Integer class object
Weird Integer boxing in Java
This is solely a reference request. I have heard a few versions of the following theorem:     If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ whenever the expectations are finite, then $X,Y$ are independent.   And there is a similar version for characteristic functions. Could anyone provide me a serious reference which proves one or both of these theorems? Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$ Theorem: There are infinitely many primes congruent to $3 \mod 4$. Proof: Assume that $p_1 = 3, . . . , p_n$ are primes of the form $p_j ≡ 3 \mod 4$. We will construct a new one by looking at $N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work).  There is more to this proof but the rest of it I understand, what I don't get is where it says &quot;$N = 4p_1 · · · p_n − 1$ (putting $N = 4p_1 · · · p_n+3$ would also work)&quot;. I do not understand why we are writing $4p_1 · · · p_n − 1$. Is there a more clear way to prove this theorem? Movie/TV series with a scene of spiky, black goo growing out of a lab container? There was a scene from a sci-fi horror video, not animated, don't know if it's a movie or TV series, where there was this black goo in a glass container and some scientists were looking at it under a microscope.   The pitch black goo grew and grew so fast, eventually breaking out of the inner box and the scientists that were inside the "inner lab" were begging to get out but the scientists outside that inner lab refused to open the door. The black goo was spiky (had spikes).  It's not any of the "Alien" movies, "The Blob", "Life", or "The Thing". It's not vintage. It was made after 1990, I'm pretty sure. (semi)-Automatic pluralization around a citation I've had a couple of answers today where the OP indicated via a comment that I solved their problem, but the question wasn't upvoted or accepted.  In both cases the person probably wasn't able to upvote since they were new, but they could have accepted my answer. I felt a little guilty asking them to accept the answer, but since it solved their problem I felt that it would help others who stumbled on the question trying to solve their own problem to know that my solution really was the answer. Is asking the OP to accept your answer when they've said that it solved their problem a reasonable thing to do or does that feel like nagging for reputation? I'm looking for the best / friendliest way to reboot my rooted android 4.1.1 device. I found these solutions so far:   su -c "reboot" - Causes problems with wifi after restart on my device... I read that this can cause a currupt file system in some cases... Doesn't work via ssh for me. toolbox reboot - Same concerns here, but works via ssh. reboot -d 8 -f - causes problems after restart e.g. some apps wont start busybox killall system_server - "Hot Reboot" (not really a system restart) start|stop - Starts/stops Android Runtime (not really a system restart)   What is the device doing exactly when I'm pushing the (hardware) power button? I guess that's the most friendly way. Macroscopic quantum phenomena and tunneling Payment from Apple for developer How to tell a lambda function to capture a copy instead of a reference in C#? I've been learning C#, and I'm trying to understand lambdas.  In this sample below, it prints out 10 ten times.  class Program {     delegate void Action();     static void Main(string[] args)     {         List&lt;Action&gt; actions = new List&lt;Action&gt;();          for (int i = 0; i &lt; 10; ++i )             actions.Add(()=&gt;Console.WriteLine(i));          foreach (Action a in actions)             a();     } }   Obviously, the generated class behind the lambda is storing a reference or pointer to the int i variable, and is assigning a new value to the same reference every time the loop iterates.  Is there a way to force the lamda to grab a copy instead, like the C++0x syntax  [&amp;](){ ... } // Capture by reference   vs.  [=](){ ... } // Capture copies Shell command to sum integers, one per line? I am looking for a command that will accept (as input) multiple lines of text, each line containing a single integer, and output the sum of these integers.  As a bit of background, I have a log file which includes timing measurements. Through grepping for the relevant lines and a bit of sed reformatting I can list all of the timings in that file.  I would like to work out the total. I can pipe this intermediate output to any command in order to do the final sum.  I have always used expr in the past, but unless it runs in RPN mode I do not think it is going to cope with this (and even then it would be tricky).  How can I get the summation of integers? It appears that in anticipation of D&amp;D Next Wizards of the Coast has removed much of the Dungeons and Dragons, 3rd Edition Web content. I didn't perform a thorough search to determine if all the content is removed (e.g. I know the Three Dragon Ante Web enhancement  and the Mind's Eye column about psionic tattoos  are both gone--better not to ask why those are my go-to articles), but it all might be.  What's the best way--and by best I mean both legal and convenient--to continue to access this content? What do I need to run a D&D 5E campaign? I have GM'd several RPGs before that are not D&amp;D (Fate, Deathwatch, Star Wars). We first tried to play D&amp;D using the 3.5 edition and it went horribly — too many books and too many options with no idea of where to start.  I have been told that 5E takes care of all that and is easier and more fun so I want to try that but I would like a definitive list of what I need.  I expect that the kinds of books we need divide up like this:   Rulebook for me as GM Rulebook for players Fluff for everyone Monster book for me as GM   Links to these would be helpful as we got very confused with the 3.5 books — who should use what books confused us.  What other things do we need to play a campaign? I expect things like:   Dice: what kinds and how many of each kind, roughly. Models and maps. Do we need these? Does 5E need models and a grid or can it be played without (which is preferred)?   Is there anything else that we need that I haven't anticipated? I've only just begun studying group theory (up to Lagrange) following on from vector spaces and I am still finding them almost frustratingly  arbitrary. I'm not sure what exactly it is about the axioms that motivated them defining groups.  My textbook asks you to list 'common features' of vector spaces and then later defines a set of axioms for vector spaces under addition, scalar multiplication and both, noting that the axioms under addition form an Abelian group. So are groups just a generalisation of vector spaces under any binary operation?  My main problem is that the book notes that 'the axioms may seem rather arbitrary' and links groups with vector spaces but doesn't elaborate.   When introducing groups, you are tasked to complete Cayley tables for the symmetries of an equilateral triangle and square.  Then, similarly to the delivery of vector spaces, notes that the tables have common properties (Closure, Identity, inverse and association) and defines a group as a set of elements under a binary operation that has these features.  So what's so important about these 4 properties? For example, if 1 or 2 the properties were excluded form the  axioms, or we added an extra few properties as axioms how would that cripple the effectiveness of groups?  Are the group axioms ever difficult to work with or do they always work, forgive the crude Littlewood analogy, like a mathematical skeleton key?  What is it about these 4 properties that make groups such a powerful tool in mathematics and physics?  My best guess is that a group is the best way to express our sense of  symmetry and what is symmetric mathematically, but I would prefer some elaboration. How do the Chitauri "ships" propel themselves? In the 2012 The Avengers film, the Chitauri army arrives through the portal along with these big robot alien whale Chitauri dudes. Here's one chasing Iron Man:  These guys basically swim through the air like... giant robot alien whales. I don't see any means of propulsion. Other, more humanoid Chitauri soldiers fly around on things that seem to be mechanical &quot;speeders&quot; of sorts. What are these guys? Are they ships, creatures, or both? Is there an explanation anywhere in the Avengers universe for how they defy gravity and swim through the air? There are several spells that require the target to be "humanoid" such as , , etc.  However, if the target is Polymorphed after that spell has been successful, then what happens?  Does the change in form to Beast end the spell effects? Does it suppress the spell until the correct form returns? Does it do something else? What is the SKU of a motor? I came across an 'N20' motor, and I don't know what that means. As far as I can tell (and please correct me if I'm wrong), N20 is the SKU of the motor. What is the SKU? In viewing the weekly list of rep change, I see  on top: razpeitia2 5 16  member for: 2 years, 7 months link #1 week rank +8529 change 727 total reputation 2,286 week reputation    How can someone with 727 total have 2286 for the week with no bounties?  Call me curious.  Is this a bug or something else here? Force newlines with cat wildcard printing I want to use cat with wildcards in bash in order to print multiple small files (every file is one sentence) to standard output. However, the separate file contents are not separated by a newline, which I'd like to for ease of reading.  How can I add a file delimiter of some sort to this command? Can't execute a MySQL stored procedure from Java Why does the reputation need to be publicly displayed? Possible Duplicate:          The idea of getting greater privileges with greater reputation is good, but what is the benefit of publicly displaying that reputation? Since SO claims to be about good questions and answers, that purpose is better served if the reputation is only visible to the account owner (and, of course, the site admins). This would better ensure that content gets pushed up solely by its merit, and not based on the author. (See )   Edit (copied from comment to an answer below): Once you have gathered high reputation, you can also gather more reputation with ordinary answers, especially from newbies (newbies on the topic, not on the site) who usually choose to accept or upvote an answer on the assumption that "since a high-rep user has posted it, it is probably right". Can you guarantee that doesn't happen often?