Sum of cosines with a multiplicative factor in the angle and different interval
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
What do they do with all the plates and cups in Star Trek? Proof for $A \cup B = B$ if and only if $A \subset B$ I am trying to define a proof for  $A \cup B = B$ if and only if $A \subset B$  I started with:  $$A \cup B$$ $$x \in A \lor x \in B$$   but I am unsure on how to continue. Compiz Problems (Plugin Missing, Performance Issues, Development) Why do we need to use `int main` and not `void main` in C++? Why do we need to use int main and not void main in C++? Is there a way to avoid SSH typing delay? Ship an application with a database If your application requires a database and it comes with built in data, what is the best way to ship that application? Should I:   Precreate the SQLite database and include it in the .apk? Include the SQL commands with the application and have it create the database and insert the data on first use?   The drawbacks I see are:   Possible SQLite version mismatches might cause problems and I currently don't know where the database should go and how to access it. It may take a really long time to create and populate the database on the device.   Any suggestions? Pointers to the documentation regarding any issues would be greatly appreciated. Why crontab scripts are not working? Find the value of $\space\large i^{i^i}$? Is $\large i^{i^i}$ real ? How to find it?   Thank You! Surface area inside cylinder Find the surface area of the part $\sigma$: $x^2+y^2+z^2=4$ that lies inside the cylinder $x^2+y^2=2y$  So, the surface is a sphere of $R=2$. It looks there should be double integral to calculate the surface, but how, which way? Android cancel Toast when exiting the app and when toast is being shown I have a virtual machine running ubuntu and I am trying to host some files on ubuntu and map the drive in windows PC.  Following the steps , I am able to see (from windows) the "work" folder after typing in \ubuntu_ip. But when trying to access or map it with "svc_acct" from windows, I get "0x80070043 error the network name cannot be found". I guess I am not accessing correctly from windows.   SAMBA config below (svc_acct is an account set up under linux). When accessing the folder from windows, I get prompted for username/password. Not sure what credential to type in exactly.  samba config: [work] path = /home/svc_acct/work valid users = svc_acct available = yes read only = no browsable = yes public = yes writable = yes force user = svc_acct create mask = 0777 directory mask = 0777   UPDATE:  All I did to resolve this is by changing samba config's path from path = /home/svc_acct/work to path = /home/svc_acct following  post  (last sentence). Then no more prompt for password in windows when I try to click into the folder. Thanks to @sancho.s for suggesting the link. Associativity of Cartesian Product Punctuation of direct speech, edge cases I recently learned that I have developed a consistent, but entirely wrong approach to punctuating direct speech in fiction. I am in the unenviable position of trying to relearn.  Previously I wrote such things as:     "I'm done." She said.   when the quoted speech was definitely, absolutely the end of a sentence. So now I know I need.     "I'm done," she said.   This follows the rule that a period is only allowed when the end of the spoken sentence is also the end of the sentence in the narrative. For example:     "I'm done." She slammed the door on the way out.   So, it now looks odd to me when there are multiple sentences in the speech:     "I can't take her. I'm done," she said.   Can you reassure me that is correct, or give the correct form? Please don't suggest rewriting the sentence to put 'she said' in the middle - I'm aware of that: I'm specifically asking about the punctuation rules.  The other odd case is speech ending with an ellipsis. Do sentence terminating ellipses (four periods normally) become:     "I can't take her. You know, ...," she said, nodding towards Jane.   If so, are non-terminating ellipses dealt with the same way?     "I can't take ...," she nodded towards Jane, "any more!"   or can non-terminating ellipses be used unadorned?     "I can't take ..." she nodded towards Jane, "any more!"   I'd be very grateful if you could point me at references as well as answers. For the record I am a British writer writing for both British and US publication, so any variation is also interesting to me! Why don't Muggle-born wizards use Muggle technology to fight Death Eaters? We know that wizards in the Harry Potter universe are subject to regular physical harm (e.g. witness injuries from being hit by Bludgers or just colliding with things when playing Quidditch).  Therefore, it's almost a certainty that an average wizard would be vulnerable to, say, a bunch of bullets.   There may likely be spell(s) to protect from projectiles - witness Dumbledore's  deployed when Voldemort sent a bunch of glass at him during the  at the end of Harry Potter and the Order of the Phoenix (according to , possibly an unusually powerful Protego or the Silver shield).   But:   those spells obviously take effort/energy/time to cast (not everyone's Dumbledore) AND more likely than not most Death Eaters wouldn't recognize a Muggle gun for a threat (or realize what kind of threat) till too late.   So, the guns should at best allow an over-matched OotP member (e.g. Harry or Hermione) to greatly equalize the power between any regular Death Eaters and themselves, and even perhaps help against Voldemort (who can't be killed with a bullet, but, at best, would need to expend magical energy and time into conjuring a shield, and, at worst, be stopped/interrupted/driven off).  So I'm looking for an explanation - ideally in-universe, but possibly just some statement by JKR - of why the Muggle-born OotP - who are likely very much at ease AND familiar with Muggle technology and live in the late 20th century - do not use guns. Or, for that matter, ANY Muggle technology of the late 20th century? Cue Arthur C. Clarke's "indistinguishable from magic" meme.  Even if they are on some kind of idiotic moral crusade to never kill their opponents (even the Jedi aren't this dumb), given the time-frame, non-lethal weapons would have already existed, such as rubber bullets and tasers.  NOTE: Please don't offer the "if they do it, Death Eaters would start using guns as well" theory. First, Death Eaters would have used the guns if they knew how to, anyway. Second, the guns, like any "secret weapon", could be reserved for strategic battles, say the defense of Hogwarts in Deathly Hallows.    The origin of the question stems from two things.  First, Harry's fascination with all things that are different in the magical world (e.g. moving photographs), based on his knowledge of the Muggle material world, as well as the somewhat amusing cluelessness of the "Muggle artifacts" expert, Mr. Weasley, regarding Muggle items and how they work.   Basically, from the books, it's clear that the Wizarding world wouldn't know details about guns or what they are for or how they work.  The second thing is it's clear, at least initially, that wizards are afraid of Muggles finding out about them. Hence all the efforts to cloak their society (basically, do you REALLY want every Muggle gunning for you, even with Magic)? The idea of how control over the Muggle world seems to be more indirect, by Death Eaters asserting mind-control over the government. This means there's an implicit understanding by Death Eaters that they don't stand a chance against armed Muggles even given the magical disparity.  Considering Harry and Hermione's overall adaptability and inventiveness (and brains in the latter case), it's mind-boggling that the idea of fighting Death Eaters with modern technology completely slipped their mind. I mean, it's a basic part of human myth (see Steel vs. Magic themes in Conan books, or Beowulf, or heck, A Yankee in King Arthur's Court). So it's not like the idea of using technology against magic would be impossible to come up with. The question begs itself - why not? Considering the fact that Rowling generally tried to be logical and consistent in building the HP universe, I feel like there must be some in-universe explanation for this that I just didn't notice.   (in-universe answers only unless there are some authoritative out-of-universe statements that are part of canon). How do you properly use namespaces in C++? I come from a Java background, where packages are used, not namespaces. I'm used to putting classes that work together to form a complete object into packages, and then reusing them later from that package. But now I'm working in C++.  How do you use namespaces in C++? Do you create a single namespace for the entire application, or do you create namespaces for the major components? If so, how do you create objects from classes in other namespaces? Add self-answer delay for all users TL;DR:  I believe there are still some issues with self-answers, particularly near-immediate self-answers, which are not addressed by the current system.  This could be remedied by imposing an automated restriction on how soon self-answers will be displayed in the thread.  Allow users to submit self-answers at any time, but do not display them until certain reasonable conditions (a relatively short timeout, or the posting of a competing answer) are met.    History  This thread covers a good deal of the concerns surrounding self-answers, and some mechanisms in place to prevent "bad" self-answers from new users and other abuse of the self-answer system.    As I understand it, the following restrictions apply:   Users with &lt;100 rep cannot self-answer within 8 hours of posting a question. Self-answers cannot be accepted within 48 hours of posting. Self-answers do not provide rep from being accepted. Accepted self-answers are not pinned to the top of the thread.   Problem  This does a good job of preventing users from posting answers which should probably be comments (or not posted at all), allows superior answers to rise above accepted self-answers, and prevents some other abuses of the system.  However, there is a less tangible element of self-answers which this does not address:    Self answers are a disincentive to other users who may otherwise be willing to post more accurate, detailed material stemming from broader or deeper knowledge and/or experience than the asker has.  When someone posts an answer to their own question, it presumably means that the problem which spawned the question is solved to their satisfaction.  This is fine for the purposes of sharing information with the community, but it deters others from providing solutions to the question which may be more complete or accurate since there is not so much likelihood that the self-answerer will accept a competing answer.  Worse, in the case of near-immediate self-answers, this can remove the incentive for other users to gain reputation via up-votes because the asker has an unfair head-start.  Unless everyone is required to view new answers to questions where they have already voted on an answer, most people probably vote on a good answer and never look at the question again.  This can put (potentially) better answers at a disadvantage even when the head-start is within an hour.  Suggested Solution  Add a delay to the posting of self-answers.  The delay should be the least of these:   Until a competing answer has been posted. A reasonable amount of time to allow competing answerers a chance to post, without preventing self-answers outright.  (Suggestion: 2 hours)   To better facilitate this, and avoid completely turning people off from appropriate self-answering, I suggest the delay be handled through automation more than user limitation.  That is, the user should be allowed to submit the self-answer at any time.  But the answer will not actually be displayed to other users until one of the above conditions have been met.  This could also be applied to the existing 8-hour delay for low-rep users.  Example:  T:0 - A user finishes resolving a tough problem, just before he would have gone to SE for assistance, and decides to share his new-found knowledge with the community.  He posts a question describing his problem.  T:5 minutes - The user then posts a self-answer.  There has not yet been another answer posted to the thread.  The user is given a notice describing the restrictions in place regarding self-answers, and the answer is submitted into the database but not displayed to other users.  (Similar to how suggested edits are only displayed to the user suggesting them, until they are approved.)  T:1 hour, 15 minutes - Another user sees the unanswered question, and posts their answer.  Their answer is displayed immediately, and the self-answer is now also displayed.  T:2 hours - Had the second answer not been posted, the self-answer would automatically be displayed after this point. How do I figure out the right size font / text for a given read distance? To avoid printing single letters at varying sizes and measuring how far away I can see it from a distance is there a formula for determining what size font for a particular read distance? Is it better to take the midpoint between the ascender line and x-height or to go purely off of the x-height (since going purely off the ascender line could leave lowercase letters difficult to read)? How does vertical height play into this? Would I need to then figure the hypotenuse distance instead of a straight distance?  For example if I'm shooting for a 20' read distance but the sign is to be placed about 30' up should I use a distance of  35' instead of 20'?  I'm shooting for a 20' read distance for the headline and then possibly a 10' read distance for additional content depending on how it all fits on the active area. How to prove that a simple graph having 11 or more vertices or its complement is not planar? A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$. All Stack Exchange data dumps