How to pass a container of derived type to a function needing a container of base type
Getting a vector into a function that expects a vector
So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?  Suppose that we roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by six? How to print the name of missing files in a folder? Correlations with unordered categorical variables Can the category of chain complexes be realized as a functor category? As the title says, is there some sort of category $\mathsf{C}$ which can be thought of as the "walking chain complex", so that the category of chain complexes in some other category $\mathsf{A}$ can be realized as $\mathsf{A}^\mathsf{C}$ (or perhaps some subcategory thereof)? I need to prove that $$\sum_{n=1}^{\infty} {\sin{100n}} \; \text{diverges}$$ I think the best way to do it is to show that $\lim_{n\to \infty}{\sin{100n}}\not=0$. But how do I prove it? I have a Canon 550D with 70-200 f4 and 50mm prime lenses. Although the camera has built-in 9 focal points, I sometimes face a strange problem. Here's a sample photo:    In reference to the above pic, you can see that both of the faces are NOT in focus. I used 70-200 f4 for this shot at max aperture. Still, I couldn't get both of them in focus. Why? I also try decreasing the aperture to attain a greater DoF but still, I couldn't get both of them into focus.  Another thing: Although the cam has 9 focal points, why can't I use all of them to focus, say, 9 points in a portrait shot? In manual mode, it has the option to select one of the 9 focal points. And in auto mode, it sometimes select more than one focal points.  This is just an example image. I've faced this problem zillions of times. I have the following shortcut which opens an SSH instance. How can I modify it so that when SSH closes, the terminal stays open?  [Desktop Entry] Terminal=true Type=Application Name[en_US]=ssh Icon=/logo_sprite.png Exec=gnome-terminal --geometry=... --window-with-profile=... --title=... -e 'bash -c "ssh -t -i ~/dsa.key cle@12.210.9.17 sudo -s"' How to install updates via command line? When I log into my web server via SSH I see the information:  88 packages can be updated. 80 updates are security updates   I tried apt-get update then apt-get upgrade but each time I log in I still see the message about updates. How do I install them? Is there an alternative way to express "has them " other than "makes them "? For example, in the following sentence, can I replace have them with makes them, or is there another verb that more correctly I could use instead of has?     Since the manufacturers are so deeply involved, in some cases Wal-Mart even has them handle their own distribution, saving the retailer big bucks and increasing profit margins on cheaper goods.   Another example could be the following one.     The doctor sends my father and Uncle Johnnie out for all the ice they can get. Then he has them dump the ice in the bathtub, add cold water almost to the top, whereupon my aunt is wrestled into the tub and submerged. Alignment of the titles in a ToC and \Roman{section} There is a problem with the alignment of the numbering of the ToC: When we use   \renewcommand{\thesection}{\Roman{section}}   the numbers encroach on the titles. When the command is commented out, the numbers are all aligned [from the first number on the left] but the titles do not begin at the same position.  What I want is to use \Roman{section} but with the numbers being displaced after V (or 9 in arabic) so that the first letters of the  titles are all aligned !  An illustration:  %\RequirePackage{fix-cm} \documentclass[a4paper, 11pt, twoside]{article}  \renewcommand{\thesection}{\Roman{section}}  \begin{document}   \tableofcontents \normalfont %\cleardoublepage  \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY} \section{QWERTY}  \end{document} Let $G$ be a group and $c\in G$. Define $*$ on $G$ by: $x*y=xdy$ for all $x,y\in G$, where $d$ is the inverse of $c$. Prove $(G,*)$ is a group. Let $G$ be a group and $c$ be a fixed element of $G$. Define a new operation $*$ on G by:   $$x*y=xdy$$   for all $x$ and $y$ in $G$, where $d$ is the inverse of $c$. Prove that $G$ is a group under the operation $*$.    If you want to check, this problem is in the book “A Course In Group Theory”, by John F. Humphreys (problem $3$, page $28$)   I know what are the axioms that $(G,*)$ must obey in order to be a group and I did show that all the axioms where obeyed except the inverse axiom.  My problem is that, whenever I try to verify what would the inverse be for some element $x$, I get an equation where the $x$ is cancelled in both sides.  Can please someone guide me?  Thank you!  (P.S.: This is NOT a homework assignment, I’m studying Group Theory by this book and got problems solving this question) Solution to German Tank Problem Is there a formal mathematical proof that the solution to the  is a function of only the parameters k (number of observed samples) and m (maximum value among observed samples)? In other words, can one prove that the solution is independent of the other sample values besides the maximum value? Most of the time when I mixed different nuts in a bowl, I observed that the big Brazil nuts were always on top while the small peanuts settled near the base. No matter how you take it, if the big nuts are put at the bottom and then the small nuts are poured, then also after some time the big ones will come to the top. Will not the gravity attract those big nuts more and eventually will they not remain at the base? But it doesn't happen!   I googled it and found the term Brazil-nut Effect but couldn't find any proper explanation. What is the physical explanation for this effect? Oven temperature for multiple ducks? Do I need to adjust the oven temperature in a roast duck recipe if I want to put more than one duck in the oven at a time.   I suspect I should keep the same temperature but keep them in longer.  Should I cover each duck in foil individually or together?  Does it matter if they are on the same pan? How do I read an entire file into a std::string in C++? NULL values inside NOT IN clause I was reviewing  for , and noticed that nobody voted to close it, even though the page reports a duplicate.      Why does this happen? Should I really have been awarded mortarboard on a Per-site meta? Let's say I have a node type "Article" which has a field "File" which is set to handle public files. A lot of articles and files get added.  Now the specs suddenly change and the "Article" will move behind a login and therefore also the attached files must be changed to be not publicly accessible anymore.  I already found out  pretty easily by reimporting the manually updated field.storage.node.field_file.yml config. But: this only affects new files that will be added after the switch. It doesn't work for existing files. They still are accessible publicly. Many thousand existing files would need to be manually reuploaded to also make them private.  Does anybody of you have solved that in D8 before? If so, then how?  As all I can think of right now is to programmatically query all "Article" nodes, then foreach through all nodes, get the files, temporarily store them somewhere else, empty the field out, then try to reupload the files programmatically (probably my next question) and then resave each node.  Does that sound reasonable? Or can you think of any other approach that might work here (in D8)? Are there other schools for witches and wizards in the rest of the world? In the books they only speak of 3 schools, but what about Asian or American people?  And even more, were they affected by the events happening in Europe?