Sum of the roots of unity, $z_{1}^p+...+z_{n}^p$
How to prove sum of powers property of roots of unity?
Coding for an ordered covariate I am performing ordinal regression, I have 5 response categories and several predictors both continuous and categorical. I would like to add a predictor which is categorical but ordered (1, 2, 3, 4). I don't think it would be appropriate to apply the usual dummy coding for unordered categorical predictors, but when I searched for how to code this I did not find much information.  In  "linear coding" or "assuming linearity of the predictor effect" is mentioned, but without further details.  Does it mean I just use my ordered values as they are, i.e. use them as a continuous variable? Interpret geometrically the equation The function $f$ is convex when:  $$f(tx+ (1-t)x', ty + (1-t)y') ≤  tf(x,y) + (1-t)f(x', y')$$  for all numbers $0≤t≤1$ and all pairs of points $(x,y)$ and $(x',y')$ in the domain of $f$ (the whole of $R^2$)  How would I interpret this geometrically? Also what is an example of a convex function whose graph is not a plane? I forgot my iPhone 5 passcode when I was changing the code. A window appeared on the device screen saying that iPhone is disabled.  I have Apple ID and password for it. After signing in to iCloud I have erased the device in order to remove the passcode from my iPhone but it still says that device will be erased when device will connect to internet. What would i have to do? How can I pass a command line argument into a shell script? I know that shell scripts just run commands as if they were executed in at the command prompt.  I'd like to be able to run shell scripts as if they were functions... That is, taking an input value or string into the script.  How do I approach doing this? I'm a little confused about the output I'm seeing in my routing table, particularly the 'metric' column:  $ route -n Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface 0.0.0.0         192.168.0.1     0.0.0.0         UG    0      0        0 wlan0 172.16.35.0     0.0.0.0         255.255.255.0   U     0      0        0 vmnet1 192.168.0.0     0.0.0.0         255.255.255.0   U     9      0        0 wlan0 192.168.82.0    0.0.0.0         255.255.255.0   U     0      0        0 vmnet8   According to the man page, metric indicates the 'distance' to the target. I was a little confused about what exactly "target" was. I assumed it was my router (it goes to gateway 0.0.0.0, which then goes to my router at 192.168.0.1). Thus, I expected the metric to be a single hop to my router. However, it's 9! Why is this so number high? Do iOS app visits count to your consecutive visits Cancel/kill window.setTimeout() before it happens I have a few places where I use the line below to clear out a status, for example.  I have a few of these that hang out for 10 seconds or more and if the user gets clicking around the action can occur at incorrect time intervals.  window.setTimeout(function() { removeStatusIndicator(); }, statusTimeout);   Is it possible to cancel or kill this with some jQuery or JavaScript code, so I don't have this process hanging around? How to use GROUP BY to concatenate strings in MySQL? Basically the question is how to get from this:   foo_id   foo_name 1        A 1        B 2        C   to this:   foo_id   foo_name 1        A B 2        C Why can't energy be created or destroyed? How to download packages from a command-line given repository? It is not about the common download &amp; install thing, what apt (aptitude, etc) does, it is a scripted download a package file.  I found the dget tool for this task, which works quite well. But, unfortunately, it doesn't have any option to specify a different repository URL as it is given in the /etc/apt/sources.list.  Is it somehow possible? Actually, a dget-like functionality would be the best, but where I can also specify the repo URL.    P.s. thank you very much the scripts, but I would like to prefer a debian tool for this very simple task. It will be part of a buildscript, for external usage, and any unneeded complexity has intolerable collateral costs. It must be done by a debian tool.  P.s.2. Finally I solved this with updating the system-wide repos, and downloading the packages with dget. Thank you very much the scripts! How to understand intuitively the Stolz-Cesaro Theorem for sequences? Does not the mass of those living on the Earth add on to the mass of the Earth or is it too negligible to be cared for? : Earth weighs about 13,170,000,000,000,000,000,000,000 pounds (or   5,974,000,000,000,000,000,000,000 kilograms). Since Earth is too big   to be placed on a scale, scientists use mathematics and the laws of   gravity to figure out Earth's weight.   So, this seems to be a constant. But I guess it doesn't consider the things that are on the earth, the trees, buildings, people, animals, water etc...  So, are all the above mentioned things' mass is too small or negligible to be left off? Key Presses in Python ${a^2}{\mid}({b^3} + 1)\;$and$\;{b^2}{\mid}({a^3} + 1)$ How should I apply brick to an interior wall? Citing a range of papers using numeric keys as in \cite{a, b, c} -> [1-3] How to echo output of a top into a text file? I want to write batch or something, that will write output of top into a file on login.  I did top &gt;&gt; output-file, but it contains some strange character!  Can somebody give a simple tutorial about how to write batch file in Linux? When should comments be flagged/deleted on per-site metas? We all know , but that guidance is, naturally, geared toward main sites, where we want to keep things clean and focused.  Meta, on the other hand, is a site's "second place", with some different rules and conventions.  For example, questions on main sites can be closed as primarily-opinion-based, but meta is all about opinions.  There's a "discussion" tag and such questions collect many opinions.  Meta is different.  Occasionally I see comment flags on metas and I'm never sure what to do with them.  Setting aside things that are blatantly offensive or spam (that's a no-brainer), is there such a thing as "too chatty" or a comment discussion that should be moved to chat on meta?  I am very conservative in deleting things on per-site metas (except on  posts, which like main should stay focused).  Are there any guidelines specific to per-site metas?  I'm specifying per-site metas and not MSE because MSE seems to have conventions that fall somewhere between "main site" and "per-site meta".  If the answer is the same for all metas then great, but I don't want to assume it'll be the same. Why is $A^TA$ invertible if $A$ has independent columns? How can I understand that $A^TA$ is invertible if $A$ has independent columns? I found a similar , phrased the other way around, so I tried to use the theorem  $$ rank(A^TA) \le min(rank(A^T),rank(A)) $$  Given $rank(A) = rank(A^T) = n$ and $A^TA$ produces an $n\times n$ matrix, I can't seem to prove that $rank(A^TA)$ is actually $n$.  I also tried to look at the question another way with the matrices  $$ A^TA = \begin{bmatrix}a_1^T \\ a_2^T \\ \ldots \\ a_n^T \end{bmatrix}   \begin{bmatrix}a_1 a_2 \ldots a_n \end{bmatrix} = \begin{bmatrix}A^Ta_1 A^Ta^2 \ldots A^Ta_n\end{bmatrix} $$  But I still can't seem to show that $A^TA$ is invertible. So, how should I get a better understanding of why $A^TA$ is invertible if $A$ has independent columns? Is it possible to exclude questions I've already answered from the search criteria? Recently I asked if it were possible to find questions with just one answer and as a result we got an .  That's great, but ...     Is there a way to restrict the search to questions where that one answer isn't mine? That would help. :-)   It's certainly possible to search for , but it's not possible to exclude your own posts as far as I can tell:   -user:me searches for posts that . user:1-67 doesn't search for posts from user #1 to user #67, but searches for .  (And I'm not sure that will help anyway since I don't think it would be possible to simultaneously exclude 69-max(userID).) -Ericson searches for posts that , but since my last name is in the the metadata and not the searchable portion of posts: no joy.   And of course none of this will actually work to eliminate the questions that that I've answered already and want to ignore.  In general, If I'm involved in a Q&amp;A (or ) the notification procedures do a good job of keeping me up-to-date with developments.  But when I search, it's often to find questions I've not noticed before.  So being able to eliminate questions I have already answered would be a generally useful feature for me.