Writing an instance(s) of a class in a file in json or xml
Scala 2.10 + Json serialization and deserialization
Suppose we have a natural number $n \ge 0$.  Given natural numbers $\alpha_1,\ldots,\alpha_k$ such that   $k\le n$ $\sum_i \alpha_i = n$   what is the maximum value that $\Pi_i \alpha_i$ can take?  I'm quite sure that there is a theorem telling me the result, but I cannot find it. For sure an upper bound is $n^k$ but I'm searching for a real upper bound. I'm pretty sure that upper the bound should be $n^2$, but I don't know I could prove it. Why is the [I'm Done] button unavailable after only flagging comments in the First Posts review queue? I just flagged two comments during a review of a question in the First Posts queue (on another SE site). Then I wanted to select the button I'm Done, but it's unavailable (I can only select No action needed). Even if I refresh my page (while still on that review page), it remains the same.  If however I also downvote the question (only temporary, as a test, since I don't want to downvote the question being reviewed), then it seems to work as I'd expect it to: the button I'm Done becomes available, and No action needed becomes unavailable.  Why is the I'm Done button unavailable after only flagging comments in the First Posts review queue?  Notes:   I'm not convinced that you're supposed to review the actual post, and not (only) the comments underneath it (as mentioned in 's comment). Because "if" I would post a new comment, or just upvote an existing comment, I can actually select I'm Done. While in this case I flagged existing comments which IMO had become obsolete. Flagging comments is "acting on comments". And if my flag gets accepted (in this case: "no longer needed"), and the comment is actually deleted (by the mod), then it makes the question a bit more readable (= don't waste your time digesting a comment which is obsolete). Therefor "IMO", in the end I also "acted on the post". Think about all those posts with a zillion of comments, of which many are obsolete (e.g because the post got updated already). I am not sure (yet) if a similar issue exist in any other review queue (i.e. the Late Answers queue). Definition respective derivation of angular momentum formula I am reading An Introduction to Mechanics by Kleppner and Kolenkow (2014). On page 241 is the definition of the :      Here is the formal definition of the angular momentum $\vec{L}$ of a particle that has momentum $\vec{p}$ and is at position $\vec{r}$ with respect to a given coordinate system: $$\vec{L}=\vec{r} \times \vec{p}$$   In the book there is no explanation why this formula should be true. From this equation the formulas for torque and moment of inertia are derived.   My question is: Why is the formula above correct? Why isn't the formula for angular momentum something completely different, like $\vec{L}=\sqrt{(\vec{r} \times \vec{p})2\pi M}$? Is the formula for angular momentum just a mere definition and if not, how to derive it? How did people come across that particular formula? Alternative to Photoshop or Paint.NET Downgrade Windows 7 Ultimate to Home Premium without a clean install Currently I've got an installation of Windows 7 Ultimate x64. I would like to downgrade to Windows 7 Home Premium x64 without a clean install. I've got a (legal) retail disc and tried the following tricks:        Still the Windows setup keeps telling me I can't upgrade because I've got a higher version installed (Ultimate). The trick seems dead. Does anyone know a way to change from Ultimate to Home Premium without the hassle of a clean install? Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able. Guid vs INT - Which is better as a primary key? Predefined Coordinate Systems missing in QGIS 2 in QGis 1.8 were lots of predefined coordinate systems (national projections). Where have they all gone in qgis 2.0? I specifically need the Gauß-Krüger-Projections Zone 1 to 5.  Is there any plugin to load those coordinate systems? Not able to execute a .sh file: /bin/bash^M: bad interpreter I wanted to execute a shell script:  -rwxr-x--x 1 root root   17234 Jun  6 18:31 create_mgw_3shelf_6xIPNI1P.sh   I tried to do a standard procedure, but I got this error:  ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0  DEBUG   cd/etc/opt/ldapfiles/ldif_in ; ./create_mgw_3shelf_6xIPNI1P.sh  localhost 389 -l /opt/fews/sessions/AMGWM19/log/2013-06-06-143637_CLA-0 **ERROR  sh: ./create_mgw_3shelf_6xIPNI1P.sh: /bin/bash^M: bad interpreter: No such file or directory**   What does it mean? I was doing this as the root user under the root group.  Does it mean that the file does not have the correct permission for the root user? Practical way to implement prevention of IP Spoofing I am an undergraduate Computer Science student and was hoping to gain some knowledge of ways to help prevent IP spoofing but all the resources I have tried out elaborate this concept in a theoretical way. I want to try out my hands at one of the techniques like:      How do I simulate this whole situation in my own system were I myself am the attacker and I myself have to defend it? And once I have gained an understanding of it, then how do I start translating that into programming terms? Deployment error regarding translations when generating package version Segmentation fault error occurs for a simple function I have coded Let $X$ be a set and consider the collection $\mathcal{A}(X)$ of countable or cocountable subsets of $X$, that is, $E \in \mathcal{A}(X)$ if $E$ is countable or $X-E$ is countable. If $X$ is countable, then $\mathcal{A}(X)$ coincides with the power set $\mathcal{P}(X)$ of $X$. Now suppose that $X$ is uncountable. Assuming the axiom of choice, we can conclude that $\mathcal{A}(X) \ne \mathcal{P}(X)$, since $|X| = |X| + |X|$. So the question is:     Can we prove in ZF that $\mathcal{A}(X) \ne \mathcal{P}(X)$ for every uncountable set $X$?   I'm assuming that a set $X$ is uncountable if there is no injective function $f : X \rightarrow \mathbb{N}$. Let $f:\mathbb{R}\to\mathbb{R}$ continuous such that $\lim_{x\to\infty}f(x+1)-f(x)=l$.  How can I prove that $\dfrac{f(x)}x$ converges for $x\to+\infty$ ?  I am just trying to prove the convergence, not that it converges to $l$ (that part be deduced immediately by Stolz-Cesaro and the sequential characterization of limits) I am trying to print a large quantity (several megabytes) of UTF-8 encoded text which consists of Chinese and Latin characters (and maybe a sprinkling of others). I would like to print it in several columns per page, in a very small, condensed font, preferably with control over line spacing. I'd quite like inter-column lines, but I can live without them. The aim is to print to PDF for transfer, as well as to paper.  I have tried enscript and a2ps, but neither of these support Unicode.  I have also tried paps, but this produces bitmapped outputs which cannot be PDF'd effectively, and also look terrible.  Is there a modern way to print UTF-8 text like this without resorting to something like constructing it manually in Python? Here's what is happening; everytime I go to Stack Overflow (stackoverflow.com, NOT meta) with Firefox, it gives me the "Welcome back" tab that pops up from the top. Whenever I click in the "click here to refresh the page" link, all it does is refresh the page without logging me back in.  Even if I try to log in using the "log in" button at the top, all it does is pop up the tab that says "Welcome name here, you're being redirected." The problem is I'm not being logged in, not to mention that it keeps refreshing the page over and over again without giving me a choice to log in with Facebook.  For some reason, I was capable of logging in to Meta Stack Overflow using Firefox. I am still unable to log in to Stack Overflow. Any ideas? Is there any pair of 128-bit strings M and K such that AES$_K$(M) = M?  If yes, how do I go about (efficiently) finding such a pair? What are the origins of the word orientated?  As far as I know, the correct spelling is oriented and orientated is not an alternative spelling but an error that is in common use.  Is it for example more commonly used in a certain country or by a certain people? Is there a reason for people choosing to say or write orientated instead of oriented? Is there anyway to restore the Blender default Cloth settings? Or is there anyway to find what the default settings are?  I didn't realize at the time that by changing the values I was overriding the default values.  Using Blender v2.76. Best VNC / remote desktop software for assistance Poll on best VNC / remote desktop software for assisting others on Windows/Mac machines from Ubuntu?    I've heard good things about TeamViewer and Fog Creek Copilot, but I'm wondering if the included GNOME Vinaigre VNC client is good enough for this.  To specify, I'm looking for best option based on:   SIMPLEST ease-of-use for client to download/use on their end. See #1. Works cross-platform I am able to control client's mouse and/or keyboard from remote machine.