necessary permissions). Also if there is any installation/write done in the application limited to /opt it should be allowed.  To achieve this I plan to,   Add user to group root and make the directory /opt 775 ?   Is it safe to add a user to group root?  What is the option otherwise which will enable users rwx in the directory?  I am open for any other better solution as well.
How to avoid using sudo when working in /var/www? I want to stop having to use sudo everytime I work in /var/www. How can I do that? I simply want to put all of my sites into this directory and work with them without too much pain.
How to read and write excel file Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$ How to split bibliography into "works cited" and "works not cited"? I need two bib-like sections: a "References" giving works explicitly cited in my text, and a "Bibliography" (or "Further reading" if you prefer) giving everything from my bibfile that didn't already appear in "References". The first is of course completely standard, but the second... I'm stumped.  Further loose constraints: I'm somewhat committed to biblatex and the biblatex-apa style. But I'll happily accept an answer not related to them if there's any chance I can adapt it. How to send email from MySQL 5.1 Why can't the Polynomial Ring be a Field? I'm currently studying Polynomial Rings, but I can't figure out why they are Rings, not Fields. In the definition of a Field, a Set builds a Commutative Group with Addition and Multiplication. This implies an inverse multiple for every Element in the Set.   The book doesn't elaborate on this, however. I don't understand why a Polynomial Ring couldn't have an inverse multiplicative for every element (at least in the Whole numbers, and it's already given that it has a neutral element). Could somebody please explain why this can't be so? Can't connect to wireless networks on a Dell Latitude D430 As stated above, I can't connect to my home wi-fi with natty but can with Windows 7. The strange thing is I that I have gotten it to connect to other password protected networks with natty, it's just mine that it dosn't like.   I am using a WPA2 pass-code with AES Encryption and all other devises work fine on my network. Laptop used is a Dell Latitude D430. Integration of $e^{ax}\cos bx$ and $e^{ax}\sin bx$ I am curious about the proof of these two integrations. It would be great if you could point me in the right direction : $ \int{e^{ax}\cos({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\cos(bx)+b\sin(bx)] + C $ &amp; $ \int{e^{ax}\sin({bx})dx}= \dfrac{e^{ax}}{a^{2}+b^{2}}[a\sin(bx)-b\cos(bx)] + C $ Why do PBX systems use -48 V? It seems common that PBX and other telephone hardware use a positive-ground power supply, where the "hot" line is at -48v.  What's the reason for that? Contour graphing algorithm I am not sure if this belongs on Mathematics Stack Exchange, but it is somewhat relevant here.       The Problem If you've installed any graphing/plotting apps on your smartphone, you will notice that the app will only take the equation in form of a single variable for 2D (e.g  $y=f(x)$) or in 2 variables for a 3D plot (e.g $z=f(x,y)$). This is problematic as many equations are tough to reduce to the form of $y=f(x)$ or $z=f(x,y)$. The plotters like this because this is the only way they can plot it in form of lines connecting multiple points. These plotters compute the $y$ value at fixed intervals of $x$ and join the point to the previous one. The brute force approach to counter this is to check if the function satisfies it at each point on the image. The problem is that this not only takes more time, but gives discontinuous graph for the function as the image cannot have infinite resolution.         The Question The only way to fix this is to identify which point comes after the next in the plot and join them together by a line. That is where I am stuck. How do you identify which point is sequentially the next one for a given function? Keep in mind that for a human, this might be very easy to do. But, for a computer, this requires a general algorithm. Any ideas? Is every Lie subgroup of $SU(2)$ closed? How is the notation $X\sim N(\mu,\sigma^2)$ read? Is it $X$ follows a normal distribution? Or $X$ is a normal distribution? Or perhaps $X$ is approximately normal..  What if there are several variables that follow (or whatever the words is) the same distribution? How is it written? Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$ Suppose that $f(x)$ is differentiable on $[0,1]$ and $f(0) = f(1) = 0$. It is also   known that $|f''(x)| \le A$ for every $x \in (0,1)$. Prove that   $|f'(x)| \le A/2$ for every $x \in [0,1]$.   I'll explain what I did so far. First using Rolle's theorem, there is some point $c \in [0,1]$ so $f'(c) = 0$.  EDIT: My first preliminary solution was wrong so I tried something else. EDIT2: Another revision :\  I define a Taylor series of a second order around the point $1$: $$ f(x) = f(1) + f'(1)(x-1) + \frac12 f''(d_1)(x-1)^2 $$ $$ f(0) = f(1) + f'(1)(-1) + \frac12 f''(d_1)(-1)^2 $$ $$ |f'(1)| = \frac12 |f''(d_1)| &lt;= \frac12 A $$  Now I develop a Taylor series of a first order for $f'(x)$ around $1$: $$ f'(x) = f'(1) + f''(d_2)(x-1) $$ $$ |f'(x)| = |f'(1)| + x*|f''(d_2)|-|f''(d_2)| \leq \frac{A}{2} + A - A = \frac{A}{2} $$  It looks correct to me, what do you guys think?  Note: I cannot use integrals, because we have not covered them yet. How do I install the VirtualBox version from Oracle to install an Extension Pack? I downloaded VirtualBox OSE from the Ubuntu Software Center but it seems that that version is limited. I prefer to have the complete version and don't really care if it's closed source or not.  Can I install it via a terminal or do I have to download something from a website?  I don't know how to install software I download from the web. So far I've only used the Software Center. still frame camera solve I've found a number of how-tos for solving video but I'm just looking to put an element in a photo and can't seem to find a how-to for that.  Is it possible in blender to do a camera solve with a still image?  Thanks. How to make a field NULL using MySQL GUI Tools? I'm using the MySQL Query Browser (part of the ) and need to change a field to NULL, but I can't figure out how to do it - if I delete the value it tries to update it to ''. Typing "NULL" makes it try to update to 'NULL' (a string).  I know I could just write a query to do it, but that defeats the entire purpose of the tool, no? jQuery call function from a string One of my players has a +1 shortbow, and recently found some +1 arrows. If he fires a +1 arrow from a +1 bow, will the bonus to attack and damage be +1, or +2? Does an electrolytic capacitor degrade each time it receives reverse voltage? I am using Blender to mix the video from my camera with the audio from my external recording setup.  It works great mostly and I am very pleased with it.  But the problem is that I can't start the audio recorder an even number of thirtieths of a second from when I started the camera.  And Blender seems to only let me move the audio track in the VSE by whole frames (1/30 of a second).  Here are a couple screenshots:   The track on top is the external audio and the one on the bottom is the camera's audio.  Between the two screenshots I have only moved the audio track by one frame.  But as you can see, I need to move it by about 1/2 frame to line up the audio properly with the video.  So can I move a track in the VSE by fractions of a frame? Given the galois extension $L/K$, where $L=\mathbb{Q}(\zeta, \sqrt[3]{2})$. I've already calculated that $[L:\mathbb{Q}]=6$. I'm trying to prove that the number of intermediate fields is also 6, including $L$ and $\mathbb{Q}$ as intermediate fields. I'm told that the fundamental theorem of galois theory can be useful here, but I can't find a use for it.