How do I install Pillow and/or Pip in Blender Python in Windows OS
Using 3rd party Python modules
Can I visit other Schengen countries on a long-term Schengen visa or residency permit? I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France? I have to prove by induction that $$\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$$, using the identity $\begin{pmatrix}n \\ r-1 \end{pmatrix}+\begin{pmatrix}n \\ r \end{pmatrix}=\begin{pmatrix}n+1 \\ r \end{pmatrix}$. I'm fine with everything except the inductive step, where I only managed to get as far as $$\sum_{r=0}^{k+1}\begin{pmatrix}n \\ r \end{pmatrix}= \sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}+\begin{pmatrix}n \\ k+1 \end{pmatrix}$$ I tried to then use the identity and substitute $\begin{pmatrix}n \\ r \end{pmatrix}=\begin{pmatrix}n+1 \\ r \end{pmatrix}-\begin{pmatrix}n \\ r-1 \end{pmatrix}$ but all this did was just take me around in a circle. I also couldn't substitute $2^k$ for $\sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}$ since this didn't properly simplify to give $2^{k+1}$. However, I think that I have to obtain the expression $\sum_{r=0}^{k}\begin{pmatrix}n \\ r \end{pmatrix}$ since it simplifies to $2^{k+1}$. But I've not been able to obtain this in anyway so I'm wondering if anyone can guide in what I need to or what direction I need to take to complete the inductive step. How should I handle possible revenge downvotes? I don't like such kind of questions on Meta, so I will try to make it a good question and describe all with a details.  Today I down-voted  added a comment with explanations why I down-voted it, and flag it as non constructive (my flag was marked as helpful). An hour later  was downvoted, without any comment left about the reason. Yes, that wasn't my best answer, but in my opinion it answers the question. Well, even if somebody considered my answer incorrect he could add the correct answer, or up-vote the competitive ones. I checked the  who made competitve answer, and he didn't get any rep today for that answer.   It was my second down-vote on Stack Overflow, so I was a little bit down, after that. I think who could considered my answer so completely wrong, and that I thought that maybe it was revenge down-vote. So I checked  of the user I down-voted today, and it was clear that he down-voted some answers today. After I checked that that user cast only 19 downvotes in 8 months, so chances were very big that this was revenge down-voting.  I came to this meta, and searched what I should do in this case. I found that most questions about down-votes, were closed as duplicates. After I found , and found that a team member of Stack Exchange suggested to cast a flag for moderator attention, and explain the situation there.  I did that, and create next flag:     I think after I down-voted this question (and a comment about this), the OP down-voted me in revenge; it's clear from his today's reputation and from timing of my down-vote of his question, and time when one of my answers was downvoted. I cannot be 100% sure about that, but if somebody can check this, and point him that it's not the good way to do.   As you can see, I didn't ask for returning any reputation, or banning that user, I just wanted, somebody to point him, that he did wrong. And after I get this respons on my flag: "declined - flags should only be used to make moderators aware of content that requires their intervention." So in the end I also lost 10 points of the flag weight.  After describing all situation in details, I want to know were exactly I was wrong here. And what should I do next time something like this happens? Why do the $n \times n$ non-singular matrices form an "open" set? Why is the set of $n\times n$ real, non-singular matrices an  open subset of the set of all $n\times n$ real matrices? I don't quite understand what "open" means in this context.  Thank you. I have this recipe for cheese curds that I want to try: , but it specifically calls for raw milk which is near to impossible to get here. I make yogurt with pasteurized milk and it works no problem, but does cheese somehow work differently? How can I see flags I cast from all sites? Can I still use logistic regression if some variables are not applied to all the observational units? Some of the variables are questions that are not being asked to every single person in the questionaire depending on how they answered previous question(s). So would I still be able to use a logistic regression if some of the questions (the independent variables) are only measuring the responses of SOME of the respondents? Proof for the funky trace derivative : $d (\operatorname{trace} (ABA'C))$? Given three matrices $A$, $B$ and $C$ such that $ABA^T C$ is a square matrix, the derivative of the trace with respect to $A$ is:  $$ \nabla_A \operatorname{trace}( ABA^{T}C )  = CAB + C^T AB^T $$  There is a proof . However, I was not able to understand the second line of the proof. it says something like this:  $$ \nabla_A \operatorname{trace}( ABA^T C )= \nabla_\bullet \operatorname{trace}(f(\bullet)A^{T}C) + \nabla_\bullet \operatorname{trace}(f(A) \bullet^T C) $$  Where  $f(A) = AB$  I tried searching the proof or any hint using google, but I couldn't fine anything. Could anyone please help me with this second line. I cannot sleep. I am obsessed with this proof. I am considering to use iCloud Photo Library to store a growing number of family photo albums, shared to web or set of AppleIDs.  I dont need to keep original photos on iDevices for 99.9% of photos.  How much space will be used on the photo-originating set of devices (iOS, OS X, Windows)? I.e. what (roughly) is the function from the original size and number of photos, device storage space available, any other variables? "Failed to create user" due to regular expression error I'm running Ubuntu 12.10 desktop 32 bit. Currently I have only a user, type administrator. I'd like to create another administrator user but I keep getting the following error:  Failed to create user GDBus.Error:org.freedesktop.Accounts.Error.Failed: running '/usr/sbin/adduser' failed: /usr/sbin/adduser returned an error (1): adduser: Please enter a username matching the regular expression configured via the NAME_REGEX[_SYSTEM] configuration variable.  Use the `--force-badname' option to relax this check or reconfigure NAME_REGEX.  Any suggestion is appreciated. I have used the code shown below to draw a static CMOS inverter. I have tried to use the TikZ library calc to calculate the point at which drains of the PMOS and the NMOS devices meet; and the mid-point of the line which connects the gates of the two devices. Apparently calc gets the y coordinates of the points right. However, calc seems to get the x coordinates of the points wrong. What could I be doing wrong?  Here is the TikZ code:  \documentclass{standalone} \usepackage[americaninductors]{circuitikz} \usetikzlibrary{calc} \begin{document} \begin{circuitikz} \draw % Draw MOSFETs: (0,0) node [pigfete,yscale=-1,anchor=S] (M1) {} (M1.D) node[nigfete,anchor=D] (M2) {} (M1.G)--(M2.G) % The line connecting the gates of the MOSFETs. ; % Draw the power rails: \draw ($(M1.S)-(2.0,0)$) -- (M1.S) -- ($(M1.S)+(1.2,0)$); \draw ($(M2.S)-(2.0,0)$) -- (M2.S) -- ($(M2.S)+(1.2,0)$); % Input and output nodes: \node (I) at ($0.5*(M2.G)+0.5*(M1.G)$) {}; % The mid-point between the gates. \node (O) at (M1.D) {}; % The point at which the drains of the MOSFETs are conneted. % The Input and output lines. \draw ($(I)-(.8,0)$) -- (I); \draw (O) -- ($(O)+(0.8,0)$); \end{circuitikz} \end{document}   Here is the figure that I get: Note that that input and the output lines are not connected to the rest of the circuit. Can we attribute the problem of the lines not being connected, to the rest of the circuit, to the way I am using calc? Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$ Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$   Here's what I did so far:  Let $\sup A, \sup B$, and $\sup (A \cup B)$ denote upper bounds of $A,B$, and $A \cup B$, respectively. If $x \in A$, then $x \le \sup A$. If $x \in B$, then $x \le \sup B$. In either case, $x \in (A \cup B)$. So either $x \le \sup A$ or $x \le \sup B$. In either case, $x \le \max \{\sup A, \sup B\}$. So $\max \{\sup A, \sup B\}$ is the upper bound of $A \cup B$, which means $\sup (A \cup B) \le \max\{\sup A, \sup B\}$.  I do not know if there's a better way to go at it, but all I did was show the inequality. Can I do this, and show the reverse inequality? If so, how can I go about doing that? I have a ~23000 line SQL dump containing several databases worth of data. I need to extract a certain section of this file (i.e. the data for a single database) and place it in a new file. I know both the start and end line numbers of the data that I want.  Does anyone know a Unix command (or series of commands) to extract all lines from a file between say line 16224 and 16482 and then redirect them into a new file? What exactly is an environment variable? The probability of two dice summing to k is simple enough, make a diagram of the throws,  $$ \begin{array}{c}  &amp;|&amp;1&amp;2&amp;3&amp;4&amp;5&amp;6\\\hline 1&amp;|&amp;2&amp;3&amp;4&amp;5&amp;6&amp;7\\ 2&amp;|&amp;3&amp;4&amp;5&amp;6&amp;7&amp;8\\ 3&amp;|&amp;4&amp;5&amp;6&amp;7&amp;8&amp;9\\ 4&amp;|&amp;5&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}\\ 5&amp;|&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11\\ 6&amp;|&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11&amp;12\\ \end{array} $$  and the probability of a sum is just the length of the corresponding diagonal divided by $36$. For instance, $\mathrm{P}(\mathrm{sum} = 10) = \frac{3}{36} = \frac{1}{12}$. However, it's not as easy to draw a diagram for three dice or more, so how would a general formula look? I'm looking to view and archive all my old DMs in Twitter, since I would like to revive conversations that took place 1 year ago.  Acording to Twitter they don't delete old messages, they simply archive them in their database.  Is there a way to view and download all of these messages, just like you can view all your old public tweets with third party apps?  UPDATE: I found  but apparently it's not working for DMs now Question mark or bold citation key instead of citation number Intellij shortcut for quick call hierarchy Is there a shortcut key to bring up the call hierarchy of a method inline with the code, in the quick menu format, rather than bringing up the call hierarchy panel? Is there any IC that interfaces any 3.3V Input/Output to 5V Output/Input? I need it primarily for an Arduino Due but if there any bidirectional IC that works like that it would be great.  Some people advised me to use the SN74AHC125 and CD4050 ICs, but I don't understand how they work or how to interface with them. What are the costs of books and materials in Harry Potter? In the first book, Harry sees his Gringotts vault for the first time.  (Quotes thanks to Slytherincess!)     Griphook unlocked the door. A lot of green smoke came billowing out, and as it cleared, Harry gasped. Inside were mounds of gold coins. Columns of silver. Heaps of little bronze Knuts.      "All yours," smiled Hagrid.      All Harry's -- it was incredible. The Dursleys couldn't have known about this or they'd have had it from him faster than blinking. How often had they complained how much Harry cost them to keep? And all the time there had been a small fortune belonging to him, buried deep under London.      Hagrid helped Harry pile some of it into a bag. "The gold ones are Galleons," he explained. "Seventeen silver Sickles to a Galleon and twenty-nine Knuts to a Sickle, it's easy enough. Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh."      Harry Potter and the Sorcerer's Stone - pages 58-59 - US Hardcover Edition   Jk Rowling posts in the Harry Potter Lexicon      JKR has stated in an interview (Comic Relief 2001) that she estimates the value of one Galleon to be "about five pounds," which works out to around US$9.75 (the exchange rate at the time of the interview was US$7.33). In the introduction to both QA and FB, US$250-million is stated to be the equivelent of 34 million Galleons. That also works out to a value of £5 to the Galleon, at the exchange rate of the time. The price listed on the back of the books, however, is not correct, since US$3.99 would equal less than half a British pound, or 8 sickles and 15 knuts. The book instead incorrectly lists US$3.99 as being equal to 14 sickles and 3 knuts. (Unfortunately, CNN.com uses this incorrect value for their Knuts-to-dollars converter.)      This gives us approximate values as follows:      1 bronze Knut = £0.01 (US about 2 cents)      1 silver Sickle = £0.29 (about US$0.57)      1 Galleon = £5.00 (more or less US$9.75)      These rates vary as the exchange rate fluctuates - see the Wizarding World Currency Converter for the current rate.   Now looking at the quote      Hagrid helped Harry pile some of it into a bag.   and     Right, that should be enough fer a couple o' terms, we'll keep the rest safe for yeh.   Obviously "some" is unspecified, but presuming the costs of ...     Typical elementary-school textbooks cost more than $100 each   He would be carrying at least 10 galleons for each school book, and going by the list of books just for his first year,  (Thanks Ibid!)     COURSE BOOKS      All students should have a copy of each of the following:         The Standard Book of Spells (Grade 1) by Miranda Goshawk   A History of Magic by Bathilda Bagshot   Magical Theory by Adalbert Waffling   A Beginners’ Guide to Transfiguration by Emeric Switch   One Thousand Magical Herbs and Fungi by Phyllida Spore   Magical Drafts and Potions by Arsenius Jigger   Fantastic Beasts and Where to Find Them by Newt Scamander   The Dark Forces: A Guide to Self-Protection by Quentin Trimble         (Harry Potter and Philospher's Stone, Chapter 5)   That's 80 Galleons just for books. This does not include the list of other expenses Harry has for his school years (wand, potion reagents, etc.)  How many Galleons is "some" or is Diagon Alley selling supplies for third world prices?  Sidenote, is this just a case of bad JK maths?