Let $n$ be a positive integer. Prove that  \begin{equation} \sum_{d \vert n} \varphi(d)= n \end{equation}  where $\varphi$ is the totient function of Euler.

If $k$ is a positive natural number then $\phi(k)$ denotes the number of natural numbers less than $k$ which are prime to $k$. I have seen proofs that $n = \sum_{k|n} \phi(k)$ which basically partitions $\mathbb{Z}/n\mathbb{Z}$ into subsets of elements of order $k$ (of which there are $\phi(k)$-many) as $k$ ranges over divisors of $n$.  But everything we know about $\mathbb{Z}/n\mathbb{Z}$ comes from elementary number theory (division with remainder, bezout relations, divisibility), so the above relation should be provable without invoking the structure of the group $\mathbb{Z}/n\mathbb{Z}$. Does anyone have a nice, clear, proof which avoids $\mathbb{Z}/n\mathbb{Z}$?


I cannot understand why tutorials, examples, etc. contain examples like this:  I have played  or  Have you been to Moscow?  Why Past Simple cannot be used in these sentences? Where is the "border" when I can use Past Simple?

If I seem tired, can I say: "I haven't slept last night"? If not, why have I been told that we use present perfect for actions that have present effects?


How would you find eigenvalues/eigenvectors of a $n\times n$ matrix where each diagonal entry is scalar $d$ and all other entries are $1$ ? I am looking for a decomposition but cannot find anything for this. For example:  $\begin{pmatrix}2&1&1&1\\1&2&1&1\\1&1&2&1\\1&1&1&2\end{pmatrix}$

This question aims to create an ""  of numerous questions that ask about determinants of specific matrices (I may have missed a few):              The general question of this type is  Let $A$ be a square matrix of rank$~1$, let $I$ the identity matrix of the same size, and $\lambda$ a scalar. What is the determinant of $A+\lambda I$?  A clearly very closely related question is  What is the characteristic polynomial of a matrix $A$ of rank$~1$?


Recently, I just won a scholarship from my government for pursuing a master's degree in some Canadian universities. I checked the minimum requirements for the English level and I noticed that almost all of them are asking for at least an overall score of 93 points or 100 on the toefl ibt examination (6.5 for IELTS but only 2 or 3 are asking for this last exam).   I recently received my score from ETS and I got 85 points in overall (26 points on the writing section as my strongest point). Although I know I am still missing a few more points, I have published one paper on the IEEE computer society, I have won 3 scholarships for continuing my education (70% scholarship in my home university, 100% scholarship for doing a summer internship in Canada and 100% scholarship for studying 6 months in Sweden), and I worked as a full time employee during my last semester as a web developer and programmer.   My bachelor is Computer Systems and IT. I am trying to pursue a MCs degree in Computer Science oriented towards data mining and cloud computing. The universities I am interested are McMaster, Dalhousie, University of Alberta, UBC and Waterloo.    Despite the fact that I don't have the "minimum English requirement", should you recommend me to retake and work on my English skills or should I try to apply for any of these universities?  All comments, suggestions and proposals are welcome :)

I work with some students who will attend graduate school in the US. The schools they are applying for list minimum required TOEFL scores. Some have just reached the minimum scores required for admission to their schools of choice. Do admissions departments ever care about how close this number is to the minimum? In other words, will the students be at any greater advantage if they retake the test and get a higher score, or is the "score level met" simply a "met" or "not met" variable that goes into deciding whether or not the students are accepted?


How can I remove from "previously installed apps" list in the PlayStore the applications that are already installed on my phone? For example, the application anyconnect shows up in the "previously installed apps" list:  Even though it is already installed on my phone:  I use Android 9  on Samsung Galaxy S9 with PlayStore 17.8.14.

In the new Android Market/Play Store (3.5.15) they have now got a list of "all downloaded" apps.   I have had an android phone for a good 2/3 years now and the list is huge, plus sightly more questionable apps which should have been lost in the ether of the internet have now been dredged back up to haunt me.  Can I remove apps from here?  Thanks


I'm trying to get all the factors of a number provided by a user and after a button click displaying all the factors on a MessageBox.   This is what my code code taken from  answer by  looks like, I thought I was pretty close, but I'm displaying the number of factors not the actual factor numbers.   For example if the user types in 10 and uses a button click, the MessageBox displays the number 4, but i'm wanting it to display the actual factors of 10 which should be 1,2,5,10.  *how can I display the factors?  public int Divisors(int fact)     {         int number = int.Parse(textBox2.Text);         int factorCount = 0;         int sqrt = (int)Math.Ceiling(Math.Sqrt(number));          for (int i = 1; i < sqrt; i++)         {             if (number % i == 0)             {                 factorCount += 2; //  We found a pair of factors.             }         }          // Check if our number is an exact square.         if (sqrt * sqrt == number)         {             factorCount++;         }          return factorCount;     }  private void ShowallButton_Click(object sender, EventArgs e)     {         int input = int.Parse(textBox2.Text);         double output = Divisors(input);          MessageBox.Show(+output + "");     }

All numbers that divide evenly into x.  I put in 4 it returns: 4, 2, 1  edit: I know it sounds homeworky.  I'm writing a little app to populate some product tables with semi random test data.  Two of the properties are ItemMaximum and Item Multiplier.  I need to make sure that the multiplier does not create an illogical situation where buying 1 more item would put the order over the maximum allowed.  Thus the factors will give a list of valid values for my test data.  edit++: This is what I went with after all the help from everyone.  Thanks again!  edit#: I wrote 3 different versions to see which I liked better and tested them against factoring small numbers and very large numbers.  I'll paste the results.  static IEnumerable<int> GetFactors2(int n) {     return from a in Enumerable.Range(1, n)                   where n % a == 0                   select a;                       }  private IEnumerable<int> GetFactors3(int x) {                 for (int factor = 1; factor * factor <= x; factor++)     {         if (x % factor == 0)         {             yield return factor;             if (factor * factor != x)                 yield return x / factor;         }     } }  private IEnumerable<int> GetFactors1(int x) {     int max = (int)Math.Ceiling(Math.Sqrt(x));     for (int factor = 1; factor < max; factor++)     {         if(x % factor == 0)         {             yield return factor;             if(factor != max)                 yield return x / factor;         }     } }   In ticks. When factoring the number 20, 5 times each:   GetFactors1-5,445,881 GetFactors2-4,308,234 GetFactors3-2,913,659       When factoring the number 20000, 5 times each:   GetFactors1-5,644,457 GetFactors2-12,117,938 GetFactors3-3,108,182


The following question is a question that confuses my mind long since.  I'm sorry if it looks nonsense.     If mathematicians who had made important discoveries in mathematics such as Bernhard Riemann, Carl Friedrich Gauss, Évariste Galois, Joseph Fourier, Leonhard Euler, Niels Henrik Abel and others had joined today's mathematics olympiads ( for example , IMO)  would they all won the gold medal (perfect score) ?   Should the mathematician who did mathematical discoveries be an Olympiad winner in the past?  These questions can actually be dealt with in $1$ single question.     A person who has not joined IMO, can contribute to mathematics in the future?   Thank you and Best Regards.

I am extremely poor in solving a problem quickly, which leaves me doing badly in olympiads and other contests. But, if I just don’t give up on a problem, no matter how much time it takes, I usually end up solving it. To have a future in mathematics or physics, is it necessary for me to excel at contests, because these days children excelling at contests have an advantage over those who don’t (not complete advantage, but advantage nonetheless)?


I'm new to Java, and I can't find the way to get or choose a random object from my list products. I tried so many different ways, but is always giving me an error. public class VendingWorking {          List<Product> products= new ArrayList<>();          public void registerProducts() {         CStamp stampOne=new CStamp("1 Jan 2000", "Collectable Stamp");         CStamp stampTwo=new CStamp("1 Jan 2000", "Collectable Stamp");         CStamp stampThree=new CStamp("14 Feb 2000", "Collectable Stamp");         CCoin coinOne= new CCoin("25 Jan 2019", "Collectable coin");         Ccar carOne= new Ccar(2015, "Tin Car Toy");         Ccar carTwo= new Ccar(2018, "Tin Car Toy");                  products.add(stampOne);         products.add(stampTwo);         products.add(stampThree);         products.add(coinOne);         products.add(carOne);         products.add(carTwo);     }      public void getRandomElement(List<Product> products){          Random random = new Random();          Product index=products.get(random.nextInt(products.size()));      }       public List<Product> getRegProducts() {         return products;     } }

How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum.


A witch that's using the flight hex to fly 20 ft. up in the air fails her saving throw against my halfling bard's hideous laughter spell. The  spell description says that an affected creature  collapses into gales of manic laughter, falling prone. The subject can take no actions while laughing, but is not considered helpless.  Does the witch become prone in the air? Would the phrase take no action effectively mean that the witch falls to her death, grappled and subsequently slain by her own foolishly placed black tentacles?

As per the title. The specific example I'm thinking of is an Archer Battle Master Fighter using Trip Attack on a Druid shapeshifted into an Air Elemental floating 120 feet off the ground. If the answer is different for this and the more general case, then answer each separately.  As noted in the tags, I'm looking at strictly RAW here, not RAI or house-rules, so references to specific pages of the PHB are appreciated. If there are any official answers on this, links to those would be helpful as well.


My younger brother (10) likes to play Garry's Mod, but when he plays online, he sees lots of bad words in the text chat. Is there a way he can play online, but with the text chat disabled? Or if that's not possible, can I set it up so that the profanity is filtered out?

Given that the  is so extensive, is there a command to disable text chat? I feel that text chat is commonly used for trolling and harassment, as voice chat has a higher barrier for such behavior.


This question is different from . Yes they both talk about shortcodes, but they are asking different things and therefore should be separated out. Otherwise all "shortcode" questions on this site would need to be marked as duplicate.  Original question:  My shortcode won't pass the attribute through to the function.  Here is the shortcode used inside my post: [points custom_field="company_location"]  Here is the function for my shortcode:  // Add Shortcode function points_shortcode( $atts ) {     // Attributes     $atts = shortcode_atts(         array(             'custom_field' => '',         ),         $atts,         'points'     );     return bg_calculate_points ($custom_field); } add_shortcode( 'points', 'points_shortcode' );   When performing a var_dump on my function it shows NULL when I was expecting to see the company_location string that was passed through by the shortcode attribute.  function bg_calculate_points ($field) {     var_dump($field); }   What am I doing wrong?

I want to build a shortcode that takes a single attribute.  Everything online is telling me to make it using an array:  // Add Shortcode function bg_comparison_points_shortcode( $atts ) {     // Attributes     $atts = shortcode_atts(         array(             'custom_field' => '',         ),         $atts,         'comparison_points'     );     return bg_calculate_points($custom_field); } add_shortcode( 'comparison_points', 'bg_comparison_points_shortcode' );   But in my mind something like this would be much simpler  // Add Shortcode function bg_comparison_points_shortcode( $custom_field ) {     return bg_calculate_points($custom_field); } add_shortcode( 'comparison_points', 'bg_comparison_points_shortcode' );   Is there a problem doing this simpler version?


Which site to ask a software technology's theory? Such as , there have the source code, but I don't know the deep theory. there is also no detail description of it. is there any site I can ask this type question? the StackOverflow only accept the code questions, not appropriate.  EDIT-01 My first example(ngrok) is not good. if there is a practical technology, such as VPN, such as PPTP, GRE and so on, I want to know its theory, still no site in SE suitable? if you say , but it only accept questions under layer 3. the VPN technology is belong to application layer.

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


I am able to find all the screens dimensions using below code but how can I find which screen my application is about to run? public partial class MainWindow : Window {     public MainWindow()     {        int length = System.Windows.Forms.Screen.AllScreens.Length;     } }

What I am looking for is the equivalent of System.Windows.SystemParameters.WorkArea for the monitor that the window is currently on.  Clarification:  The window in question is WPF, not WinForm.


My code are follows:  \documentclass[10pt]{book} \usepackage[T1]{fontenc} \usepackage{newtxmath,newtxtext} \usepackage{linguex}% \usepackage{tikz}% \usetikzlibrary{decorations.text,calc,arrows.meta}% \usepackage{tikz-qtree}%  \usepackage{adjustbox} %\usepackage{showframe} \begin{document}  \ex. \Tree [.CauseP [.DP \edge[roof]; {`the zog'} ] [ [.{\scshape cause} ] [ [.{\scshape past} ] [.vP \edge[roof]; {`dissolved the house'} ]]] ]  Throughout this monograph, I will focus on the reusable linguistic ingredients of the system and how they are efficiently deployed in the recursive combinatorics in building propositions. Reusability (and by extension polysemy) will be a seen as a design feature of the system rather than a bug. As a methodological principle, then, I will be guided by the fact of polysemous items and seek analytic unities to underlie them.  \ex. \textit{Achievements and accomplishments with result states}\\ %\begin{tikzpicture}[baseline=(current bounding box.north)] \begin{adjustbox}{max width=0.91\textwidth} \Tree [.InitP [.{\textsc{initiator}} ] [ [.Init ] [.ProcP [.{\textsc{undergoer}} ] [ [.Proc ] [.ResP [.{\textsc{resultee}} ] [ [.Res ] [.XP \edge[roof]; {\sc ground/final state} ] ] ] ] ] ] ] %\end{tikzpicture} \end{adjustbox}  \end{document}   and the output came as:    Is this possible to make the diagonal lines to be straight as marked in the below picture?    Diagonal line should be straight in all Trees. Please suggest...

I'm new to tikz-qtree, and can't find an automatic way to do something that qtree did very nicely.  With qtree, if you don't have a label for a single intermediate node, you get a straight line from the grandmother to the granddaughter.  With tikz-qtree, you get a "kink".  Compare the following:  With qtree:  \documentclass{article} \usepackage{qtree}  \begin{document}  \Tree [ Wiiiiiiiiiide [ nar- -row ] ]  \Tree [ nrw [ wiiiiiiiiiiiii- -iiiiiiiiiiiide ] ]  \end{document}   With tikz-qtree  \documentclass{article} \usepackage{tikz,tikz-qtree}  \begin{document}  \Tree [ Wiiiiiiiiiide [ nar- -row ] ]  \Tree [ nrw [ wiiiiiiiiiiiii- -iiiiiiiiiiiide ] ]  \end{document}   Is there any way to get the nice straight line in tikz-qtree, or do I have to adjust it manually?  Thanks in advance.


I'm using Bash in Ubuntu 20.04. I have file: Hello hi 123 if a equals b you one abc two three four dany uri four 123  I need to found with sed only- the lines with only 4 words . This is the code I wrote and it does not work, it prints exactly the file. sed "/[a-Z0-9+]{4}/g" F1

I would like to print lines in my file which containing 3 words seperated my 2 spaces.  for example:   AAA BBB CCC BB AA CCCCCCCC   only AAA BBB CCC sshould be printed.  I already use grep for it but I cant handle the spaces.


Can someone explain to me the proof of $${n+1\choose k} = {n\choose k} + {n\choose k-1}$$?

I'm trying to prove that ${n \choose r}$ is equal to ${{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$.  I suppose I could use the counting rules in probability, perhaps combination= ${{n} \choose {r}}=\frac{n!}{r!(n-r!)}$.  I want to see an actual proof behind this equation.  Does anyone have any ideas?


I'm a Linux newbie. I installed Linux on my laptop, without dual-booting it with Windows, so I think I replaced Windows with Linux. Now I want to reinstall Windows without deleting Ubuntu, dual-booting to the existing Linux and to Windows. Because I'm a newbie, if possible, can I have a step per step guide? Thanks in advance.

I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only!


This question has probably been asked before: how can I play Overwatch without WiFi? When I do have WiFi, I can play against AI, but that's kinda pointless if I can just play online; with friends. So, is there a hack or game-code change I can use to play with AI with no  WiFi?

I would like to practice my skills in Overwatch. Do you have to be online in order to play in training mode?


Working on P.D. Magnus. forallX: an Introduction to Formal Logic (pp. 154, exercise D. 7). It is the last exercise of Chapter 16. This is what I got so far.   Is my $IP$ strategy correct ?  $\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}} \fitch{}{  \fitch{¬(((A \to B) \to B) \to B)}{    \fitch{¬((A \to B) \to B) }{      \fitch{¬(A \to B)}{        \fitch{B}{          \fitch{A}{            B           } \\           A \to B \\           \bot         }       }     }   } }$  P.S: Here is a link to the open-source book:

Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? I started with the hypotheses $(p \implies q) \implies p$ and $\sim p$. However, from these hypotheses I did not get the desired contradiction to solve the question.  Thanks sb45


On iOS 14.4.1, I deleted the Lyft app (long pressed on the app icon and then clicked "Remove App"). I then reinstalled the app, and when I opened it, I was already logged in. My understanding of iOS's privacy model suggests that this should be impossible - all local data should be wiped, and the app shouldn't be able to detect that it was reinstalled (as opposed to installed for the first time). How might Lyft have done this?

I had the Facebook and Instagram apps installed on my iPhone (latest iOS). I deleted both apps and checked that there was no data from either app stored on iCloud (I went to Settings - iCloud - Manage storage and there was no mention of them storing anything on iCloud). Then I reinstalled Instagram, opened it, clicked on Login and the page still showed “Login as MYFACEBOOKNAME”.   How is this possible? How can I delete my FB login info once and for all on my iPhone?


I'm an undergraduate studying computer science at a local community college. Currently, I'm enrolled in an intro computer programming class that I unfortunately am unable to test out of (I asked my advisor). It is the prerequisite to the OOP class at my college (the class that AP Computer science would transfer to), which I took four years ago as a freshman in high school. I have already taken data structures and algorithms and am presently taking discrete math. The point being, I have very little to learn from this class. Last night, I received an email from my professor saying that my code on a recent assignment was identical to the solution in the textbook. I will admit that I did search to find the answer code because:  The autograde is extremely bad and requires spaces and other punctuation to be identical, all while not telling you what is wrong unless you look closely. It runs a series of units tests and compares the text output. Again, I won't learn from this class, so I'm not hurting myself by not properly learning The tests are worth 80% of the score, and I have been doing those fairly, so anything I do on the assignments will have little affect on my grade. The problems are incredibly fake and are nothing like the real world problems I engage in at work.  Generally, I've been searching to find a solution to a similar problem and then editing it until the autograde accepts it (so what I'm copying serves as a template to save time). In this case, I stumbled upon what turned out to be the actual answers. So technically I did copy the answers, but it was not me attempting to get out of work that I would actually learn from or need to do to pass the tests. I am very frustrated with how awful this class is and please note I would not do this for any other class. What I am not sure of is what to do now. I already have received a zero for that week's work (a tiny percentage of my grade) so I could go forward as if nothing had happened and ignore the remaining assignments (each week is about 55% easy work that I have been doing, 45% horrible labs that I often skip) and end up with about 85% on the course assuming my future test scores represent those in the past. Looking at the academic policy on the syllabus, as my first offense I will likely not see any other actions against me, but I don't want my professor to think I am a cheater. I have never cheated in any class and I don't consider what I did in this case to be a problem (I would argue it breaks the letter, but not the spirit, of the rules). How should I respond to this and go forward?

I got caught cheating in a two-hour engineering exam consisting of 100 multiple choice questions which was done online through the  e-learning software. I feel like my life is almost over.  Having not studied well and having no time to study, I decided to cheat. I know there are no excuses for cheating. Before the exam I dug up research about moodle exams, and it turned out you can take the exam anywhere you want to as long as you have the quiz password. Taking advantage of this, I went up to my engineering library and asked a close friend who was taking the exam to send me the quiz password before he starts.  What I had prepared:   Calculator (was not allowed during the quiz). Printed material (consisted of more than 200 pages). Google search engine (on a laptop ready to help). Whatsapp (to ask questions for a friend who took the quiz last year).   As I sat down, I did the first 50 questions, suddenly the quiz froze and moodle told me:      you are not allowed to take the exam from this location.   While I was leaving, one instructor responsible for the course (there are 5) came and found me. She accused me of cheating, took my mobile and made come with her to a huge office where two instructors searched all my mobile (took the name of my friend who gave me the password), and started talking to me, asking for all details of this crime. They took and confiscated my phone and looked at everything: Whatsapp conversations, all my emails, and images. The instructor took the mobile from my hand without asking me and kept it with her. It seems that the instructors are going to report me as well as my friend who sent me the password for the exam.  The university's Student Code Conduct said that cheating will result in one of the following: a Dean's Warning, Suspension, or Expulsion. If any of that happens, my future is over. A dean's warning will cancel my financial aid. A suspension would be for at least two years, and coming back would require a lot of work. An expulsion will be definite.  I've learned the lesson about cheating, now how can I fix this? How can I prevent the five instructors from reporting me? It's obvious that I should speak to them, but what should I say? What can I do? My future is almost over, but many of you are teachers and instructors here, what can I do to fix this?    EDIT: Wow, it has been almost 3 years. I would like to update on how I dealt with the situation.   Lesson: It was obvious to never ever cheat under any circumstances, and it was not whether you'd get caught or not.    Consequences: I received a Dean's warning but the financial aid wasn't revoked. However, I couldn't stay in the department as engineering was not for me and I was even ashamed to stay in the university.  What happened next: I transferred to an ABET-accredited Computer Science institution and I graduated with distinction in 2.5 years. It was extremely stressful as I had taken 6 major courses (18 credits) in one semester, but I had to do it.  Future plans: I'm going for an MSc in Computer Science in St Andrews next year.


, Microsoft intentionally leaves the master database at the previous compatibility level after an in-place upgrade. I recently performed an in-place upgrade from 2012 to 2017 on AWS RDS. RDS architecture does not allow its customers to be db_owner for the master database, so therefore, I cannot change the compatibility level of master to 2017 to match the rest of the system and user databases. AWS tech support has confirmed this. Is it safe to leave it this way? Is it bad practice? Will I lose any functionality by keeping it at 2012 on a 2017 instance? It feels like this isn't ok - what happens in a couple years when I upgrade this instance a version or two further? At some point I'd imagine that master should be at a more recent compatibility level than 2012.

Background  My workplace infrastructure team ran a typical in-place upgrade of an RDS MSSQL instance to update the version from 2012 to 2017. After the upgrade, while logged in as the "master user", I was able to update all user and system databases to 2017 compatibility level except for master and rdsadmin. (I'm not worried about the latter.) Keeping the master database at 2012 compatibility level concerns me.  Is it recommended that I also update the compatibility level of the master database to 2017? I presume that leaving it at the 2012 level means that I'd be sacrificing some functionality. (I opened a github issue with  for clarification.) () If that is a yes, here is my problem I cannot change the compatibility level of master. The "master user" assigned to this RDS instance is not the db owner for the master database. The db owner of the master database is rdsa, which as you're probably aware, is a disabled AWS sysadmin user that I cannot utilize. Troubleshooting  I tried running  ALTER DATABASE master SET COMPATIBILITY_LEVEL = 140;  But I got this error User does not have permission to alter database 'master', the database does not exist, or the database is not in a state that allows access checks.   This makes sense. The "master user" that I am logged in as is not the db_owner of the master database.  Next, I asked the infrastructure team to reset the Master User password. According to these links, resetting the password should reset anything wrong with the db_owner role:       Unfortunately, this didn't change the db_owner of master. It was still rdsa. I rebooted the instance just in case and got the same results.  Then I tried adding the "master user" account as dbo in the master database.  USE [master] GO  CREATE USER [mymasteruser] FOR LOGIN [mymasteruser] GO  USE [master] GO  ALTER ROLE [db_owner] ADD MEMBER [mymasteruser] GO  That didn't work either, as expected. User does not have permission to perform this action.  Help Are there other steps on the configuration side that I can try? That side of things is a bit of a black box for me so any insight is appreciated. My next step is to contact AWS support.


Most leptons can do this so I'm curious to see if photons or any bosons at all can.

In quantum mechanics, a particle may tunnel through a barrier it would not be able to surmount in a classical sense.  My question is this:  What are all the factors that may prevent a photon from propagating (thus it would need quantum tunneling to do so), and can they be described in a general way for any given material?


Suppose that the function $f:[0,1)\rightarrow \mathbb{R}$ is uniformly continuous on $[0,1).$ Prove that the function $f$ is bounded. (i.e. that the range$(f)$ is a bounded set)

I need to prove that if $f: (0,1) \rightarrow \mathbb{R}$ is Uniformly continuous then it is  bounded.   Thank you.


In the trailer for Ant-Man and the Wasp, Hank Pym shrinks a multi-story building to just a few cubic feet. He then wheels it away like luggage. You can see it at the 30 second mark:                                  The "shrinking" technology works by removing the empty space within and between atoms. So shouldn't the building still weigh many many tons? Is there an in-universe explanation as to how Hank can take it with him?

Is there a canonical explanation for how Ant-Man's weight works when he shrinks down that's consistent with the various events depicted in the film?    I think the explanation given in the film is roughly "the suit compresses the space in-between atoms, so your size decreases, your density increases, and your total mass stays the same", however it seems to be portrayed in contradictory ways.  For instance:   He can float in water, and even be sent shooting through the air by a relatively gentle flow of water filling a bathtub.  This wouldn't happen if he retained his original mass, as he'd essentially be the densest thing on the planet and should sink like a stone even in a vat of molten lead. Upon landing after being ejected from the bathtub, the ceramic tile underneath him shatters.  That takes a significant amount of force, and similar effects are used at other points in the movie where he falls onto (or straight through) various things. He's able to get sucked into a vacuum-cleaner.  One that didn't even appear to be a high-end, extra powerful vacuum-cleaner, let alone one capable of sucking up a 200 pound piece of dust.   He can run along the barrel of a gun as someone shoots it, apparently without causing them to drop the weapon or even have trouble continuing to aim it.     Does a more consistent explanation exist in other media, that would fit with the above examples?  Or is this simply a case of the power being made to do whatever happened to be most convenient at the time?


A biased coin has probability p of showing heads. We toss the coin repeatedly until three heads or three tails occur in row. What is the probability that three heads occur before three tails? Cannot understand the previous explanation... What will be the easiest way to explain it?

A biased coin has probability p of showing heads. We toss the coin repeatedly until three heads or three tails occur in row. What is the probability that three heads occur before three tails?  I know how to solve this for two heads and two tails.  $$ P(A) =  p^2 + pq \cdot P(A|HT) + pq \cdot P(A|TH)  $$  Then, it is easy to relate $$ P(A∣HT)=p \cdot P(A∣TH) $$ and $$P(A∣TH)=p+qP(A∣HT) $$  And find solution. However for three we will have equation like this:  $$ P(A) = p^3 + p^2q \cdot P(A|HHT) + p^2q \cdot P(A|HTH) + p^2q \cdot P(A|THH) + q^2p \cdot P(A|HTT)  + q^2p \cdot P(A|THT) + q^2p \cdot P(A|TTH)  $$ How can we relate these conditional probabilities? The link for case with 2 tosses:


In my biology class we got the question if saltwater fish need to drink. We need to use the term osmosis, but I cannot think of a valid answer and we were allowed to ask help.

With the osmolarity of the average vertebrate being around 300mOsml, and salt water having an osmolarity of 1000mOsml, why does the water from the shark not leave to the salt water around it?   I presume the scales must act as a barrier to stop water form leaving, but with the blood vessels being exposed to the saline water in the gills, why does water not leave the body?


From my understanding, neural networks are universal approximators, which was proven by Cybenko in 1989 for sigmoid activation functions with output units being linear. Castro showed, that this property also holds true even if the output is not linear, but is a squashing function (non-decreasing with values in $[0,1]$). But did someone manage to prove that this property is also true for modern NNs with ReLU activations? I'm quite new to this topic and I haven't been able to find such work, I'd be grateful for your help.

Does the universal approximation theorem for neural networks hold for any activation function (sigmoid, ReLU, Softmax, etc...) or is it limited to sigmoid functions?   Update: As shimao points out in the comments, it doesn't hold for absolutely any function. So for which class of activation functions does it hold?


Okay, so I want to sell another car to the garage but it takes a full game day.  Do I need to be logged in with my game on to do this, or can I turn it off, come back in 48 minutes, and sell again?  Also, do I have to wait 48 minutes, or will it be at midnight of the following GTA-day that they will start purchasing again?  THANKS!

I was wondering: How much time does it take until the cooldown resets and I can sell another car in the GTA Online LS Customs Garage?


There are some apps on iOS that I trust with Health information. These apps are fully capable of working offline. Is there any way to prevent specific third-party apps from accessing the internet on iOS? One possible use case would be to prevent the app from logging private data that it has access to. For example, there may be an app which acts as a fitness dashboard and allows you to visualize your fitness data in a "dashboard" fashion. Or there may be an scanner app, or a calculator app, both of which can run offline. It would be nice to be able to safeguard data that these apps have access to, such as health data in the case of fitness dashboards, or clipboard data, in the case of other apps, by ensuring that this data can't be sent anywhere.

Sometimes I need to find the URLs that are accessed by iOS apps to block their Internet connection. In a web browser, I can get the URLs directly from the address panel. But how can I get the URLs accessed by apps?


I want to show that for every odd prime $p$ the following congruence holds:  $$ 2^2\cdot4^2\cdot\dots\cdot(p-3)^2\cdot(p-1)^2 \equiv (-1)^{\frac{1}{2}(p+1)}\mod{p} $$  How would I approach this problem?

Assume $p$ is prime and $p\ge 3$.  Through experimentation, I can see that it's probably true. Using Wilson's theorem and Fermat's little theorem, it's equivalent to saying $2^2 4^2 6^2 \cdots (p-1)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$, but I can't figure out any more than that.


After  I ran PowerCfg /energy on an Admin Powershell which created a html "Power Efficiency Diagnostics Report" that included this bit as and "error":     Power Policy:PCI Express ASPM is disabled (Plugged In)   The current power policy for PCI Express Active State Power Management (ASPM) is configured to Off.   What exactly does that mean? Should I enable it? Where?  Is "Active Sate Power Management" the same as ? This would mean this is about this setting, correct?

In the Windows 7 Power Options, under "PCI Express", I can adjust "Link State Power Management".  The options are:   Off Moderate power savings Maximum power savings   What do these settings do?  Is there any reason to enable it when my laptop is plugged in?


The given values are   double double1 = 1.0814449990040142E7;  double double2 = 7.0164302885665664E17;  result is double1  + double2 = 7.016430288674711E17  in Java   Manually calculated value is 701643028867471089  Can anyone resolve my issue.

public class doublePrecision {     public static void main(String[] args) {          double total = 0;         total += 5.6;         total += 5.8;         System.out.println(total);     } }   The above code prints:  11.399999999999   How would I get this to just print (or be able to use it as) 11.4?


I put together a basic calculator where the user can type their equation into a text box and click solve. Any equation that includes addition, subtraction, multiplication and/or division can be entered example: 1*2+18/2+(7+2)  The problem is when decimals are used. I've found that there's no simple solution in JavaScript or jQuery to handle them in the context of a calculator. Every single JavaScript calculator tutorial doesn't work correctly with decimals.  I think the best way to handle them is to convert them to integers? I thought about multiplying the decimals by 100000, doing the math, then dividing by 100000 but this only works with addition and subtraction. What method would work to convert decimals to integers when the equation contains mixed operations such as 1*2+18/2+(1.2 + 0.64) then convert it back?  Fiddle:   HTML  <input type="text" id="userProblem" size="100"> <input type="submit" id="solveButton" value="Solve">

   JavaScript  solveButton.onclick = function () {     var answer = eval(userProblem.value);      answerDiv.innerHTML = answer; };

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


i am just trying to destroy my session with session_destroy but its not getting destroy this is my code of logout.php  <?php session_destroy(); //print_r($_SESSION);exit;   ?> <script type="text/javascript">     location.href=root_path+"index/"; </script>   i am getting a waring  Warning: session_destroy(): Session object destruction failed in F:\xampp\htdocs\synthesis\module\login\logout.php on line 3   if i remove third line from comment and click again on logout its showing me array of $_SESSION with all data and if i do comment it again without refreshing browser and then refresh the browser then session is getting destroy i am calling this page from my index page and on index page i have written session_start

I have heard mixed responses on this topic, so what is a sure fire way to destroy a PHP session?    session_start(); if(isset($_SESSION['foo'])) {    unset($_SESSION['foo'];    ... } session_destroy();   In the most simple of cases, would this sufficient to truly terminate the session between the user and the server?


In a similar vein to , I'm having an issue with the "new questions with activity" feature on SO.  It works fine on any other Stack Exchange site.  I've left the window open for about 20 minutes now, and it doesn't update the list with any interesting questions with activity.  I even threw in the C# tag into my favorites to make sure that it wasn't just my favorite tags.  I'm using the latest version of Chrome on Xubuntu Linux.

Stack Overflow is not getting refreshed automatically. I have to press F5 explicitly to refresh the website. What might be the issue?


The directory tree and filesystem concept seems to be close. Can we say that the directory tree is the external interface of a partition of a volume and that the filesystem job is providing it? In other words, the filesystem allows us to see a partition of a volume as a (convenient) directory tree.

I am new to Linux so pardon me for the possible confusion you may encounter in this question. From what I understand, filesystem specifies how a partition stores/manages file, with standards such as ext2, ext3, reiserfs, xfs, etc. Occasionally I see people seem to refer to each "directory" as     /boot filesystem     /usr/bin filesystem     /root filesystem     /bin filesystem  Why would we refer to these as filesystems? If each of them is a partition, that confuses me because as far as I know, /usr and /usr/bin tend to be in the same partition, but I saw people refers to both "/usr filesystem" and "/usr/bin filesystem". If filesystem here is equivalent to Window's directory, it's not clear to me as apparently filesystem is something more than just directories. Also, as far as I know, Linux does not have "directory" concept; all are files.


I made a teleportation loop with a command block in my world and the command block is super far away. What do I do? (I'm not great with downloading things and I don't know the cords)

I set a command block to /tp. It was supposed to activate only if you had 0 time left, and to activate the command block with a hopper clock to keep giving it power.   But it is not checking if you have 0 time left, so it keeps teleporting me. I can't get close enough to the command block to break it, so I'm stuck in a neverending teleport loop.  Any ideas?


I recently tried out Pantheon DE and after I purged it from my system, I am seeing a whole host of problems with the DE - improperly sized panels, misfitting windows title etc. The only option is left to reinstall Unity as Pantheon messed by GTK. How do that???

I tested out Unity 5, and of course, it broke things, so I tried downgrading by    sudo apt-get install ppa-purge sudo ppa-purge ppa:unity-team/staging   It removed Unity completely.    apt-get install unity   seemed to work, but the login screen now offers only Gnome.  How do I get back to Unity 4?


I too have lost my horse (white) due to an ambush by many bandits that gang up on me and killed me. Once I got back in game I also received this brown horse Tennessee. I looked at the map and that horse was the only horse that had the white saddle icon. I went to the stables to check and i even went to camp where I can receive any of my horses but the best horse that I used is gone. What happened ? Any clue? Maybe the bandits took it and switch off with there’s ?

At some point I accidentally ran off a cliff with my War Horse which resulted in a death. After respawning, I noticed my War Horse was gone and the default Tennessee Walker was my main horse.   How did the War Horse disappear and is it possible to retrieve it?


As you can see in the below screenshot, my partitions are essentially empty.     I just installed Ubuntu today, I had created a brand new partition to support my Ubuntu OS. However, after it successfully partitioned itself my Windows 7 partition no longer works at all. At this point I do not care about restoring my Windows 7 OS, I just want to combine my much larger currently unallocated partition of +600GB with my new Ubuntu partition. I have installed GParted and read other forums on the issue. However, whenever I try what they have suggested (as far as I can tell) resize/move only adjusts the size of the current partition. It has nothing to do with combining two separate partitions (which are both primary). Many other suggestions wanted me to delete the partition with the file system on it. I can't do that because that is the file system that I am currently using so it won't let me delete it.   I can't think of what to do. I am seriously worried that I have ruined my computer.

I have  a 220g partition with ubuntu. And a empty partition 100g. How can I expand the partition with ubuntu? I boot from liveCD, start gparted, sgrink 1 partition, and could't expand the 2 partition.


I'm looking to know how to update Ubuntu through the Terminal command line.  I want to update the operating systems software for when and if the people behind ubuntu launch an update for v16.  This works on 14.04 sorry for making it look alike.

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?


When I try to install tor I get:  Reading package lists... Done Building dependency tree Reading state information... Done Package tor is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package tor has no installation candidate   I was able to install it a few days ago, then I had to remove it sudo apt-get remove --purge tor  And now I cannot install it.  Any idea why?

I tried to install Tor on my new version of Ubuntu, but it seems that Tor is not available in the repositories.  How else can I install and use Tor?


i have following code in my class:  public class Subclass<T> extends Superclass<T> { //...  @Override public boolean equals(Object obj) {     if (obj instanceof Subclass) {         return str.equals(((Subclass<?>) obj).getStr());     }     if (obj instanceof Identity) {         return str.equals(((Subclass<?>) obj).getStr());     }     return false; } }   my superclass:   public class Superclass<T> {  @NotNull  String str;   @Override  public boolean equals(Object obj) {     if (obj instanceof Identity) {         return str.equals(((Identity<?>) obj).getStr());     }     return false;  }   @Override  public int hashCode() {     return str.hashCode();  }   and checkstyle warns me Definition of 'equals()' without corresponding definition of 'hashCode()'. do i have to override hashcode() in my subclass even thou i dont need it anywhere or is there a better solution to get rid of this warning?

What issues / pitfalls must be considered when overriding equals and hashCode?


I've downloaded MDic dictionary from [1]:  but I don't know how to install it. The file has named as mdic-0.8.1.tar.gz  Please guide me to install.

I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file?


I have some software installed manually without using apt or dpkg. Consequently these don't show up in the dpkg -l list and I can only check if its installed by invoking <binary> --version when the symlink in /bin is configured.  How do I add them to the dpkg -l list?

I installed program (call it, for example,progA) by building it from source code, and then finally calling sudo make install and sudo ldconfig.   However, it seems apt-get hasn't gotten the memo, because when installing progB, which depends on progA, apt-get recommends I also install progA. Why is this, and what could I do?


How can I receive notifications on iOS app for questions that I am interested in but which are asked by other people.

Right now there isn't a great way to monitor the questions that I am interested in following. What I seem to do now is go to my recent history for questions I have commented on, and then link to the questions from there. The problem is, if I am really interested in a question, I have to monitor it closely. Sometimes I will "favorite" a question so it is easier to access more quickly, because I do not have a lot of favorites. But favoriting is not the right thing to do. I think you should only favorite a question if you really really like it, not to make it easier to follow.  I propose that you can mark questions as "interested" or something like that. What this means, is that you will get notifications for everything associated with a question: any time a new answer is posted, the answer/question is edited, and any comments to any of the answers (or question). This would make it much easier to follow questions. Especially if someone adds a new answer or comment way down the road, after you have long forgotten about the question.  It would also be nice if such a feature allowed you to write a sentence or two to associate with the question to remind you about something. In fact, if this is done, we could just use this feature to implement  to allow an edit to notify downvoters. Instead of that specific feature, you can mark a question as interested after downvoting and add a comment, "remove downvote when fixed".  What do you all think? Do you propose a better way to manage monitoring questions of interest? (The other thing I do is keep a bunch of browser tabs open with questions I am following... and this is messy :-( ).


Why is it so easy to blow out a candle from a significant distance, but nearly impossible to suck enough air to do the same?  Even without focusing the airflow through a nozzle or something, this affect seems to be present. For example, it's easy to feel the air coming out of a box fan, but very hard to feel the air going into one.

Alternatively, why does the force created by blowing out air feel so much stronger than the force created by sucking in air?  Ok, so forget the human factor involved in blowing out candles. Consider a vacuum cleaner with a suction end and a blower end. Anyone who has tried it out notices the blower end creates a much stronger force than the suction end, despite the discharge being (more or less) equal at both ends.  Why does this happen?


im currently working on a CAD model (using Siemens NX12) and want a more realistic render than NX is able to provide. I've tried a number of methods and came to the conclusion that exporting as STL file works best. When i import said file into blender and render it, the once round surface looks like its just a high side count polygon. So far i've tried to subdivide the mesh and enable the autosmooth function, but i dont see any improvement. Im really new to blender, i actually downloaded it just for this purpose, so im on the newest version. I'll try to add one of the renderings, it was done using cycles with a sample rate of 1100 and full hd resolution (cropped to reduce the size) and took just around 90 seconds. You can best see my problem on the inside of the outer ring on the right hand side. I appreciate any help.

I frequently come to the problem of having a mesh with parts I would like to render smooth and "hard" edges connecting them.   How can I set the mesh to show the sharp edges but render everything else smooth?  In the example I would like the sides of the individual cylinders render smooth but the intersection between bottom and top to be sharp/flat


Suppose f:A→B and g:B→A are both surjective, does this imply that there is a bijection between A and B. I was told that the statement above is true only with Axiom of Choice. Can someone provide an example of why that is the case?

To prove two sets are isomorphic is it sufficient to find 2 injections $f:A\to B$ and $g:B\to A$ or 2 surjections $h: A\to B$, $j:B\to A$?


Assume $1\le k \le p-1$ and $p$ is a prime number.      Prove:      a) ${p \choose k} \equiv 0$ (mod p)       b) ${p-1 \choose k} \equiv (-1)^k $ (mod p)   Probably the statement can be proved using Lucas's theorem. But I'm not sure about the right way to use if so. So any hints how to prove the statement?

Question : If $p$ is prime, and $0< k< p$ show that $ p \mid {p \choose k}$  ${p \choose k}$ can be rewritten as:  $${p(p-1)(p-2)\dots(p-(k-1))(p-k)! \over (p-k)!\cdot k(k-1)(k-2)\dots3\cdot2\cdot1}$$  Now the $(p-k)!$ cancels out. Since in the numerator we have k consecutive  integers, k divides one of them (not p as p is prime and $k <p$). Then k-1 divides another one or two terms in the k consecutive terms (again not p). This reasoning continues until  3 and 2.   This means that ${p \choose k}$ can be rewritten as pq implying $p | {p \choose k}$  What if any of this proof is wrong. I am worried about any 'overlaps', i.e. say k-6 divides terms that k-3 divides invalidating the argument.  P.S. I hope the above is legible as I am new to this site. Thank you!


Could you tell me please, how to disable the transition to a new line when I use enumerate ? I need to do it as in the picture. For No1, I do not use enumerate but for “a” and “b”, I use enumerate

This might seem like a very simple question, but what is the easiest way to turn a normal vertical list into a horizontal one?


I log in to the rhel5 machines at my school from home via ssh and it automatically sends me to the computer with the least load. So ssh -Y itsme@myShcool.edu will send me to either mySchoolA.edu mySchoolB.edu, or mySchoolC.edu. I can log into the individual computers with no issue but when, but when I use itsme@myShcool.edu , sometimes I get a message about a man-in-the-middle attack and possible DNS spoofing, and I'm directed to ~/.ssh/known_hosts to remove the offending key. Removing the offending key works the first time I log in (I'm prompted to add the host to known_hosts, which I confirm).  Is it possible to log in using itsme@myShcool.edu and not get this message nor have to manually remove the offending keys each time?  One thing I tried that doesn't seem to work is adding the following to ~/.ssh/config  Host hostIPaddress StrictHostKeyChecking no  UserKnownHostsFile=/dev/null   Any help would be much appreciated.

I regularly ssh into a computer which is a dual-boot OS X / Linux computer. The two OS instance do not share the same host key, so they can be seen as two host sharing the same IP and DNS. Let's say the IP is 192.168.0.9, and the names are hostname and hostname.domainname  As far as I understood, the solution to be able to connect to the two host is to add them both to the ~/.ssh/know_hosts file. However, it is easier said than done, because the file is hashed, and has probably several entries per host (192.168.0.9, hostname, hostname.domainname). As a consequence, I have the following warning  Warning: the ECDSA host key for 'hostname' differs from the key for the IP address '192.168.0.9'   Is there an easy way to edit the known_hosts file, while keeping the hashes. For example, how can I find the lines corresponding to a given hostame? How can I generate the hashes for some known hosts?  The ideal solution would allow me to connect to seamlessly to this computer with ssh, no matter whether I call it 192.168.0.9, hostname or hostname.domainname, nor if it uses its Linux hostkey or its OSX hostkey. However, I still want to receive a warning if there is a real man-in-the middle attack, i.e. if another key than these two is used.


Question) How to put an existing lighting component, within another lighting component.

I have a form that needs to let the user select 3 out of 5 products, something similar to Order > Add Product (Modal). I was wondering if there was a way to bring that piece into my component (markup) and add some sort of filter that only shows the products I want to show.  What I found so far:  <lightning:listView objectApiName="Products2" listName="productsView" showActionBar="true" enableInlineEdit="true" showRowLevelActions="true"/>   But Product2 is not supported for that component.  also these from browser inspector:  forceMultiAddUsingLVM forceListViewManager   These are data-aura-class attributes when rendered.  I'm looking for directions here. Thanks in advance.


It used to be so that the icon shape itself was the selection area in 18.04 and you also had the option of not snapping the icons to grid, all of that seems to be gone now in 20.04. Could someone please help with that? I've included a snapshot of the problem .

I've just upgraded from Ubuntu 18.04 to its newest LTS version - 20.04. While it comes with some interesting changes, the Desktop icon system was messed up in my opinion. When you hover the mouse cursor over the icons, you see a huge space marked around them that cannot be violated (as you can see in the image below) so that they need to be placed very far apart from each other.  18.04 allowed you to place icons much closer to each other and didn't have that marked space around them. This new way leaves much less space on the Desktop to organize large amounts of icons - including folders, files and shortcuts. Is there a way I can significantly reduce the size of icons and their "spaces" or go back to the old system of organizing files? On "Settings", there is a tool to change the size of Dock icons, but not of Desktop icons.  Also, every time I move or delete something, the Desktop "flashes" and the icons seem to rearrange themselves automatically, nothing of which happened in 18.04. I also can't move anything directly to the Desktop; I need to move to the Desktop folder on Nautilus. This makes me start to think about downgrading Ubuntu back to 18.04.


I am in a group that says we play party bridge and the rules for honors are different than for rubber bridge. What exactly are the differences between party bridge and rubber bridge, and why are they different?  For example, are the honors scored the same in both party bridge and rubber bridge?

In scoring contract rubber bridge, if you make 2 or more games out of 3 you get 500/700 pts for a rubber.  If you make 2 games consecutively before your opponents make a game at all you get 700 pts.  But if your opponents get a game before you make 2 games in a row you only get a 500 rubber.  My question is: in party bridge do you score this the same or do you score 300 pts to each parnership that scores a game and then an additional 200 or 400pts depending on if  they score another game before opponents can score a game? In other words, do you get any additional points for making a game if you don't win the rubber, other than the 100 or 120 below the line?


Let $(a_n)$ be a convergent sequence. Suppose that $\lim_{n\to\infty}$ $a_n$ > 0. Use the definition of a limit to prove that there exists N ∈ (N) (naturals) such that $a_n$ > 0 for all n ≥ N. Use definition of a limit ($|a_n-L|$<$\epsilon$) and definition of convergence of sequences. I have no idea how to even start this proof, or what I should be doing with it. I know I'm trying to solve that $a_n$ > 0, but I don't know how to get there. Not looking for a full proof, just some help of what I should be doing, what I should choose N to be, etc.

Here is the question from my textbook,      "Suppose that the sequence ${a_n}$ converges to $a$ and that $a>0$. Show that there is an index $N$ such that $a_n>0$ for all indices $n \ge N$"   by the definition of convergent sequence:  because ${a_n} \to a$, for all $\epsilon > 0, \exists N \in \mathbb{Z}^+$ such that for all $n>N$, $|a_n-a| < \epsilon$.  But then I don't know how to proceed. I can figure out the situation (even if it is an oscillating sequence around a), if ${a_n} \to a$, then there exists a positive integer $N$ such that for all $n>N$, $a_n > 0$.  p.s.: this is the first time I post a question. If there are any unclear/ improvement, please let me know


I have seen the equations that show the coefficient of reflection etc.  But I'm searching for an intuitive rather than solely mathematical explanation for why waves change phase by π when reflected (eg- from a solid wall)?

Can anyone please provide an intuitive explanation of why phase shift of 180 degrees occurs in the Electric Field of a EM wave, when reflected from an optically denser medium?  I tried searching for it but everywhere the result is just used.The reason behind it is never specified.


In windows I can paste the clipboard content using the key combination Ctrl + V  However if I try to achieve the same in Linux terminal using the same Ctrl + V key combination, I get the output:  ^V   How to paste clipboard content to terminal in Linux using keybord?

When I copy something to the clipboard and press Ctrl + V in Bash, nothing happens; However, right clicking and selecting Paste does the job.  Why? Is there any reasonable issue (I'm sure there is) behind this behavior in Linux?


I have a custom form with 2 select fields, first (Country Select) has an ajax callback which when is triggered the options from second (Country Currency) callback are changed. Options are replaced in select list but on  submit or selecting another country the validation is not passed.  The error I get is on line #362 in FormValidator.php     An illegal choice has been detected. Please contact the site administrator.     elseif (!isset($options[$elements['#value']])) {     $form_state->setError($elements, $this->t('An illegal choice has been detected. Please contact the site administrator.'));     $this->logger->error('Illegal choice %choice in %name element.', array('%choice' => $elements['#value'], '%name' => empty($elements['#title']) ? $elements['#parents'][0] : $elements['#title']));   }   Current options were changed but select is still keeping the value from previous options and \Drupal\Core\Form performRequiredValidation() method throws above error.  Any ideas how to fix/avoid this are welcome.

Create a settings form for a module in Drupal 8 - when a user selects a View from a list, the drop down under it should populate with the displays in that view.  While the form updates the option list for the user, it also throws an error message on the screen "Illegal choice has been detected".  Here is the code (it doesn't paste very well):    getViewDisplays is the ajax callback that is populating the options.  Some people who have posted about this around the internet say to set #validated on the select field to TRUE, though, that doesn't necessarily feel right. I still want to validate the submission to do some checks.


I currently have the following code in my drupal_set_message()  1778 function drupal_set_message($message = NULL, $type = 'status', $repeat = TRUE) { 1779   if ($message) { 1780    if ($type == 'error') { 1781        $message .= ' '. print_r(debug_backtrace(), 1) .' '; 1782    } 1783 1784     if (!isset($_SESSION['messages'][$type])) { 1785       $_SESSION['messages'][$type] = array(); 1786     } 1787 1788     if ($repeat || !in_array($message, $_SESSION['messages'][$type])) { 1789       $_SESSION['messages'][$type][] = $message; 1790     } 1791 1792     // Mark this page as being uncacheable. 1793     drupal_page_is_cacheable(FALSE); 1794   } 1795 1796   // Messages not set when DB connection fails. 1797   return isset($_SESSION['messages']) ? $_SESSION['messages'] : NULL; 1798 }   I'm trying to do a debug_backtrace on this function to find out which module is causing my error. Whenever i reload the page, I only get a white screen of death.  What could i be doing wrong here? Or what other quick methods like this can I find a module that is causing issues?

How can I see the error messages when the site I am working on gets a white screen?


I believe that the question title describes it all... but I just bought 2 brand new 2560x1440 monitors and I need to make use of my NVIDIA GeForce 680m card instead of the Intel HD Graphics 4000 card. Can anyone point me in the right direction?

I have a Dell N5110 laptop with integrated Nvidia GeForce GT 525M and an Intel HD Graphics 3000 card; My problem is the default card is the Intel one, and it provides a very bad performance with Windows 8. So can I force to use the Nvidia one all the time including "Desktop Windows Manager" ?


I'm googling for this, but the terms are so generic I'm getting way too many false positives, so what the hey, I'll ask here.  I'm sure there's a simple answer but I don't generally script in *nix.  I'm trying to write a database refresh script to our test environment.  The backups are mounted from an smbfs share, something like /data/backups/prod, but the subfolders get a little tricky.  It looks like myproddbserver/yyyymmdd, with a bunch of files underneath.  I want to execute a command restore that will collect the files with known names from the most recent yyyymmdd directory.  For example, if I had:  myproddbserver/20130630/foo.bak myproddbserver/20130630/bar.bak myproddbserver/20130731/foo.bak myproddbserver/20130731/bar.bak   I would want to restore myproddbserver/20130731/foo.bak and myproddbserver/20130731/bar.bak.  How would I reliably get those paths?

I have a list of dated files as below...      filename_20120101.dat     filename_20120102.dat     filename_20120103.dat   I need a script which selects the most recent file based on the date in the filename (not the file's date stamp).


I have downloaded Ubuntu 18.04 Desktop on my 2012 Mac Book Pro and mounted it to two different USB drives using two different softwares: Etcher and unetbootin. When I restart I held down option/alt, and chose the USB. And I got to this screen.     I have chosen every option and I get the same result.    I don't know what I'm doing wrong and could really use some help.

If you select "USB" and "Mac" on , it gives a series of command line instructions to make a USB key which the MacBook will boot into Ubuntu from.  I've followed them to the letter two or three times on different USB keys, and it doesn't work. There's a very great deal of technical discussion about EFI etc. but this set of instructions seems to suggest it should just work, but it doesn't.  Help? I'm increasingly unhappy with the more locked-down approach Apple is taking, and I'd quite like to start using Linux with a view to transitioning over to using it as my main operating system, but booting from the CD takes forever, runs slowly and I'm really hoping to get it moving off USB.  Can anybody help me?


I have just got familiar with some methods of dimensionality reduction, and one of them was PCA. So we have data $X\in \mathbb{R}^{n\times n}$ and want to reduce its dimension to $k$. PCA just takes the covariance matrix of our data, and choose $u_1, u_2, ..., u_k$ eigenvectors of the covariance matrix, so that $ \lambda_1 \geq  \lambda_2 \geq ...\geq \lambda_k \geq ... \geq  \lambda_n$, and projected our data to the $k$ dimension subspace with axes $u_1, u_2, ..., u_k$. As I have seen in some practical examples the covariance matrix of the projected data is diagonal, in other words the features of projected are not correlated. So I want to know whether it is true for all cases, and if it is true, some mathematical proof of it.

I'm reading up on PCA, and I'm understanding most of what's going on in terms of the derivation apart from the assumption that eigenvectors need to be orthogonal and how it relates to the projections (PCA scores) being uncorrelated? I have two explanations provided below which use a link between orthogonality and correlation but fail to really explain it: , .  In the second picture it says that the condition $a_{2}^{T}a_{1}=0$  is imposed to ensure that the projection $y_{2}=Xa_2$ will be uncorrelated with $y_{1}=Xa_1$. Can someone provide an example to show why orthogonal vectors ensure uncorrelated variables?  What would happen in PCA if I chose vectors which are not orthogonal; is this even possible? I have read elsewhere that orthogonality is just a by-product of the covariance matrix being symmetric which would suggest that it's not possible to have non pairwise orthogonal eigenvectors. However in the first picture in search of the most 'suitable' matrix it almost seems as we are choosing $p_{1},\ldots,p_{m}$ to be orthogonal to give us a more convenient matrix $\textbf{P}$ one which has nice properties.  I've read other posts on this topic but have been unsatisfied with incorporation of the intuition with uncorrelated variables. I really appreciate any help in understanding this confusion!!


I'm a Mexican citizen and don't need any kind of visa to travel to the UK. I can just travel with my passport and stay there for up to 6 months. I was in the UK for 5 months and 2 weeks, from February 1st to July 17th 2017. I was there visiting some friends and traveling around as well.  I would like to visit my best friend in 2018, from February 28th to May 28th, just 3 months. Will I be able to stay in the country again for this period of time? Of course, my friend could give me an invitation letter and prove that I'm staying with him for those 3 months, and that he will cover all my expenses.

I am a US citizen and have recently visted the UK  with simply a passport which allowed me to vist for 6months I have heard rumors that I am obligated to stay in the US for a Equal amount of time that I have visited the UK before I am able to return, but I am struggling tour no any proof of this obligation .. Am I missing somthing or is it simply not true


I was wondering how I could make my program exit a loop when the user inputs a specific keyword? I have already figured out how to do this with integers, but I want to know how to incorporate this with Strings.   public class Test {      public static void main(String[] args) {         Scanner input = new Scanner(System.in);           while (true) {             System.out.println("type words.");             System.out.println("type stop to exit the program.");             String uInput = input.nextLine();               if (uInput == "STOP") {                 System.out.println("exit successful");                 break;              }          }     } }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


In the following post we can see that some guys are walking on . As far as I know that, we can not predict the exact amount of strain if we predict some forces. therefore the curve will not be linear.  But my question is that, why does  not obey Newtonian dynamics?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else.   What is it about a non-Newtonian fluid that makes it go hard when having a force suddenly exerted on it? How does it go from being more like a liquid to a solid in such a short amount of time? Does it change its state as soon as the force has made contact with it?


During my recent work I encountered a weird type of differential equation containing scalar factors. In order to understand them better I thought it would make sense to look at a simpler example like:  $$ \dot x(t) = x(2t)$$  How does one solve this equation? Does it even have a solution? It seems kinda related to  which I am not familiar with.

The exponential generating function counting the number of graphs on $n$ labeled vertices satisfies (and is defined by) the equations $$ F'(x) = F(2x) \; \; ; \; \; F(0) = 1 $$ Is there some closed form or other nice description of this function? Does it have a name?    Of course, the series itself does not converge for any nonzero $x$, but like the Lambert W function (counting trees) it has combinatorial meaning. And the Lambert W function has a nice description as the inverse of $x e^x$; maybe there is a similar description of $F$?


Playing off  a little bit, I'd like to know how the SO team prioritizes and processes requests such as fixing bugs and implementing new features.  It strikes me that the current system is a bit 'loose', where things are fixed or implemented on a whim. This may or may not actually be true, and I'm not saying there's anything inherently wrong with the current system, but at the same time, I think there is room for improvement.  In particular, sometimes there may be hidden or higher motivations for some decisions, which I think should be explained and/or discussed, sometimes in far greater detail than has been exposed in the past. What are these motivations, and how do they relate to the overall vision for the sites? If the community knows more about these motivations, we can collectively solve the problem in a way that meets everyone's needs.  How can we improve the current process to better satisfy both the community and its leaders?

On UserVoice, it's clear how the bug/feature request procedure works:   Enter a bug Gain votes (or don't) Get declined by an admin or get a bug fix   How will this work on Meta (this site? Is there any suggestion for this? I would like to see the status of my requests.   How should I tag feature requests? How should I tag bug reports? In what way are bugs handled? In what way are feature requests handled?


Just now I was studying the Magnetism and Earth's magnetic field source. when I read that the earth's magnetic poles are not fixed and keep changing ( the north becomes south and the inverse) every few million year? can someone tell me why does that happen?

I have always been told that the geomagnetic field acts "as if" there were a bar magnet inside the Earth. I now this is not true, but I feel that knowing what is actually going on would help me understand the answer to the question that I'm about to ask:  Why does geomagnetic reversal happen? Is it something gradual or relatively fast?  (What is the origin of the geomagnetic field? Can we answer my questions starting from this mechanism?


This is the message that appears at startup. there was a problem starting c:\users\name\appdata\local\conduit\backgroundcontainer\backgroundcontainer.dll the specifiedmodule could not be found. Windows 7 home premium.

When I start my desktop it gives me an error about BackgroundContainer.dll.    How to get rid of it?  I found nothing when i started regedit.exe and searched (F3 or CTRL+F) for BackgroundContainer.dll


When I write a multi-page paper with imported images, I usually try to group the picture with the text referencing it.  Sometimes, there is not enough room at the end of the page for the picture, and the picture is moved to the top of the next page.  This often leaves some white space at the end of the previous page.  In order to remove the white space, LaTeX automatically fills the space with text that is meant to come after the image.  Is there a way to prevent this?

How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference


I'm searching for a solution for a problem/question I'm almost 100% sure was asked before but I can't find it.  It is a generic question, no way that it wasn't asked before but no matter how many ways I try to search I just can't find it.  I don't want to ask a dupe question only for the reason to get closed in 5 minutes, of course I would get my answer but this still sounds kinda selfish.  What should I do?

Too many times I just know something's a dupe but can't for the life of me find the original question that is duplicated.  I search the sites from Google to find things, but in coming up short there I usually leave it and rely on someone else to clean it up [sigh].  What are other ways to do it better?  (or maybe this is one that gets closed employing said techniques...)


If I do console.log(66.91 - 15);  I get the desired result of 51.91 But if I do console.log(66.91 - 35);  I get 31.909999999997 Why is that? I there an easy way to prevent that? Thanks in advance.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I'd like to know what's the best method to store images into a MySQL database with the best performance. (assume a big database)  Solution A: Use LONGBLOB type and put the binary content  Solution B: Store the files on the hosting and save the URL how a VARCHAR type  Thanks in advance

So I'm using an app that stores images heavily in the DB. What's your outlook on this? I'm more of a type to store the location in the filesystem, than store it directly in the DB.  What do you think are the pros/cons?


I got a rather unsatisfactory answer on Stack Overflow but the subsequent discussion with the answerer (in the comments below) was helpful. Should I accept his answer? Or is there a way to accept a specific comment?

I'm trying to go through and provide answers to every unanswered question (search "closed:0 answers:0"), somewhat following the spirit that was blogged about at  .  However, I'm finding this much more difficult than it needs to be, as many of the questions have already been answered without the use of an "answer" - but instead, in the form of a comment by either the OP or another poster. I wouldn't mind reading through and skipping these, as long as there was some appropriate action I could take to at least assist with preventing these questions from being seen again from the same query - either by myself or another SO member.  Is there such an appropriate action?  Should we vote to close?  If so, using what reason? Even if I vote to close, what are the chances that 4 other users will also view the question and also vote to close?  (i.e., will my individual vote even do any good?  Is there any report to show recent close votes, so that others may also review and contribute supporting close votes?) Should we post some sort of an answer - even just something to the effect of "this was already answered by the OP's own comment to his answer (above)"? Would something like this be appropriate to flag for moderator attention, and let the moderators deal with it?  (Or would this be considered too trivial?) Should we rename the question title to something standard that can be used in a search exclusion?  (Maybe "SOLVED:"?)  Basically, how can I help to denote questions as "This question is no longer in active search of an answer - though better answers may still be appreciated."? I've already reviewed , which was closed as a duplicate of  - but this requires effort on part of a user who may very likely no longer be active. Otherwise, is there something I should be doing to improve my search to filter out these types of questions? I've run across this many times, so I don't consider it to be a rare issue.  However, the last question like this I just ran across, prompting this question, was .  In this case, the question was self-answered by the OP in the form of a comment, this question is the OP's only question, the OP has no other visible activity on SO, and the OP hasn't been seen on SO since he registered and posted the question 5 months ago. Another one I just ran across is .  However, here the "answer" comment was posted by a reputable and recently active SO member.  Should I leave a comment directed at him, asking him to re-post his comment as an answer, or should I post my own answer echoing his comment?  (Or something else?) Yet another is .  Interestingly, the OP actually self-edited the question to include the "SOLVED:" prefix on to the question, instead of posting his resolving comment as an answer (and ideally accepting it) as he was asked to do by another comment.  This brings up another good idea - is there a "standard" we should use to rename the titles on these "resolved but unanswered" posts that could be used as a search exclusion?  (Also added to the above list.)


I have looked everywhere on google, bing, yahoo, and so far found nothing. Can anyone tell me where the longest D&D game was held?

I have been looking for a while to find the world record for the longest Dungeons and Dragons marathon because me and my friends had a plan to try and attempt to beat it and give the money from the stream (if we get any) to my school's Gaming and Anime Club.


Can Theil-Sen be defined for multiple linear regression? If so, is there an implementation in R for it?  I simply want a formula a~b+c, but the package mblm fails with the (misleading) error message: stop("Only linear models are accepted"). Of course, this is a linear model: but they mean that Theil-Sen only works for two-dimensional linear models.

Is the  in robust regression only limited to a two dimensional problem or can you use it for more than one independent variable as well?


madhusudan@ubuntu:~$ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? madhusudan@ubuntu:~$    what should I do to solve this problem?

I get this error whenever I try to install programs using the terminal:  home@ubuntu:~$ apt-get install myunity E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   Also I'm unable to install updates using the terminal.


I have 2 layout files (activity_test.xml) and (content.xml) and one java file (ActivityTest.java)  ActivityTest.java set its content layout from (activity_test.xml) as shown  ActivityTest.java  @Override protected void onCreate(Bundle savedInstanceState) { .....................  super.onCreate(savedInstanceState); setContentView(R.layout.activity_test);  }   activity_test.xml contains a recyclerView as shown  activity_test.xml  <?xml version="1.0" encoding="utf-8"?> <androidx.constraintlayout.widget.ConstraintLayout  xmlns:android="http://schemas.android.com/apk/res/android" xmlns:app="http://schemas.android.com/apk/res-auto" xmlns:tools="http://schemas.android.com/tools" android:layout_width="match_parent" android:layout_height="wrap_content" android:fitsSystemWindows="true" tools:context=".ActivityTest">  ............ some views ...........  <androidx.recyclerview.widget.RecyclerView  android:layout_width="match_parent"  android:layout_height="match_parent"  android:id="@+id/recycler_view2"  android:layout_marginTop="30dp"  android:layout_alignParentBottom="true"  android:scrollbars="vertical"  app:layout_constraintBottom_toBottomOf="parent"  app:layout_constraintHorizontal_bias="0.0"  app:layout_constraintLeft_toLeftOf="parent"  app:layout_constraintRight_toRightOf="parent"  app:layout_constraintTop_toTopOf="parent"  app:layout_constraintVertical_bias="0.0"             />   I have a RecyclerViewAdapter that inflates the (content.xml) layout as shown  RecyclerViewAdapter  public class RecyclerViewAdapter extends RecyclerView.Adapter<RecyclerViewAdapter.MyViewHolder> {  ............. @NonNull @Override public MyViewHolder onCreateViewHolder(@NonNull ViewGroup parent, int viewType) {     View itemView = LayoutInflater.from(parent.getContext())             .inflate(R.layout.content, parent, false);     return new RecyclerViewAdapter.MyViewHolder(itemView); } }   Here is the content.xml  content.xml  <ScrollView xmlns:android="http://schemas.android.com/apk/res/android" xmlns:tools="http://schemas.android.com/tools" android:orientation="vertical" android:layout_width="match_parent" android:layout_height="wrap_content" tools:context=".TestActivity">  <RelativeLayout android:layout_width="match_parent" android:layout_height="wrap_content" >  ...........   <ImageView   android:layout_width="wrap_content"   android:layout_height="wrap_content"   android:id="@+id/save"   android:src="@drawable/outline_share_black_48dp"   android:layout_toLeftOf="@+id/savePhoto"   android:layout_marginTop="5dp"   android:layout_marginRight="20dp"   android:clickable="true"   android:onClick="saveIntent"             />          The problem - Setting a click Listener on the ImageView above with the id(save) throws that error.  ClickEvents such as - OnClickListener, OnTouchLlistener, setVisibility all throws the error - "Attempt to invoke virtual method 'void android.widget.ImageView.setVisibility(int)' on a null object reference"  e.g   MainActivity.java  ..........  private ImageView save_icon;  ..........  super.onCreate(savedInstanceState); setContentView(R.layout.activity_test);  ............. save_icon = findViewById(R.id.save); ........  public void saveIntent(View view){     if(view.getId() == R.id.savePhotoIcon){          save_icon.setImageResource(R.drawable.outline_bookmark_black_48dp);     }  }   I want to change the image src of the ImageView to another Image onClick  I tried doing this without xml - (android:Clickable and android:OnClick) but still throwing thesame error.  Most likely the id(save) in content.xml is returning a null value because it wasnt't used as the setContentView layout in onCreate in MainActivity.Java file.  When I tried thesame thing on a view from (activity_test.xml), it works.   Although, Actions such as - Displaying a toast message, New Intent all works. e.g   public void saveIntent(View view){     Intent intent = new Intent(ActivityTest.this, AnotherActivity.class);     startActivity(intent); }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I am new to ubuntu. I noticed that the file manager is basically useless. I tried to remove a folder inside /opt/lampp/htdocs but nothing happens after selecting the folder and pressing the button del.  On windows I could just delete it by using the windows explorer.  Is ubuntu only designed for terminal usage?

UPDATE  I would like to know which is the recommend way of running GUI applications as root, mainly because what I'm trying isn't running smoothly. I get some annoying warnings that makes me think whether I'm doing something wrong or not. I'm using gksudo and sudo -i, which I understand, are doing the same thing. Please let me know if there is some slight differences between them. Regarding the problems I'm experiencing, I would like to start with nautilus (run as root). I can't edit the preferences file maybe because the program couldn't create its own configuration files. A warning says that the folder /root/.config/nautilus must be created. When you start an application for the first time, the program is responsible for creating the configuration files it will potentially need. So, when you are running as root, it should happen the same, shouldn't it? Furthermore, in the shell appears some strange warnings while running this application, such as the followings:  (nautilus:3406): Gtk-WARNING **: Failed to register client: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name org.gnome.SessionManager was not provided by any .service files Nautilus-Share-Message: Called "net usershare info" but it failed: The "shared network" returned error 255: net usershare: cannot open usershare directory /var/lib/samba/usershares. Error It doesn't exist the file or the folder Please ask your system administrator to enable user sharing.  Other applications like gedit or firefox complained in this way:  (gedit:3444): Gtk-WARNING **: Calling Inhibit failed: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name org.gnome.SessionManager was not provided by any .service files (gedit:3444): GLib-GIO-WARNING **: Failed to parse translated string ''Monospace 12'' for key 'editor-font' in schema 'org.gnome.gedit.preferences.editor': 0:expected value (gedit:3444): GLib-GIO-WARNING **: Using untranslated default instead. (firefox:2719): Gtk-CRITICAL **: IA__gtk_clipboard_set_with_data: assertion 'targets != NULL  I want to make a clean install of the system soon, but before that, I would like to understand how it works in case I need this stuff in the future for specific things. Though I know it's safer to use the straight sudo in the command line instead. Why this is happening? Thanks in advance


I want to print a picture for my dad, who loves history, as a gift. I'm worried the file is kinda low quality, but I'm not sure.  It's 720x900 and 255 kB. Now, to keep the ratio can I just transpose the pixel ratio to mm? For instance 500x625? At that size, will the picture still look good?

What size images do I need for common print sizes, such as wallet size, 8x10, and 16x20?  Is there a general formula?  How could that size change if, for example, a 16x20 was printed on canvas rather than photopaper?


Am making an ordered list like the following   item1 item2 item3   I need to customize ordered list's numbering color with out affecting the default numbering.  I want the result something like this. see

I'm using the following list:

This is the first footnote...

This is the second footnote...

   With the following .css:  #footnotes {list-style-type: decimal;             list-style-color: #f90;             }  #footnotes li            {color: #000;             }  #footnotes a li, #footnotes li a            {color: #f90;             }   The aim is to have the li/footer text itself black (#000), and the number styled to orange (#f90).  I've tried using the list-style-color property but this does nothing except upset the Web developer toolbar (in FF3.0.8/Ubuntu 8.04), Midori similarly doesn't display the number in orange (I thought I'd try it in the Webkit engine, just in case...).  Any ideas?  Edited the HTML (since I remembered that the  tag doesn't necessarily need to enclose anything to function as an anchor):

This is the first footnote...

This is the second footnote...

   In response to those that suggest using a  inside the
...yeah. That occurred, though I thank you for the suggestions and the time taken, but I was looking (li'l standardista that I am... ;) ) for a more...semantic option.  As it is, I think I'll probably use that approach. Though I accepted a different, Pete Michaud's, answer due to its sheer informative nature. Thanks!


It appears that it is  to get a permission from the U.S. for a solo tourist visit to Cuba. However, in various older questions, users have stated that you can easily avoid the strict US travel restrictions by flying into Cuba from another country (such as Mexico or Canada) and avoiding getting an entry stamp in your U.S. passport. According to the :  Tourist Visa (Tourist Card) The Tourist Visa or Tourist Card is only for purposes of tourism to Cuba.  It is valid for one single entrance into national territory for a 30-day trip and can be extended for an additional 30 days at the office in the hotel where one has accommodations or with the immigration authority. To obtain this visa in person at the Consulate, these documents are needed: -Valid Passport -Plane Ticket with entry and return dates -Payment of the Consular fee for this service  As far as I can tell, the Cubans don't seem have harsh tourist travel restrictions for U.S. citizens. However, according to  on Wikitravel,  While in the past Cuba did not stamp US passports, allowing US travelers to visit Cuba without detection from their government, Cuba recently started stamping US passports as a matter of policy.  In light of the recent diplomatic relations, have Cubans tightened loopholes for U.S. tourists traveling without the blessing of the U.S.? Does Cuban customs still exempt entry stamps for travelers with a U.S. passports?

A recent full diplomatic relation restoration between the US and Cuba took place, does that mean that US citizens can go to Cuba freely and vice versa?


We know students aren't allowed to do magic during the school holidays, but when does that prohibition start and end? Does the journey between Hogwarts and London count as term-time or holiday? Are students allowed to cast spells on the Hogwarts Express?  The only canonical example I can think of is Hermione casting spells on the train before the start of her first year, when the ban on magic isn't yet in operation because she hasn't even enrolled at the school yet. I haven't got the books to hand, so can't search for other examples.

Many students used magic on the train. In Goblet of Fire, Hermione used "Reparo" on the train; In Half-Blood Prince, Ginny used "Scourgify" in the train when there was "Stinksap" all over the compartment. Why didn't the Ministry of Magic consider this as underage magic when students are constantly reminded that they cannot use magic outside SCHOOL?


Facebook is showing others my latest new added friends, saying something like "Aiwnas is now friends with X." Is it possible to stop Facebook from doing this? Or make it private for a customized list of my friends?

Is there a privacy setting on Facebook that will stop the posting that is made on your friend's wall when you make a new friend?  I do not want this to appear on my friend's wall when I make a new friend


Ive purchased china rising maps for xbox but I'm low on data and was wondering if I could download Battlefield 4: China Rising from a friend's PC and save it to an USB formatted for Xbox 360? I have enough data to play online for awhile but not enough to install the new china map pack.

Due to the region restriction I cannot access Xbox Live on my Xbox, even if I purchased a Gold membership. However it seems that I can purchase games from Xbox Live Marketplace on a PC. I assume this means I can then download them on the PC, and I would like to know if I can transfer them through a flash drive to the 250GB internal HDD of my Xbox 360 console, and then run them from the HDD.


I was recently watching an episode of Smallville where Clark rips open his shirt and a button pinged off a wall. Besides making me laugh, it made me think: shirts don't open that easily without the buttons flying all over the place and needing to be repaired/replaced. Maybe there are velcro shirts he would use?  On the same track, where does he keep his clothes when he's in the red and blue?

In Superman #11 the cover reads:   Now I know covers have a tendency to be a little... misrepresentative of what is actually contained in the issue, but I've read the issue twice. There doesn't seem to be any secret about it.


Whenever I've been on a flight between two countries with a stop at a US airport, I've had to:   Disembark. Go through immigration. Reclaim my checked baggage. Go through customs. Recheck my baggage. Pass back through airport security.   At any non-US airport, my baggage has automatically been transferred to the next plane and I've simply walked through the "safe area" of the airport to the new boarding gate.  This is especially annoying when the plane arrives late and there is very little time to get to the connecting flight.  Whenever possible I now avoid any routes that pass through that country.  Is the USA the only country that does this immigration thing?

Most, if not all, European airports have international transfer zones, meaning that if you don't have to pass customs and immigration check of the country the airport is located in. On the other hand in US airports do not have international transfer zones. (Note that in case of Schengen zone countries "international" would mean out-of-Schengen).   How about rest of the world, which case is more typical?   Note: I'm not expecting full list of countries, just general indication what's the case in other regions.


In , a non-accepted answer (the one with 27 upvotes) is placed above the accepted one (with 20 upvotes).  I quickly checked some other questions and found that this behavior wasn't occurring elsewhere.  Is this a bug, or is this some SO feature that I'm missing?

What does it mean to accept an answer? How do I accept an answer, and what are the rules? Can I accept my own self-answer? What are the reputation benefits? Which answer should I accept? Should I upvote the accepted answer? What should I do if none of the answers are suitable?      For more information, see "" in the .


It is well known that the formula $$\int x^n dx = \frac{x^{n+1}}{n+1}+C$$  breaks down at $n=-1$ (we get a logarithm).  My question is, does there exist a value of $n \in \mathbb{Z}$ for which the formula $$\frac{d}{dx}x^n = nx^{n-1}$$  breaks down?

Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.   I saw some proof of $\frac d {dx} x^n=nx^{n-1}$ using binomial theorem, which is only available for $n \in\mathbb N$. Do anyone have the proof of $\frac d {dx} x^n=nx^{n-1}$ for all real $n$? Thank you.


The following is an exaggerated example: Suppose that three people wanted to express their opinions of StackExchange:  Person A: StackExchange is cool Person B: I think that StackExchange is cool Person C: I have a feeling that I would like to almost allow myself to think that StackExchange is cool  What is the speech pattern of Person C called?

What is the opposite for the straight talk idiom? How do I best call the activity when someone makes a very long preamble before he says what he wants?