How to check if a point is inside a square (2D Plane)?
How to check if a point is inside a rectangle?
What are the relationship between administrators groups of domain, dev computer and of Sharepoint services? I know-know I can search and read but anyway I would need to ask in order to escape possible typos, personal misunderstandings and to better remember.     I develop on a machine with installed Sharepoint 2010 Sever where I have local groups:     Administrators Description: Administrators have complete and unrestricted access to the computer/domain   WSS_Admin_WPG Description: Members of this group have write access to system resources used by Microsoft SharePoint Foundation      **Does the description of "Administrators" ("computer/domain") imply all privileges of "WSS_Admin_WPG" ?    Does the description of **WSS_Admin_WPG (in part of "system resources used by Microsoft SharePoint Foundation") imply Sharepoint Server?**    The WSS_Admin_WPG group has entries of:     "BUILTIN\Administrators (S-1-5-32-544)" group   and some user domain accounts   Is "BUILTIN\Administrators (S-1-5-32-544)" group the same (alias to?) as "BUILTIN\Administrators" entry I observe among Sharepoint Farm Administrators (through "Central Administration")?       Is the entries of domain accounts excessive (or necessary)     in "WSS_Admin_WPG" if these accounts make part of "Administrators" group?     in "Farm Administrators" if these accounts are part of "BUILTIN\Administrators (S-1-5-32-544)" group?     What are relationship (difference) between "BUILTIN\Administrators" and "Administrators"? What are best practices for managing SSH keys in a team? I work with small teams (&lt;10) of developers and admins with the following characteristics:   Most members of the team have >1 personal computer, most of which are portable Team members have access to 10-50 servers, usually with sudo   I think this is pretty typical for most startups and small- to mid-size corporate IT groups.  What are the best practices for managing SSH keys in a team like this?  Should you share a single key for the whole team?  Should each person have their own key on a shared account ("ubuntu" on every server)?  Separate accounts?  Should each team member keep a separate key for each of their laptop or desktop computers? How many sequences of $n$ tosses of a coin that do not contain two consecutive heads have tails as the first toss? If you toss a coin $n$ times, there are $2^n$ possible sequences of heads and tails. Let $E_n$ be the set of sequences which do NOT contain two consecutive heads and $e_n$, the number of sequences in $E_n$.  Thus $E_3$ $=$ $\{$ $TTT$, $TTH$, $THT$, $HTT$, $HTH$ $\}$ and $e_3$ $=$ $3$.  How many elements of $E_n$ have $T$ as the first toss?  Please can anyone help me out here? How to call a function on a directive scope from the controller Can I pickle a python dictionary into a sqlite3 text field? Any gotchas I should be aware of?  Can I store it in a text field, or do I need to use a blob? (I'm not overly familiar with either pickle or sqlite, so I wanted to make sure I'm barking up the right tree with some of my high-level design ideas.) Android EditText listener for cursor position change Last year I hired someone to do some work for our website but accidentally lost the PSD files since then. It's a fairly basic concept but I am fairly inexperienced with using masks.  How can I create the black circular gradient area as shown in this image below? I need to get as close as possible where it matches existing images on the site, why I am hoping its not too hard.  Thank you! This is a story that was read on BBC radio about thirty years ago, and this is about as right as I can remember it: The human pilot of a spacecraft is doing some reconnaissance on an alien planet. He crashes but survives. For some reason, no one will know where to look for him. He sees something in the distance that looks like a building of some sort. When he gets there, it seems to be a home. Very much like a human home. There's furniture, but it's strange and uncomfortable . There's food, but it's inedible. There's a faucet but what comes out of it seems more like acid. Everything looks as though it should be right, but it's not. He leaves the house, wanders and after a few days is desperate for water. But there isn't any water anywhere. He's close to death, crawling on the ground and then something happens. There are cracks in the soil and there appears to be water bubbling up from perhaps some underground stream. The water revives him. He goes back to the house and tries the food again. It's delicious and he eats enough to gain back his strength. Then he decides to try the water again. It's pure and wonderful. He takes a shower and the last line of the story is how refreshing the water is on his skin and something about him lifting his tail. Are expletives (cursing, swear words or vulgar language) allowed on SE sites? Are antiparticles just particle-shaped holes? If particles are simply regions of space where certain quantum fields have non-zero divergence, are anti-particles simply the corresponding regions of opposite divergence?    This seems like the intuitive answer, especially when considering the process of annihilation.  I have heard before that anti-particles are analogous to particles moving through time in reverse, which seems to indicate that an annihilation event is just a point of symmetry in that (arguably, single) particle's history.  This analogy breaks down, however, when it comes to gravitation, since there seems to be no evidence of a negative-mass particle.    So what then is the meaning of an anti-particle, when their symmetry is preserved across certain fields, but not other? I'm stuck underground.   I can't mine any further to reach lava. There is no water nearby, and zombies can't reach me.  I can't see to find any blocks to suffocate my character.  NBTEdit and similar programs don't work on Mac, so I can't edit my save file to escape. I have hardly any blocks so cannot jump and lay my way up. I can't see, and do not have any torches, so can't make a staircase back up. I don't want to make new save as I have an awesome house filled with stuff that took me ages to find.    How can I get back to the surface? array package: problem with >{declarations} in preamble: Extra alignment tab has been changed to \cr I have a document that uses both the longtable and the array package. At first I ascribed the problem to an interaction of both. After testing, it seems array is the only culprit.  Here's a minimal example.  \documentclass{article} \usepackage{array} \begin{document}  \begin{tabular}{p{0.4\textwidth}&gt;{\raggedright}p{0.4\textwidth}} 1 &amp; a \\ 2 &amp; b \\ 3 &amp; c \\ \end{tabular} \end{document}   It produces the error  ! Extra alignment tab has been changed to \cr. This is a follow up question to my previous question  Let $k$ be a field and $V \subseteq \Bbb{A}^n$ and $W \subseteq \Bbb{A}^m$ be algebraic sets. Then it should be true that $I(V \times W ) = I(V) + I(W)$ where by $I(V)$ here we mean the extension of $I(V)k[x_1,\ldots,x_{m+n}]$. Now I believe I have proven this (see the proof at the bottom of my question) but when I look at Martin's answer , it is instead claimed that we  actually have  $$I(V \times W )= \sqrt{I(V) + I(W)},$$  and for $I(V) + I(W)$ to be a radical ideal we need $k$ to be algebraically closed.           My question is: What's going on here? I believe my claim is true even without the assumption that $k$ is algebraically closed.           Here's a proof user Sanchez told me of, which I have simplified:       First it is clear that we always have $I(V) + I(W) \subseteq I(V \times W)$. For the reverse inclusion consider a polynomial $f \in I(V \times W)$. Then we can always write $$f = \sum_{i=1}^n f_ig_i$$ where $f_i \in k[x_1,\ldots,x_n]$ and $g_i \in k[x_{n+1},\ldots,x_{m+n}]$. Now take any $b' \in W$. If for all $i$ we have $g_i(b') = 0$ then since $b'$ is arbitrary, $g_i \in I(W)$ for all $i$. Then $f \in I(W) \subseteq I(V ) + I(w)$ and we are done. Otherwise suppose there exists $b \in W$  and $i$ such that $g_i(b) \neq 0$. Then wlog we may suppose that  $g_1(b) \neq 0$.   Next, $\sum f_ig_i(b) = 0 $ on all of $V$ by assumption of $f \in I(V \times W)$. So $\sum f_i g_i(b) = p$ for some $p \in I(V)$. Now write $$f_1 = \frac{ p - g_2(b) f_2 + \ldots g_n(b)f_n}{g_1(b)}.$$  Substituting this for $f_1$ in $\sum f_ig_i$, followed by taking things mod $I(V)$ we get an  expression with only $n-1$ terms $\mod{I(V)}$. Continuing this process we will finally get an expression with $0$ terms $\mod{I(V)}$ so that $f \in I(V)$. This shows $I(V \times W) \subseteq I(V) + I(W)$ which completes the proof. How do I define global variables in CoffeeScript? Asymptote: when white isn't white I'm trying to display a white 3D ball with Asymptote (3D PDF), but it always turns up gray:    import graph3; import solids;  defaultrender.merge=true; size(10cm,0);  currentprojection=orthographic(-Z);  //currentlight=Headlamp; //currentlight=light(-10,1,1); //currentlight=White; currentlight=Viewport;  draw(unitsphere,rgb(1,1,1));   I understand it's a lighting issue, and I've tried playing with its settings (the lines commented out in my source are some of my attempts), but I never manage to have white be white. If I understand correctly, I need a whiter diffuse component in my light, but I cannot see how to achieve that. And the documentation is not very clear…    This will be part of a molecular model, and the rendering I'm going for it something like this: Booting Ubuntu Failure : error: attempt to read or write outside of disk 'hd0' I have installed Ubuntu 12.10 in a Western Digital external hard drive (320GB). This is a complete installation, not a live USB.  When I plug it in my HP desktop I go to the BIOS settings and boot off the hard drive, everything work perfectly as it should. Now this works on every single computer and laptop in my house (all HP), except for ONE. My HP ProBook 4530s.  When I select to boot of the USB I get the message:  error: attempt to read or write outside of disk 'hd0'   Now, I have removed the hard drive from my laptop and the external drive is the ONLY drive plugged in. Below is a screenshot of the message on the screen. After the message I navigate to ls / (as shown below):    After here I try to acces other folders under ls /, for example, I try to go to ls /boot to get to the grub folder. Then I get the same message as before: as shown below:    grub rescue&gt; ls /boot  error: attempt to read or write outside of disk 'hd0' grub rescue&gt; _   The only folders I can access without getting the message again are /home, /run and /usr.   So how do I:   Boot Ubuntu from GRUB2 (this screen) manually Set to automatically boot Ubuntu If possible an explanation for this problem   Thanks! Why, historically, do we multiply matrices as we do? Multiplication of matrices &mdash; taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product &mdash; is not a very intuitive operation: if you were to ask someone how to mutliply two matrices, he probably would not think of that method. Of course, it turns out to be very useful: matrix multiplication is precisely the operation that represents composition of transformations. But it's not intuitive. So my question is where it came from. Who thought of multiplying matrices in that way, and why? (Was it perhaps multiplication of a matrix and a vector first? If so, who thought of multiplying them in that way, and why?) My question is intact no matter whether matrix multiplication was done this way only after it was used as representation of composition of transformations, or whether, on the contrary, matrix multiplication came first. (Again, I'm not asking about the utility of multiplying matrices as we do: this is clear to me. I'm asking a question about history.) As the title says. How do I get from  $\frac{n}{\varphi(n)}$ to $\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?  I know that $$\frac{n}{\varphi(n)}=\frac{\sum\limits_{d \mid n} \varphi(d)}{\sum\limits_{d \mid n} \mu(d)\frac{n}{d}},$$ and I suspect it is down this road I should go. But I get totally confused by the sums and I have no clue on how to divide them and "combine" them into one again. Any hints or advice would be much appreciated. What is the difference between image size and image quality? Run multiple instance of a program in parallel