Prove that for all positive integers $n$, $$\sum_{k=1}^{n}(-1)^kk!S(n,k)=(-1)^n$$ where $S(n,k)$ are the Stirling numbers of the second kind. I recognize that $k!S(n,k)$ is the number of surjections from an n-element space to a k-element space. I think there might be some kind of symmetry as well, but I am unsure how to evolve this thought into the proof. For instance, $$k!S(n,k) = 1 \text{ for } k=1 \text{ and }k=n$$

Consider the identity $$\sum_{k=0}^n (-1)^kk!{n \brace k} = (-1)^n$$ where ${n\brace k}$ is a Stirling number of the second kind. This is slightly reminiscent of the binomial identity $$\sum_{k=0}^n(-1)^k\binom{n}{k} = 0$$ which essentially states that the number of even subsets of a set is equal to the number of odd subsets.   Now there is an easy proof of the binomial identity using symmetric differences to biject between even and odd subsets. I am wondering if there is an analogous combinatorial interpretation for the Stirling numbers. The term $k!{n\brace k}$ counts the number of set partitions of an $n$ element set into $k$ ordered parts. Perhaps there is something relating odd ordered partitions with even ordered partitions?  As an added note, there is a similar identity $$\sum_{k=1}^n(-1)^k(k-1)!{n\brace k}=0$$ A combinatorial interpretation of this one would also be appreciated.


This is a screenshot of gnome-center    I can see that the Software Center is installed, I can find it in Unity as well. But when I click on it, it doesn't seem to want to open. So, I tried the command line method, but that is not working either.  I cannot seem to open the Ubuntu Software Center by either the normal way or by using the command line software-center, which results in command not found.   What am I getting wrong here and how can I fix this?

How to install Ubuntu Software Center on Ubuntu Gnome 17.04 Zasty Zepus (NOTE: Different from Ubuntu Software)?  As we know, Ubuntu GNOME comes with GNOME Software by default. However, I'd need the old Ubuntu Software Center for the sake of few packages that can be found there. I already tried to search through Synaptic Package Manager, but with no luck. I also tried to run sudo apt-get install software-center, but it resulted into the following:  Package software-center 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 'software-center' has no installation candidate   What I am particularly looking for, is GStreamer plugins for mms, wavpack, quicktime, musepack (thorugh Ubuntu Software Center).  Thanks!


I have a really strange output result from toString() built in function   Here is my code:  function strangeFunction(num) { return num.toString(); }   alert( strangeFunction(121.112*100) ); //output: 12111.199999999999  alert( strangeFunction(.1*100) );  //output: 10  alert( strangeFunction(1.33*100) ); //output: 133 alert( strangeFunction(133.33*100) ); //output: 13333.000000000002  alert( strangeFunction(133.33*100) );//output: 13334      Any suggestions how to fix that issue? It seems that ther is some kind of bug or number formatting issue.

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


I am using the following latex code to highlight some row of a table useing rowcolor command. However the table borders in those rows are overwritten by the row color. Why is it happening? How can I solve this?  Thanks  code  %% Compile and read me! \documentclass[a4paper,12pt]{article} \usepackage[table]{xcolor} \definecolor{gray}{cmyk}{0,0,0,0.17} \begin{table}[h] \centering \begin{tabular}{| c | c | c | c |} \hline User & Action & Time \\ \hline \rowcolor{gray} $A$ & $a_{1}$ & 1 \\ \hline \rowcolor{gray} $B$ & $a_{1}$ & 2 \\ \hline \rowcolor{gray} $A$ & $a_{2}$ & 2 \\ \hline \rowcolor{gray} $C$ & $a_{1}$ & 4 \\ \hline \rowcolor{gray} $B$ & $a_{2}$ & 4 \\ \hline $C$ & $a_{2}$ & 5 \\ \hline $D$ & $a_{2}$ & 8 \\ \hline $E$ & $a_{1}$ & 8 \\ \hline \end{tabular} \caption{Action Log} \end{table} \end{document}   Output:   Using midrule

I've created a table where the rows alternate in colour however /hline is acting unusually.  The first and second /hline work normally however after this alternating /hlines only show as a small dash next to the vertical column line  \usepackage[table]{xcolor}  \begin{table}[ht]    \rowcolors{2}{gray!25}{white}   \begin{tabular}{l | l|}     \hline     \rowcolor{gray!25}     text part 1 & test part 2  \\                    Priority & High \\ \hline     text part 1 & test part 2  \\                    Priority & High \\ \hline %this hline doesnt show     text part 1 & test part 2  \\                    Priority & High \\ \hline     text part 1 & test part 2  \\                    Priority & High \\ \hline %this hline doesnt show     text part 1 & test part 2  \\                    Priority & High \\ \hline     text part 1 & test part 2  \\                    Priority & High \\ \hline   \end{tabular}   \end{table}   Does anybody know what I'm doing wrong? Thanks.


I am making sauerkraut I have the cabbage and salt in the crock. I mixed it together really well as I did this.  I know it takes several days to be ready to can. Do I stir it some more while it is fermenting?

I haven't done this for a very long time. I am following , which conveniently fits perfectly into a little hack-job of containers I already had. (Related: ) @Athanasius' answer to that question led me to what I'm doing with this batch. At this point I feel pretty comfortable with it:    The two containers are identical, and I have a few inches of water in the top container so that it weighs down the cabbage in the lower container. It seems to be working pretty sweet. I'm three days in and it's starting to smell like something is happening. There is a funk in the air.  So far so good.  Now I am dying to stir it...to do something! Everything I have read (including Athanasius' answer) suggests that in a less awesome container I might have to stir, but now I don't necessarily have to do anything but scoop off scum which has yet to appear.  That's killing me.  Is there a reason not to stir? Will stirring offer any benefit?


Hi i am reading Topology by Munkres and i have one doubt at the last line of lemma 23.2. It is written that  Hence Y must lie entirely in C or in D.  I can't understand the above quoted statement. Everything else i was able to understand . I am attaching the screenshot where the lemma and its full proof is illustrated and i have highlighted the above statement(that i was not able to understand).The theorem's statement reads as: If the sets C and D form a separation of X, and if Y is a connected subspace of X, then Y lies entirely within either C or D.

Let ($X,\tau)$ be a top space. Suppose $Y \subset X$ is a connected subspace given the subspace topology. If $A \cup B$ is a separation of the space $X$ then $Y$ lies entirely in $A$ or $B$. I just want a verification: Suppose other wise then $\exists a \in Y$ such that $a \in A$ and $\exists b \in Y$ such that $b \in B$. I claim that $$Y \cap X = Y \cap (A \cup B) = (Y \cap A) \cup (Y \cap B)$$ Forms a separation of $Y$. As $Y$ inherits the subspace topology, the topology on $Y$ can be given by $$\tau_Y = \{Y \cap U \mid U \in \tau\}$$ Then since $A,B \in \tau$ we have that $Y \cap A,Y \cap B \in \tau_Y$, i.e., are both open in $Y$. Clearly both are nonempty by existence of $a,b$ up top. Lastly for disjointness, suppose $\exists \alpha \in (Y \cap A) \cap (Y \cap B)$, then $\alpha \in A \cap B$ contradicting $A,B$ being disjoint (since they were assumed to form a separation of our parent space) and thus $$(Y \cap A) \cap (Y \cap B) = \emptyset$$ hence $$Y = (Y \cap A) \cup (Y \cap B)$$ forms a separation of $Y$ contradicting it being a connected subspace $\blacksquare$


By default, theorems (using amsthm) are printed like Theorem 1.1. Is it possible to print them as 1.1. Theorem? I have the following:  \documentclass{article} \usepackage{amsmath, dsfont,   amsthm , enumerate, graphicx, tikz,stmaryrd} \newtheoremstyle{stelling} {\topsep}   % ABOVESPACE {\topsep}   % BELOWSPACE {\itshape}  % BODYFONT {0pt}       % INDENT (empty value is the same as 0pt) {\large\bfseries} % HEADFONT {.}         % HEADPUNCT {5pt plus 1pt minus 1pt} % HEADSPACE {}          % CUSTOM-HEAD-SPEC    \theoremstyle{stelling} \newtheorem{theorem}[subsection]{Stelling}  \begin{document}  \begin{theorem} Some text \end{theorem}  \end{document}

I would like all my theorem-like environments (theorem, example, etc.) to be numbered but such that the number appears before the environment's name, more or less like this:  1. Theorem  2. Example  How can I do this?


I am attempting to sort a list of names in alphabetical order and I keep getting the error Exception in thread "main" java.lang.NullPointerException and I don't know why.  import java.io.File; import java.io.FileNotFoundException; import java.io.IOException; import java.util.Arrays; import java.util.Scanner;  public class alphabeticalOrder {   static String names[];  static int count = 0;  static String sorting;   public static void main(String[] args) throws IOException {   // TODO Auto-generated method stub    String[] names = new String[500];    File namesFile = new File("names.txt");   Scanner inputFile = new Scanner(namesFile);    while (inputFile.hasNextLine()) {    String line = inputFile.nextLine();    String[] namesDetails = line.split("     ");    names[count] = namesDetails[0];    count++;   }    sort();    System.out.println(Arrays.toString(names));   }   public static void sort() {    int namesLength = names.length;    for (int i = 0; i < namesLength - 1; i++) {    for (int j = 0; j < namesLength - 1; j++) {     if (names[j].compareTo(names[j - 1]) > 0) {      sorting = names[j - 1];      names[j - 1] = names[j];      names[j] = sorting;     }    }   }   }  }   Customers txt has these names   Smith, Alexandra  Downes, Trish  Akbal, Maria   and the array must equal 500

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 know ballpark figure means estimate, but I don't understand why it means estimate. Literally, how does ballpark make figure an estimate? Ballpark means a baseball stadium or field from google definition.

I'm wondering where the term "ballpark estimate" comes from? Sometimes "ballpark" is said stand-alone to mean a rough estimate, as in "these numbers are a ballpark". I understand it must come from baseball or some other sport. Does it refer to the idea that a batter might point in the direction he'll hit the ball? Or is it something that relates to a rough guess at the attendance that day? What part of the ballpark or sports does one use a rough estimate?


When you visit a question that you have asked or an answer you have given you can see on the left hand side of the screen buttons for up-voting and down-voting as well as the number of people of votes for the question.  When one clicks up-vote, a message appears telling you that you can't vote on your own question. I'm just wondering why the up-vote and down-vote buttons are even visible if they cannot be used.  When you hover over your own comments it doesn't give you voting buttons...so why should it do so on questions and answers that you own?

Currently, the system makes you think you can upvote/downvote your own question/answer but then you get notified that you can't. Why have the up/down vote buttons there then?   In general, if some operation is not allowed, then don't put UI for that up or make it disabled so it is apparently disabled - no post operation error panels please?  ps: hope this is not a dupe, but if so, just comment it and I will remove  (+a joke: a user notification panel message: I deleted this file. Is this a problem? Yes/No.)


Let $G$ be an abelian group, $a \in G$ be an element of finite order, $(\text{ord} \, a, n) = 1$. Prove that the equation $x^n = a$ is solvable in the group $G$. I tried to apply a corollary from Lagrange's theorem, but I am concerned that the group can be of infinite order, and I do not know what to do with it

let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $\forall g \in G$ we can write $g=x^n$ for any $ x \in G$


My rhydon was almost 1300 CP as of last night and I haven't played since. When I turned on the game about a half hour ago, it was at almost 2000 CP. I still have the same amount of stardust and candy. I don't know what happened. Can someone fill me in on how this happened?

I recently upgraded my Pokémon storage to hold more Pokémon.  After doing so, I noticed the CP on my Pokémon changed - some are better, some are worse. What happened?


I've moved into a new area of the city and it would be nice to feel like I've explored the area properly. I'd like to be able to say that I've walked down every street within, say a mile.  I'm looking for an app that might help me track any I've missed.   Esentially I want an app that overlays a gps breadcrumb over where I've been walking. Googling for this hasn't got me very far because there is a app called 'breadcrumb' that let's uses mark about eight locations they want to come back to.  I'd just like to start the app, leave the house for a bit, and then see where I've got to.  Any ideas for what would be a useful app for me?

I was wondering if there was an iPhone application that would continuously read the GPS location and save it for later analysis. For example, I would like to be able to tell where I was at certain point of time, or how long did it take me to travel from one place to another. Is there such an app?


There is a theorem : In a field such that its Characteristic $n$ is greater than zero , the equality $(a+b)^n=a^n+b^n$ is true.  Does anyone know how to prove it ?  Thanks.

I remember a relation like $(a+b)^n \equiv a^n+b^n$, but I don't remember mod which numbers this is true.  Where can I learn more about this?


I need a USB cable for the above device so I can connect it to my pc and upload the pictures. does anyone know what USB cable I need? box states USB 2.0 which isn't much use to me.

How would I go about identifying a port, card or connector on my system which I am unfamiliar with?  Where would I find information on what these parts are? What would be the steps I would take in identifying a unknown port or cable?   This question comes up frequently, and the suggested solutions are usually the same. This community wiki is an attempt to serve as the definitive, most comprehensive answer possible. Feel free to add your contributions via edits.


Observe below a body of an email:-  I have been directed to send the report on the subject mentioned above. PFA.  On the Grammarly software, it is flagged as passive voice misuse. Please enlighten me about the passive voice misuse. Thanks in advance.

Whenever I create a document in Microsoft Word, it complains about a lot of my sentences being in passive voice. But, when I read that sentence aloud, it sounds fine to me. I am not sure if it is just me and will a statement in passive voice sound strange to a native speaker?  So, my question is, is it considered bad form to use passive voice generally? Or in some specific cases like written communications only?  Edit: If it is ok to use passive voice, then why does MS-Word complain?


So I was making a modpack with only 10 mods (WIP) and one of them happened to be Not enough items 1.6.1.9. I loaded up my modpack and loaded the world. The mods seemed to be working just fine. NEI was also working but when I switched the mode to cheat mode, it was still in recipe mode... My lockmode is set to -1 but its still stuck in recipe mode. Also, there are no tools in the upper left hand corner for cheat mode and "gamemode" is disabled.

When I heard that you could look up recipes and cheat items with Not Enough Items, I downloaded NEI. It worked, and then I got another mod and the all of a sudden NEI still worked, but it was locked in recipe mode only. I tried fixing it by putting it into cheat mode again, but it was still in recipe mode.  I knew the only reason this happened was probably because of a change in the mod. Then I was watching a YouTuber who had the same exact mod as me and NEI was working and not locked in recipe mode for him. I tried redownloading NEI and getting it again but I was still stuck in recipe mode.  How do I get NEI in cheat mode?


When the shaft of the helicopter rotates, it creates a low pressure. Because of the low pressure, the helicopter lifts. Is my understanding that this is just an application of Bernoulli's theorem?

What aerodynamic effects actually contribute to producing the lift on an airplane?  I know there's a common belief that lift comes from the Bernoulli effect, where air moving over the wings is at reduced pressure because it's forced to travel further than air flowing under the wings. But I also know that this is wrong, or at best a minor contribution to the actual lift. The thing is, none of the many sources I've seen that discredit the Bernoulli effect explain what's actually going on, so I'm left wondering. Why do airplanes actually fly? Is this something that can be explained or summarized at a level appropriate for someone who isn't trained in fluid dynamics?  (Links to further reading for more detail would also be much appreciated)


I read a short story years ago, however, I don't recall the title and I'd like to read it again.  The story involved a creature or alien telling the story from a first person perspective, how he sits and waits and is all alone, until either astronauts or space marines show up.   The story then shifts to a third person narrative of the astronauts/marines as one by one they're possessed by this thing, causing the eventual in-fighting and murder of each crew member.  In the end, the creature ends up back in his pit, waiting.

This science fiction short story is about a team of astronauts/space explorers who land on an alien planet. An alien entity, that exists in a gaseous state, is lurking at the bottom of a well or hole. It briefly inhabits the body of each astronaut it encounters, seeing from their POV and causing them to go crazy/die/kill the others. When one man dies the entity jumps into the body/mind of another.  The story is narrated by the alien entity, and everything is from its point of view. It overhears the astronauts' conversations as they try to figure out what is happening.   It is a stand-alone short story (maybe 6 or 7 pages), and it is not part of a larger novel. I have a feeling this may be one of Ray Bradbury's later short stories (but I could be wrong). I must have encountered this story in an anthology of relatively well-known scifi stories. I read it around 2007, but the story is probably from the 1960s/1970s.


the RMS (root mean square) value of $f(x)$ is defined as: $$f(x)_{rms}=\sqrt{\frac{\int^b_a (f(x))^2dx}{b-a}}$$ Why do we do this very specific thing of taking the square, the mean, and then the square root of the function? For an AC circuit, why does this tell us the power consumption and not something like the expression below? $$\frac{\int^b_a|f(x)|dx}{b-a}$$

What makes it a good idea to use RMS rather than peak values of current and voltage when we talk about or compute with AC signals.


I have an array like ["1,2,3,4"]. I am simply trying to convert the numbers inside this array to a pure integer array like [1,2,3,4].  This is what I have tried so far...  var a = ["1,2,3,4"]; var b = a.map(val => val.split(',')); console.log(b); // prints ["1", "2", "3", "4"] var c = b.map(x => parseInt(x)); console.log(c); // prints [1]   Why is c only prints [1], instead of looping through all the elements inside b array and print [1,2,3,4]?

From the :  [1,4,9].map(Math.sqrt)   will yield:  [1,2,3]   Why then does this:  ['1','2','3'].map(parseInt)   yield this:  [1, NaN, NaN]   I have tested in Firefox 3.0.1 and Chrome 0.3 and just as a disclaimer, I know this is not cross-browser functionality (no IE).  I found out that the following will accomplish the desired effect. However, it still doesn’t explain the errant behavior of parseInt.  ['1','2','3'].map(function(i){return +i;}) // returns [1,2,3]


I just upgrade to Ubuntu 11.10 x64 from Ubuntu 11.04 32bit. But I find a really annoying problem. When I drag executable from file explorer to shell, the shell says bash: /home/fenfei/app/android-sdk-linux/platform-tools/adb: No such file or directory it's jus over there. I also have problem executing .../java. So I delete java, and extract the java package again then execute it and it works. But for /home/fenfei/app/android-sdk-linux/platform-tools/adb that method doesn't work. All of them are marked as executable.    Anyone can help me?

I've downloaded a game (Shank) but the bin file doesn't run. The error that is shown when I try to launch the executable is:  bash: ./shank-linux-120720110-1-bin: No such file or directory


If someone calls me, and I say I can't talk to them at the moment, because I'm at school, is there any difference between the following two sentences?        I'm at school.   I'm in school.      Do they convey the same meaning or they are different?

Which of these two sentences is correct:        I am studying PhD at the university.   I am studying PhD in the university.      Should I use "at" or "in"? Or is there no difference?


I have some citation errors using mendeley and latex (texmaker). I do not know how to explain the errors so I attached the code. Please run it and help if you can.  How to make that: in text - all the articles to appear "last name et al year" ??? in bibliography - all the authors to appear and the order of the names to be "first - last" ???  \documentclass[12pt,a4paper,twoside,openright]{book} \usepackage[  backend=biber, style=authoryear, %sorting=none, maxcitenames=1, citestyle=authoryear]{biblatex}  \addbibresource{bibliography.bib} \begin{document} \textbf{ERROR In text}:\\  This is good: \cite{Chapman1964}\\  This is not good: \cite{Nie2007}, neither this: \cite{Nie2003}\\ Why do I have more than one name? \textit{\textbf{(1. I want all to be "last name et al." - how to do it?)}}\\  For bibliography errors:\\ \cite{Arrayago2015}\\ \cite{Bursi2005}\\  \textbf{ERROR In bibliography?\\}  1. Why some articles have all the authors and others just the first and "et. al" - see first two. \textit{\textbf{(2. How to modify this to be make all the authors appear in the bibliography?)}}\\  2. Why the first author is "last name - first name" and the others "first name last name"? \textit{\textbf{(3. What should I do make all the articles be "last - first name".)}}  \printbibheading \printbibliography[type=article, heading=subbibliography,title={Articles}]  \end{document}   the bibliography.bib file contains:  @article{Chapman1964, author = {Chapman, JC and Balakrishnan, S}, journal = {The Structural Engineer}, number = {1}, pages = {369--383}, title = {{Experiments on composite beams}}, volume = {42}, year = {1964} }  @article{Arrayago2015, author = {Arrayago, I and Picci, F and Mirambell, E and Real, E}, doi = {10.1016/j.tws.2015.02.012}, journal = {Thin-Walled Structures}, pages = {96--107}, title = {{Interaction of bending and axial load for ferritic stainless steel RHS columns}}, volume = {91}, year = {2015} }  @article{Bursi2005, author = {Bursi, OS and Sun, FF and Postal, S}, doi = {10.1016/j.jcsr.2004.06.002}, journal = {Journal of Constructional Steel Research}, number = {1}, pages = {67--92}, title = {{Nonlinear analysis of steel concrete composite frames with full and partial shear connection subjected to seismic loads}}, volume = {61}, year = {2005} }  @article{Nie2007, author = {Nie, J and Cai, CS and Zhou, TR and Li, Y}, doi = {10.1061/(ASCE)0733-9445(2007)133:4(530)}, journal = {Journal of Structural Engineering}, number = {4}, pages = {530--540}, title = {{Experimental and Analytical Study of Prestressed Steel Concrete Composite Beams Considering Slip Effect}}, volume = {133}, year = {2007} }  @article{Nie2003, author = {Nie, J and Cai, CS}, doi = {10.1061/(ASCE)0733-9445(2003)129:4(495)}, journal = {Journal of Structural Engineering}, number = {April}, pages = {495--506}, title = {{Steel Concrete Composite Beams Considering Shear Slip Effects}}, volume = {129}, year = {2003} }   Any help would be appreciated. Thank You!

In the header of my document I set the maximal author names to 2:  \usepackage[style=authoryear-icomp, maxbibnames=9, maxcitenames=2, backend=biber]{biblatex}   Now, when I cite texts with two authors, LaTeX gives me the following:     (Author_A/ Author_B 2012: 232)   When I have three authors or more, LaTeX makes it:     (Author_A/ Author_B et al. 2012: 232)   But I want LaTeX to just name the first author if there are more than two authors ... like this:     (Author_A et al. 2012: 232)   Any tips on how to achieve this ?


Essentially, I've set up a minecraft server but I am unable to join my own because I get the error: io.netty.channed.AbstractChannel$AnnotatedConnectException: Connection refused: no further information Here are some of the things I've done:  connected with direct connect with only my IP connected with direct connect with my IP and port allowed the firewall to give access to javaw  I have seen another question similar to this but the comments/replies didn't make sense to me at all Any help is appreciated

I am getting the following error when I try to connect to a Minecraft server:  This is all servers, not just one. The error says:  io.netty.channel.AbstractChannel$AnnotatedConnectException: Connection refused: no further information: Version 1.12  I've tried:  Restarting Minecraft Restarting Computer Uninstalling and Reinstalling Mincraft Uninstalling and Reinstalling Java Altering Firewall Restarting Internet I've messed with my port, made a second windows account, reset netsh winsock Checked hosts Made a new WINDOWS account  The overlay in the bottom right is Geforce's Overlay for game capturing. I don't have any mods installed. A Mojang support ticket wouldn't help. Im desperate.


I've been concerned about what answer to choose as accepted. I have asked two questions on Stack Overflow. On my second one, there are three answers, and I feel that one of them answers my question better than the others. However, I did not choose this answer. Someone else gave an answer that solved my entire problem, part of which was the question I originally asked. I chose that one, and completely rewrote the function to make it more efficient. I don't know if I made the right choice, and it's a big deal to me that whoever deserves credit gets it. So I guess my real question is this: Is it better to choose the most useful answer or the one that answers the question?

I asked  that turned out to have multiple correct answers. How do I pick between them to determine which to accept?  All of the answers were different. They were not the same answer given multiple times.


Me and my wife planning to visit UK as tourist. My UK tourist visa refusal letter give some valid observations, which I am going to address in second attempt. However, one observation, I hard to find out suitable answer, is that " You have not shown from the supporting documents you have any family members living in Pakistan or other countries and therefore consider you have very little way of ties to provide you with enough incentive to leave the UK on completion of your proposed visit". Now, my family situation is such that I have two daughters, both married and living with their husbands. My only son is doing his studies in UK. So, in application at the filed "Evidence of family members remaining in your home country whilst you travel" , I had no other choice except to write NIL. So, is there any suggestion, how to address this observation.

How can I prove the immigrant officers that I have significant ties in my home country?  Are there any documents that I need?


If the friction on an object is 200 N and you apply 200 N, it seems, the forces should immediately cancel each other out since the friction and your applied force go in opposite directions, leaving you with an object that is motionless. Yet, from what I've read, that's not the case. I feel like I'm misunderstanding something. Could it be I'm wrong about needing to apply 200 N initially? Might the amount of force I actually need be greater, but instantaneously decrease to 200 N?

Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?


My  Attempt :  Prime factorisation of $12769$ is $113^2$  $n^2+11n+2-113^2m=0$  The conjugate of this quadratic equation becomes:  $\sqrt {113 (113m+1)} $  which can never be a rational as (113,113m+1)=1 and 113 is not a perfect square (and its prime )  I belive this method is right,but I am asking for a modular method of doing this, which I believe will be easier. Thanks

Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer) It's obvious that if we show $113$  doesn't divide $n^2+11n+2$ we are done...


Can someone explain to me what this sentence means? I got confused about why it had "to think about" at the beginning of a sentence. "To think about income elasticity analogous to a price elasticity of demand."

As a native speaker of English, the gerund version of this sentence sounds better:  infinitive:     When used together in chains,   extension methods are an unprecedented   tool to produce extremely concise   code.   gerund:     When used together in chains,   extension methods are an unprecedented   tool for producing extremely concise   code.   But how can I explain to someone learning English how to decide in situations like these whether to use the infinitive or the gerund?


I am using Mac OS terminal (similar to Linux) and trying to find best way to search inside all files on a computer that has extension *.py  What is the best way to achieve this?  I wanted to put 1 keyword for search and quickly show the whole path of these python files are that contain requested keyword in them..

How do I list all .txt files with their full path that have a word 'Ubuntu' in them. Ignore non-text files. When comparing values you should ignore the case i.e. UBUNTU or ubuNtu or UbUnTu are treated as equal to the search phrase given.


I browse Stack Overflow quite frequently and I often find that when I come across a helpful answer I want to be able to save the best answer for later. It would be nice if I could save those snippets/answers to my account so later I can quickly find what I was looking for.

Often times I am not interested in the question so much as I am the answer. Unfortunately, the only site option for bookmarking an optimal answer is to bookmark the question. This leaves you having to remember that no the question wasn't that great, but there's an answer in here worth a million. It'd be nice to be able to favorite an answer allowing you to jump immediately to the answer that was much more valuable than the question. I understand that I can bookmark the answers link using my browser but it seems being able to favorite the answer within the site's ecosystem is useful.


I want to set a divider in my dialog I do this:     if (dialog != null) {         final int dividerId = dialog.getContext().getResources()                 .getIdentifier("android:id/titleDivider", null, null);         View divider = dialog.findViewById(dividerId);         if  (divider != null) {             divider.setBackground(null);         }   This is my whole code :    public void setParamsDialog(String componentName, String componentCode, String unit) {         dialog.setContentView(R.layout.dialog_consumables);         dialog.getWindow().setSoftInputMode(WindowManager.LayoutParams.SOFT_INPUT_STATE_ALWAYS_HIDDEN);         dialog.setCancelable(false);         dialog.show();          if (dialog != null) {             final int dividerId = dialog.getContext().getResources()                     .getIdentifier("android:id/titleDivider", null, null);             View divider = dialog.findViewById(dividerId);             if (divider != null) {                 divider.setBackground(null);             }         }         int titleDividerId = dialog.getContext().getResources().getIdentifier("titleDivider", "id", context.getPackageName());         dialog.getWindow().getDecorView().findViewById(titleDividerId).setVisibility(View.GONE);          compNameText = (TextView) dialog.findViewById(R.id.component_name);         compCodeText = (TextView) dialog.findViewById(R.id.component_code);         compUnitText = (TextView) dialog.findViewById(R.id.amount_unit);         searchEditText = (EditText) dialog.findViewById(R.id.search);         amountEditText = (EditText) dialog.findViewById(R.id.edittext_amount);          mListView = (ListView) dialog.findViewById(R.id.consumables_list);         searchConsumables = (RelativeLayout) dialog.findViewById(R.id.search_consumables);          cancelButton = (Button) dialog.findViewById(R.id.negative_btn);         saveButton = (Button) dialog.findViewById(R.id.positive_btn);          cancelButton.setOnClickListener(new View.OnClickListener() {             @Override             public void onClick(View view) {                 dialog.cancel();             }         });     }   But on android API 23 I get a null pointers  A logcat logs :  java.lang.NullPointerException: Attempt to invoke virtual method 'void android.view.View.setVisibility(int)' on a null object reference         at pl.dialog.box.DialogConsumables.setParamsDialog(DialogConsumables.java:85)         at pl.barcode.readers.BarcodeReader$2.onClick(BarcodeReader.java:198)

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 getting a NullPointerException when running the following example:  private void contractExpiryActionPerformed(java.awt.event.ActionEvent evt) {                                                   String expireDate = contractExpiry.getSelectedItem().toString();    System.out.println(expireDate);  }     Just want to printout the date to test if it is working, But I keep getting this error no matter what I do.   Exception in thread "AWT-EventQueue-0" java.lang.NullPointerException     at tetrapro.IncomeSolution.contractExpiryActionPerformed(IncomeSolution.java:865)     at tetrapro.IncomeSolution.lambda$initComponents$6(IncomeSolution.java:492)     at javax.swing.JComboBox.fireActionEvent(JComboBox.java:1258)     at javax.swing.JComboBox.contentsChanged(JComboBox.java:1332)     at javax.swing.JComboBox.intervalRemoved(JComboBox.java:1352)     at javax.swing.AbstractListModel.fireIntervalRemoved(AbstractListModel.java:179)     at javax.swing.DefaultComboBoxModel.removeAllElements(DefaultComboBoxModel.java:174)     at javax.swing.JComboBox.removeAllItems(JComboBox.java:771)     at tetrapro.IncomeSolution.setExpirationDates(IncomeSolution.java:250)     at tetrapro.IncomeSolution.(IncomeSolution.java:61)     at tetrapro.IncomeSolution.lambda$main$11(IncomeSolution.java:1007)     at java.awt.event.InvocationEvent.dispatch(InvocationEvent.java:311)     at java.awt.EventQueue.dispatchEventImpl(EventQueue.java:756)     at java.awt.EventQueue.access$500(EventQueue.java:97)     at java.awt.EventQueue$3.run(EventQueue.java:709)     at java.awt.EventQueue$3.run(EventQueue.java:703)     at java.security.AccessController.doPrivileged(Native Method)     at java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(ProtectionDomain.java:76)     at java.awt.EventQueue.dispatchEvent(EventQueue.java:726)     at java.awt.EventDispatchThread.pumpOneEventForFilters(EventDispatchThread.java:201)     at java.awt.EventDispatchThread.pumpEventsForFilter(EventDispatchThread.java:116)     at java.awt.EventDispatchThread.pumpEventsForHierarchy(EventDispatchThread.java:105)     at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:101)     at java.awt.EventDispatchThread.pumpEvents(EventDispatchThread.java:93)     at java.awt.EventDispatchThread.run(EventDispatchThread.java:82)


I'm a horrible noob at anything past mechanics, so please bear with me.  According to Einstein's theory of relativity (at least as it is known in "popular science" (lowercase)), mass-full objects can't move faster than the speed of light. They become infinitely massive which results in the F required to accelerate them to approach infinity.  Moreover, I heard, that according to his theory (not sure which one), one can choose any frame of reference for any physics calculation. If I decide, for whatever reason, that my nose is stationary and everything else moves relative to it all the physics would still work.  However, point 2 seems to contradict point 1.  I decide that my nose is the "stationary frame of reference". Then I twirl around in a circle at 60RPM. The stars are going to be going at more than $c$ (the sun will be moving at 939 474 627 996 meters/second (2*pi*1 AU/second) is around $3000 c$).  Why does this not work?

We may choose a non-rotating earth as our reference frame and ask ourselves: how about the planetary and stellar motions. A star at a distance of 10 million light years would turn around the earth in 24h with a velocity of 10^18 m/s.   A friend once told me that actually articles have been published delving into this problem, e.g. to prove that fictitious forces emerge from the choice of such a bizar reference frame that ensure that the earth is still (somewhat) flattened at it's poles.  Questions:  1) Does anybody know of such a publication?  2) I know that even such speeds of 10^18 m/s are not in contradiction with relativity because a limiting velocity only exists for exchange of information, which apparantly does not occur. Still: could anybody explain why such bizar velocities are allowed?


Here's a quite basic question, and I'd be very glad for an answer!  The multiplicity $m_V$ of an irreducible representation $V$ in the representation $W$ of the group $G$ is given by $$ m_V = \dim \left( Hom(V,W)^G \right) $$  where $Hom(V,W)^G$ is the space of $G$-module homomorphisms from $V$ to $W$.  How to see this?

I am currently working on Bruce Sagan's The Symmetric Group.  The following proposition is given without proof:  Let $V$ and $W$ be $G$-modules with $V$ irreducible. Then dim Hom($V$,$W$) is the multiplicity of $V$ in $W$.    This proposition is a strengthening of the following corollary of Schur's Lemma:  Let $V$ and $W$ be two $G$-modules with $V$ being irreducible. Then dim Hom($V$,$W$) = $0$ if and only if $W$ contains no submodule isomorphic to $V$.    I understand why the corollary is true:   Let us suppose $W$ contains a submodule isomorphic to $V$. Then clearly, dim Hom($V$,$W$) > $0$ because of the isomorphism from $V$ to the submodule. Let us suppose im Hom($V$,$W$) > $0$. Then there must be some non-zero homomorphism from $V$ to some submodule of $W$. As the homomorphism is non-zero, its kernel is not $V$, so the kernel is zero, by Schur's Lemma. Hence it is injective. As it is surjective to its image, it is an isomorphism.     How could one prove this proposition? Is the proof similar to the proof of the corollary?  Thank you very much for your help!


As above, does $\sum_{n=1}^{\infty}(\sin{n})^n$ converge? And if so, to what value.  From calculating partial sums, it appears it might, but I'm not quite sure how to proceed from there.

Does the sequence $\{\sin^n(n)\}$ converge?   Does the series $\sum\limits_{n=1}^\infty \sin^n(n)$ converge?


If I managed to exile a  from a library with  and I play the rift, does it go to the owner's graveyard or does it stay in exile?

There are a few cards that allow you to exile cards and then cast them later ( for example). After a spell cast this way resolves, does it go back into exile, or does it resolve normally including being placed in its owner's graveyard? (assuming nothing else effects where it would go after being cast)


How can I find the correlation between a categorical (dependent) variable and a continuous-scale (independent) variable? Is a Kruskal Wallis test appropriate? I'm a little confused as my independent variable is not nominal but scale!

I would like to find the correlation between a continuous (dependent variable) and a categorical (nominal: gender, independent variable) variable. Continuous data is not normally distributed. Before, I had computed it using the Spearman's $\rho$. However, I have been told that it is not right.  While searching on the internet, I found that the boxplot can provide an idea about how much they are associated; however, I was looking for a quantified value such as Pearson's product moment coefficient or Spearman's $\rho$. Can you please help me on how to do this? Or, inform on which method would be appropriate?  Would Point Biserial Coefficient be the right option?


I can see that, the derivative of tangential vector is normal vector i.e the second derivative is normal to the first derivative. but I couldn't derive a proof for it. can anyone please prove this? thanks in advance

I've seen the math, but... It just doesn't make sense to me. How is the slope going to point perpendicular to the vector that is clearly a straight line not going in that direction?


I was practicing with my daughter and most of the pics came out good but some really good ones, or what could have been really good, her face was blurred but the background was clear.

I have made a mistake with this image:    ISO 400 | 1/1700s | f/2  I used manual Aperture mode and set it to F/2 (now I believe this is too much). Kids were one meter away. It was light cloudy morning.  However, they came out blurred - and the trees behind appear in focus. I was using auto-focus mode, and I think the focus was in the middle of the photo - but between the kids :(  How come my camera auto-focused the trees behind with f/2 (i was expecting this aperture works for close objects?). Was this only a miss-focus, or my aperture was wrong as well? What should I do next time?


addresses the question of how guests get into the park, but no one knows exactly where it is.  asks if Westworld is an isolated part of the country, while the one I am asking now provides evidence for being an island, on Earth, and asks where such an island may be.  So far, we have some information about the location of the park:   It borders an ocean, we have the size of the park based on a scale, and we have potential coordinates on the title bar:      It is an island:      From the Westworld Terms and Conditions:      INVESTIGATIONS/VIOLATIONS: If Delos, Inc. or any Delos Entity believes, in its sole discretion, that a violation of these Terms has occurred, it may take any and all corrective action it deems appropriate without notice, including contacting local authorities on the mainland. All human-on-human crimes taking place within the Delos Destinations compound will first be investigated by Delos, Inc.; Delos, Inc. has successfully avoided providing personal data in response to a legal process involving outside court entities for its entire history of existence. However, Delos, Inc. reserves the right to disclose personal information requested by a law enforcement agency, and shall have no liability to you for such disclosure.   Given the above information, and introducing more if you find it,   What is a plausible, existing island that matches the size of Westworld given by the map, as well as the ~coordinates given on the top bar? If there is not an existing island at around this location, where would this island to be, plausibly??

In Westworld (2016) we see this vast area of land that is the stereotypical 'western' locale with scrubland, some prairie, a few nice buttes, and so on.  On top of one of the larger mesas is a complex that houses the maintenance crew and developers. They even mention in casual conversation about rotating back home.    Is Westworld located in some sort of giant holodeck like building, or is it in a remote locale? (I was thinking something Jurassic park like since it's written by Michael Crichton).


I have a .tiff and a .tfw file that I want to change into a GeoTIFF. When I try to open the file in ArcMap and ENVI 5.0, it is successful. However, in Google Earth it is not.  Is there anyway to create the GeoTiff in ArcMap or ENVI?

I originally had an IMAGINE Land Cover raster file that I opened in ArcMap.   I used the Extract Feature from Raster to extract only the Developed class and saved it (still IMAGINE).   Then I used the Copy Raster to convert the IMAGINE to GeoTIFF, but when I try to view the GeoTiff in Google Earth or Photoshop, it doesn't display anything.   However, in ENVI, it displayed successfully.   What am I doing wrong?


Given a quadratic number field $F = \mathbb{Q}(\sqrt{d})$, is there a way to determine whether or not $F \subset K$ for some quartic numberfield $K$ with $\operatorname{Gal}(K/\mathbb{Q}) \cong \mathbb{Z}/4\mathbb{Z}$?  Moreover, how can we find that field $K$ if it exists?  For instance, $\mathbb{Q}(i)$ is not contained in any cyclic quartic number field and neither is $\mathbb{Q}(\sqrt{-3})$.  I thought I heard somewhere that the intermediate subfield of a cyclic quartic number field must be totally real, but I am not sure.

Let $D$ be a squarefree integer. I am trying to prove that $\mathbb Q[\sqrt D]$ is contained in a Galois extension of $\mathbb Q$ with Galois group $\mathbb Z/4$ if and only if $D$ is the sum of two squares, $D = a^2 + b^2$ with $a,b\in \mathbb Q$.   The hint in the exercise in Dummit and Foote suggests considering the extension $\mathbb Q[\sqrt{s + s\sqrt D}]$ for the forward direction. However, I am unsure how to show that this extension is Galois, much less that its Galois group is cyclic of order 4.   For the reverse direction, I expressed the given Galois extension as $\mathbb Q[\sqrt{a+b\sqrt D}]$ for some $a,b\in \mathbb Q$. I showed that this extension has $\mathbb Q[\sqrt{c^2 - d^2 D}]$ as a subfield for some $c,d \in \mathbb Q$. From this, I deduced that the $\sqrt D$ and $\sqrt{c^2 - d^2 D}$ generate the same extension, so $\sqrt D = x \sqrt{c^2 - d^2 D}$ for some $x$, and hence that $D = \frac{x^2 c^2}{1 + x^2 d^2} $. It seems that there should be a way to decompose this as a sum of two squares, but I did not see how.   I did not tag this as homework as I am studying it independently.


there's:  $$\int^{2\pi}_{0} \frac{dx}{\mathrm{sin}^4x+ \mathrm{cos}^4x}$$  I was always confused if it is possible to solve this integral not using Tangent half-angle substitution? Because it takes much time for calculus only, is there another way?

How to integrate    $$\int \frac{1}{\sin^4x + \cos^4 x} \,dx$$    I tried the following approach: $$\int \frac{1}{\sin^4x + \cos^4 x} \,dx = \int \frac{1}{\sin^4x + (1-\sin^2x)^2} \,dx = \int \frac{1}{\sin^4x + 1- 2\sin^2x + \sin^4x} \,dx \\ = \frac{1}{2}\int \frac{1}{\sin^4x - \sin^2x + \frac{1}{2}} \,dx = \frac{1}{2}\int \frac{1}{(\sin^2x - \frac{1}{2})^2 + \frac{1}{4}} \,dx$$  The substitution $t = \tan\frac{x}{2}$ yields 4th degree polynomials and a $\sin$ substitution would produce polynomials and expressions with square roots while Wolfram Alpha's solution doesn't look that complicated. Another approach: $\sin^4x + \cos^4 x = (\sin^2 x + \cos^2x)(\sin^2 x + \cos^2 x) - 2\sin^2 x\cos^2 x = 1 - 2\sin^2 x\cos^2 x  = (1-\sqrt2\sin x \cos x)(1+\sqrt2\sin x \cos x)$  and then I tried substituting: $t = \sin x \cos x$ and got  $$\int\frac{t\,dt}{2(1-2t^2)\sqrt{1-4t^2}}$$  Another way would maybe be to make two integrals: $$\int \frac{1}{\sin^4x + \cos^4 x} \,dx = \int \frac{1}{(1-\sqrt2\sin x \cos x)(1+\sqrt2\sin x \cos x)} \,dx = \\ \frac{1}{2}\int \frac{1}{1-\sqrt2\sin x \cos x} \,dx +  \frac{1}{2}\int\frac{1}{1+\sqrt2\sin x \cos x} \,dx$$   ... and again I tried $t = \tan\frac{x}{2}$ (4th degree polynomial) and $t=\sqrt2 \sin x \cos x$ and I get $\frac{\sqrt 2}{2} \int \frac{\,dt}{(1-t)\sqrt{1-2t^2}}$ for the first one.  Any hints?


Is regeneration a naturally biological trait of the timelords, or is it a result of timelord science? I've seen conflicting stories, especially with the ability to give new cycles and force regeneration it does seem to be more of an unnatural ability but I'm unclear.

I saw in an question that Susan Foreman might not be a Time Lady. This made me think if she would regenerate like the Doctor. Are all people from Gallifrey Time Lords? I remember an episode where there were people who seemed to live outside of the Time Lord world. Do they all regenerate?


We started getting Alerts:  Could not connect because the maximum number of '1' dedicated administrator connections already exists. Before a new connection can be made, the existing dedicated administrator connection must be dropped, either by logging off or ending the process. [CLIENT: 127.0.0.1]  With a help of SQL job and holding table, we managed to find out that it's the SQL Server Service Account that tries to connect, approx every 4 hours e.g. 12:00 16:00 and so on, with a program name: Net SqlClient Data Provider. I've added the host_process_id column as per jadarnel27 suggestions, identified the PID, but there were no processes with the same PID in the task manager. Oddly enough, there are no entries in the log: "Dedicated admin connection support was established", just the following ones:  16:00:05 Login succeeded for user 'sql service user'. Connection made using Windows authentication. [CLIENT: ip address of Windows Failover Cluster Virtual Adapter] 16:00:05 Could not connect because the maximum number of '1' dedicated administrator connections already exists. Before a new connection can be made, the existing dedicated administrator connection must be dropped, either by logging off or ending the process. [CLIENT: 127.0.0.1] 16:00:11 Dedicated administrator connection has been disconnected. This is an informational message only. No user action is required.  No clues in Windows Event Viewer logs or Windows Cluster logs. This is only happening on an active node of AlwaysOn Availability  Group. No jobs/port scanning configured to run at those times, nor any other tasks. I have seen   but we know what account has used DAC, just don't understand why. How can we troubleshoot the issue further? EDIT: I've found the cause of the problem, it was a powershell script that synchronises server objects for Availability Groups, it was set to run on port 1433 and I have no idea why it tried to connect to DAC, however simple reboot has solved the issue! Thanks ever so much to everyone who replied!

Is there any way to find who used Dedicated Admin Connection?   Not active connection but the previous one which is already closed?


Put simply, I ask far more questions than I answer.  Not for any lack of motivation or interest, I put a good deal of effort into questions and answers making sure they are well explained and that I've done my own research beforehand; it's just that typically by the time I've come up with a solution the question has already been answered.  On top of that, frankly the people answering have far more specialized knowledge in their respective sections, and so I feel like my answers would only be muddying the page up.   I do -look- for questions that have been left alone, or that could use help and provide a fair answer, but for the most part I use the site to get practiced opinions as to the best methodology to accomplish a given task.   Even with my questions it's not so much that I couldn't -find- the answer, but that I want a persons opinion on how to implement it, and not a reference page with an agnostic list of functions.   Just curious if it's considered bad form to have a much higher Q-2-A ratio.

I have used the websites of SO a lot the past few months because I am busy with a large scale web project. I feel I get better answers here on SO than when I just do a Google search, maybe because I can be more specific here with my problem, and the responses are really fast.  Occasionally when I am not working I try to answer some questions, but the question almost always has an answer which is 'as good as' or 'better' than the answer I would supply.  So my question/answer ratio is about 20/1 something, if not more. When I look at my profile page I see a bucket-load of questions and almost nothing I answered myself.  Is this considered bad behaviour? I can see that this looks a little egoistic.  : One devoted to one's own interests and advancement.


Show that one point compactification of $\Bbb Q$ is not Hausdorff .   Suppose to the contrary $\Bbb Q$ is Hausdorff, then we take two points $x,\infty\in\Bbb Q$, $x\ne\infty$, and produce disjoint open sets $U,V$ such that $x\in U$ and $\infty\in V$. By definition, we know that $\Bbb Q\setminus V$ is a closed and compact space such that $x\in U\subseteq\Bbb Q\setminus V$.  Please help me to complete the proof.

Definition: one point compactification     Let $X$ be any topological space, and let   $ \infty$  be any object   which is not already an element of $X$. Put $ X^{*}=X\cup \{\infty  \}$, and topologize $X^*    $ by taking as open sets all the open   subsets $U$ of $X$ together with all subsets $V$ which contain $\infty  $  and such that $X\setminus V$ is closed and compact   Show that the one point compactification of $\mathbb{Q}$ which is $\mathbb{Q}^*$ is Not Hausdorff.  What to do? What...  My Attempt:  Suppose to the contrary $\mathbb{Q}^*$ is Hausdorff, then we take two points $x$, $\infty \in \mathbb{Q}^*$, $x \neq \infty$, and produce disjoint open sets $U,V$ such that $x \in U$ and $\infty \in V$  By definition, we know that $\mathbb{Q} \backslash V$ is a closed and compact space such that $x \in U \subseteq \mathbb{Q} \backslash V$  We wish to produce a contradiction such that $\mathbb{Q} \backslash V$ is not closed, or not compact. But we know that $\mathbb{Q} \backslash V$ has to be closed since $V$ is open, therefore we need to show $\mathbb{Q} \backslash V$ is not compact.  Let $\mathcal{U}$ be an open cover of $\mathbb{Q} \backslash V$. Since  $\mathbb{Q} \backslash V$ is claimed to be compact, then $\mathcal{U}$ has a finite subcover $\{U_i|i \in F\}$, $F$ is finite in  $\mathbb{Q} \backslash V$. Then for all $x \in \mathbb{Q}\backslash V$, $\exists i \in F$ s.t. $x \in U_i$ (...Ugh everything seems fine...)  Can someone provide me with some help as to how to go on with this proof? Thanks a bunch.


I have noticed that "Help" button on  is not working.    Also there is no link to Help in the footer, and  leads to "Page Not Found".  May I assume "Help" button should be removed from top navigation menu?

The help icon in the Stack Exchange site's top bar is not working.     I navigate to my  and clicked on that icon, it is not responding. In other sites it is listing the drop down list.


In Inception, near the end there are three dream levels. In Level 1, when the van enters freefall, there is zero gravity in level 2.   This means that the members of level 2 experience no gravitational force. At one point in the movie you are shown these members floating in midair.  Why doesn't this carry over to level 3? Our sensory organs (or any sensory organ you devise, for that matter), cannot distinguish between freefall and zero gravity. Shouldn't the zero-G in level 2 cause zero-G in level 3?

If level 0 is the reality, the characters in the van are at level 1. The van drops off the edge of the bridge and goes into freefall. At level 2, in the hotel, they experience the freefall as well. But then, at level 3, at the fortress, (and for that matter, in limbo) there is no freefall. Why is it so?


I came across 2 reputable sites here in our country selling DSLRs.  I wanted to buy a Nikon D90 kit with 18-55mm lens, cost 28,600.  The other store sells the 18-55mm lens for 3,308.   So it is cheaper to buy the body and lens separately from different merchants. I would save 1,692.  Is it okay to buy lens separately assuming it has the same specs with the kit?   Or is the lens from the kit better than the separate lens?

I am planning to buy a DSLR soon.  Before I zero in on the model, I want to know whether it is advisable to buy a kit (body + 18-55 lens) or not? OR should I go for the camera-body and the lens separately?


I'm rendering JSON dates that look like this: /Date(1185336000000)/ and I'm trying to convert them to a ("mmmm d, yyyy")-type format.  I tried a if...includes() and then a format() method, but they didn't work (bad syntax) and they disabled already rendered data.    JS snippet:  import firmData from '../JSON/firmDir.json';  function loadBio() {  let dateOfHire = firmData.d.results.map(function(val) {       // if (val.hiredate === null || undefined) return " ";       let newDate = val.hiredate;       if (newDate.includes('000')) {            newDate.format("mmmm d, yyyy");       }     return val.hiredate  })  $("#hireDate-id").append(dateOfHire);  }  loadBio()   JSON snippet:  {   "d": {     "results": [       {        "hiredate": "/Date(1185336000000)/",        ...

I'm taking my first crack at  with jQuery. I'm getting my data onto my page, but I'm having some trouble with the JSON data that is returned for Date data types. Basically, I'm getting a string back that looks like this:  /Date(1224043200000)/   From someone totally new to JSON - How do I format this to a short date format? Should this be handled somewhere in the jQuery code? I've tried the jQuery.UI.datepicker plugin using $.datepicker.formatDate() without any success.  FYI: Here's the solution I came up with using a combination of the answers here:  function getMismatch(id) {   $.getJSON("Main.aspx?Callback=GetMismatch",     { MismatchId: id },      function (result) {       $("#AuthMerchId").text(result.AuthorizationMerchantId);       $("#SttlMerchId").text(result.SettlementMerchantId);       $("#CreateDate").text(formatJSONDate(Date(result.AppendDts)));       $("#ExpireDate").text(formatJSONDate(Date(result.ExpiresDts)));       $("#LastUpdate").text(formatJSONDate(Date(result.LastUpdateDts)));       $("#LastUpdatedBy").text(result.LastUpdateNt);       $("#ProcessIn").text(result.ProcessIn);     }   );    return false; }  function formatJSONDate(jsonDate) {   var newDate = dateFormat(jsonDate, "mm/dd/yyyy");   return newDate; }   This solution got my object from the callback method and displayed the dates on the page properly using the date format library.


How does an RFID reader monostatic antenna both transmit and receive at the same time, are they CW or pulsed? I would like to extend the read range of a reader by using an amplifier between the antenna and the reader. Is that a feasible way to increase the range?

I am working on a prototype, one function of which is to detect whether an object is "in range" by a few cm. Right now I'm just using an Arduino and a cheap  that operates at 13.56 MHz:    I've successfully gotten it to detect the tag, but only at a distance of about 3-4 cm when the tag is oriented parallel to the antenna.  According to my  , the HF band allows read ranges of between 10 cm and 1 m for passive tags, depending on factors like antenna size, tag size and orientation, and transceiver power.  I realize this inexpensive reader is not up to task as-is, but I'm interested in building something that achieves read ranges of 15-20 cm.  Some criteria:   No need to read multiple tags; only whether one tag is in range or not. No need to write to the tag. Cannot use an active tag.   I'm not experienced with RFID reader construction (yet) but am interested in knowing what I should pursue.  Here are some things I've considered:   Ditch the embedded antenna on the cheap RFID reader and construct my own, larger antenna. I'd need to see if the onboard  is up to the task of providing additional power. Look for a different IC around which to build a reader from scratch. Find a ready-made solution instead of trying to build one (more cost-effective?). Use something other than RFID for simple proximity detection.   I am experienced with microcontrollers and basic electronics, and have made audio and lighting projects, but this is a first with RFID. Since I don't need to read multiple tags, which RFID is suitable for, I've considered maybe some sort of magnet and hall-effect sensor, but the range does not seem adequate. I considered using an ultrasonic proximity detector, but the application calls for detecting the tagged object while ignoring untagged ones (ultrasonic would produce false positives on untagged objects). I've considered some sort of reflective surface placed on the object, and detecting reflected light, but the object orientation is not reliable enough to maintain alignment.  So, in a nutshell, What modifications can I make to my existing reader, or what alternate technology should I pursue to achieve 15-20 cm detection of a passively tagged object?  I plan on connecting whatever proximity detector is used to a microcontroller using SPI.


Can anyone explain me what does the following mean (from ):  The best URL shorteners will use a 301 redirect to pass along their Google page rank to the destination web address. This helps the redirected web address advance in  search rankings.    I was going through the advantages of shortened url, when I came across this.

When you have a link from lets say twitter that is t.co/foo that links back to your website how does that effect SEO and how do the major search engines handle Shortened URLs?


I have an NTFS external hard drive with ~300GB of data on it, and I'd like to be able to start writing to this drive without having to use any third-party software or other hacks/workarounds. I've recently purchased a second external hard drive, and so now that I finally have something that's large enough to hold all of the data from my old drive, I want to copy everything over to this new drive so that I can format the old drive to use a file system that my Macbook Pro is capable of writing to without having to use any extra tricks.  My instinct was to just copy all of the files from the old drive and paste them into the new drive, but I figured this would take a long time so I wanted to see if there was a more efficient way to do this. But then when I started looking into this, I found all this stuff about people using things like "rsync" or some different types of third-party software to transfer large amounts of data between drives, and people being worried about the transfer process failing midway through and leaving them with no easy way of figuring out where to start back up from, and all kinds of other stuff like this that made me feel anxious about this whole undertaking.   Nonetheless, I still haven't been able to come across any source that gives a definitive, bottom-line answer for what the "best" way to transfer large of amounts of data like this is, which is why I'm asking this question here now.  Essentially, all I need to know is (i) Am I safe to just copy and paste all of the files from the old drive to the new drive through Finder?, and (ii) If I'm safe to copy and paste with finder, what method should I use to transfer all of these files?  The one promising method I did come across was to use the "restore" function in disk utility, but I'm not sure this will work here given that my source drive is NTFS, so it seems like restoring my new drive from the old drive would just leave me with the same problem of now not being able to write to my new drive. Is this correct?

I need to be able to copy about 2TB of data from an external drive (single USB external disk) to a another external drive (Drobo attached via Firewire).  Finder is not an option. If it hits any problem, it stops the process and I have to figure it out why it failed and start over. It could take me months to get through it.  I've read about CP and RSYNC but I'm not too familiar and I'm afraid I might get some of the switches wrong and miss files, or screw up the file dates, or worst...  Can anyone suggest how I might pull this off with minimum risk and cost?


I installed a game through the original game disc but I still need the disc for some reason. Why?

Are there any benefits/downsides to installing an Xbox 360 game to my hard drive before playing it?


I have the following code with a bit of a "spaghetti" of templates:  template <typename A, typename B, typename... Args> class C {     /*... */     Bar& getBar() { /* ... */ } public:     template <typename U>     static void Foo() {         A a = getA<U>();         Baz& bar = getBar();         bar.frob<U>(a); /* @@@ */     }     /*... */ }  /* no template */ class D : public C<SomeA, D, const SomeE&> { /* ... */ }  /* no template */ class F : public D { /* ... */}   and when I try to compile a function with the following statement:  D::Foo<F>();   I get the error type name is not allowed, on the line marked @@@. Why would I be getting that? I know you get it when you try to call a function with a type name, but it doesn't look like I'm doing it here.

In templates, where and why do I have to put typename and template on dependent names? What exactly are dependent names anyway?    I have the following code:  template <typename T, typename Tail> // Tail will be a UnionNode too. struct UnionNode : public Tail {     // ...     template<typename U> struct inUnion {         // Q: where to add typename/template here?         typedef Tail::inUnion<U> dummy;      };     template< > struct inUnion<T> {     }; }; template <typename T> // For the last node Tn. struct UnionNode<T, void> {     // ...     template<typename U> struct inUnion {         char fail[ -2 + (sizeof(U)%2) ]; // Cannot be instantiated for any U     };     template< > struct inUnion<T> {     }; };   The problem I have is in the typedef Tail::inUnion<U> dummy line. I'm fairly certain that inUnion is a dependent name, and VC++ is quite right in choking on it. I also know that I should be able to add template somewhere to tell the compiler that inUnion is a template-id. But where exactly? And should it then assume that inUnion is a class template, i.e. inUnion<U> names a type and not a function?


I wonder if it is grammatically fine to use two have/has been in the same sentence?  Example:     After you have been informed that your paper has been accepted…

Is this sentence correct as is, or should I remove the second has since that phrase is connected to the preceding one with and?     As Mr. X has replied your email and has requested the 'PDF files' of the project, here please find attached the requested files.


Some well-meaning person installed Ubuntu on my wife's formerly Windows laptop.  She hadn't used it for years before I married her.  I haven't used Ubuntu since fifteen or twenty years ago myself, so of course the GUI is completely different.  (Actually, I had Kubuntu back then.)  It has auto-login to her admin account but she doesn't know the password.  The search function in the GUI cannot locate any *.jpg in /home although I know there are hundreds of them in one folder on the desktop.  So, I want to open a shell window to use find  There are a lot of icons in the launcher/task bar/dock/whatever it's called but none of them are a terminal emulator.  The "software center" shows several terminal emulators installed, but I can't launch any of them, and the "more info" buttons do nothing.  I want to find all of her pictures to put them on a newer machine and retire this one.  I can pull the disk and hook it up directly to another laptop (where I have root access) but it would be more pleasant to just type commands.  :-)

What is a terminal? How do I open a terminal window? How do I use the terminal?


Is there a proof of the non-existence of semi-simple Lie algebras whose dimensions are, for example, $4$ or $5$?

I came across the claim  which states that there are no complex semisimple Lie algebras of dimension $4$, $5$, or $7$. As the problem suggests, we can take a Cartan subalgebra $H$ and root system $\Phi$ so that $L=H\oplus(\oplus_{\alpha\in\Phi}L_\alpha)$ where $$L_\alpha=\{x\in L:(\forall h\in H)\ [h,x]=\alpha(h)x\}$$  As shown in Humphreys' Introduction to Lie Algebras, every $L_\alpha$ has dimension $1$, so $\dim(L)=\dim(H)+\vert\Phi\vert$. I know $\Phi$ spans $H^*$, so $\dim(H)\leq\vert\Phi\vert$. Furthermore, I know that for any $\alpha\in\Phi$, the only multiples of $\alpha$ in $\Phi$ are $\alpha$ and $-\alpha$. Since $\mathbb{C}$ has characteristic $0$, this implies $\vert\Phi\vert$ is even.  Finally, another fact which may be useful is that given nonzero vectors $x_\alpha\in L_\alpha$ and $y_\alpha\in L_{-\alpha}$, if we take $h_\alpha=[x_\alpha,y_\alpha]\in H$, then $x_\alpha$, $y_\alpha$, and $h_\alpha$ span a three-dimensional subspace of $L$ isomorphic to $\mathfrak{sl}(2,\mathbb{C})$. However, I am not sure how to connect these pieces to give the desired conclusion.  As a follow-up question, would the claim still be true if I replaced the field with an arbitrary field of characteristic $0$, or is it also necessary for the field to be algebraically closed?


What is the C/C++ command for creating a file in a certain directory with the name of a certain variable read from the keyboard ? For example: a text file with the name John previously read from the keyboard, the program will create the file John.txt

I want to create a file using C++, but I have no idea how to do it. For example I want to create a text file named Hello.txt.   Can anyone help me?


I would like to compare two .tex files (before and after modifications) and then edit a .pdf with for instance, the added lines in green and those removed in red.  Is there a simple tool to do so?

I would like to find easy tool, which compares two TeX codes and generates a PDF file of the first code, in which the differences from the second code are marked by a given color. I use winedt 7.0 under windows 7.  I just noticed that latexdiff provides what I need. As far as I understand it is included in Miktex. Is there an interface (menu commands) in winedt 7.0, which allow to work with latexdiff ?


I am using node with mongodb and trying to search a particular string.In db there is a string named "xyz limited (xy)" . if i am using the below regular expression- .*+xyz limited (xy)+.* i am unable to find any match but if i use  .*+xyz limited+.* I got one result. Even if i am searching like .*+(xy)+.* I got one result but for entire string "xyz limited (xy)" no match found.

I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps?


In an exercise I'm asked to prove the following:  Let $f: [a,b] \to \Bbb R$ be a continuous function and $\{x_1,...,x_n\} \subset [a,b]$. Prove that $\exists t \in [a,b]:$ $$f(t)=\frac{f(x_1) + ... + f(x_n)}{n}$$  What I did was the following: I first proved as a lemma that if $\{x_1,..,x_n\} \subset [a,b]$ then $\exists x \in [a,b]$: $$x=\frac{x_1 + ... + x_n}{n}$$ and then used this lemma with the intermediate value theorem to prove the result. Is there a more straightforward and direct way of proving this?

Suppose that the function $f:[a,b]\rightarrow \mathbb{R}$ is continuous. For a natural number $k$, let $x_1,\cdots,x_k$ be points in $[a,b]$. Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$.    This can be proved by showing   $\hspace{130pt}f(a)<\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}<f(b)$  and using the intermediate value theorem to say there exists a point $z\in [a,b]$ such that the statement is true.  I'm not sure how to show this though. Any suggestions?


This is an extension to Partial differential equations by Lawrence C. Evans, page 291, Q15.     Fix $\alpha > 0$, $U$ is a bounded open connected set with smooth boundary. Show that there   exists some constant $C$ such that $\forall u \in W^{1, p}(U)$ with   trace $Tu = 0$ on a relatively open $\Gamma\subset\partial U$ with   $\mathcal{H}^{n-1}(\Gamma)\ge \alpha$,    $$\|u\|_{L^p(U)} \le C \|\nabla u\|_{L^p(U)}$$   [$\mathcal    {H}^{n-1}$ is the $(n-1)$-dimensional measure on $\partial U$.]   The original question solution uses Poincare inequality, and I think this extension also uses Poincare inequality. Basically, the value of the integral of $u$ is bounded by its average value plus its oscillation, and the oscillation is bounded by its derivative through Poincare inequality. Then it remains to bound the average value of $u$ by its derivative.   Since $u$ is anchored at $0$ on $\Gamma$, the average value of $u$ can't deviate too far from zero without causing a big derivative. But how to turn this quantitative is hard.  By mimicking the solution to the original question, I have found that, letting $T: W^{1,p}(U) \rightarrow L^p(\partial U)$ be the bounded trace operator.  $$\|Tu\|_{L^p(\partial U)} \le C\|\nabla(Tu)\|_{L^p(\partial U)}$$  This does not help though, since taking the trace gives the wrong direction for the inequality  $$ \|Tu\|_{L^p(\partial U)} \le C\|u\|_{W^{1,p}(U)}$$  when I really need to bound $\|u\|_{W^{1,p}(U)}$ from above.

The following is the well known  for $H_0^1(\Omega)$:       Suppose that $\Omega$ is an open set in $\mathbb{R}^n$ that is bounded. Then there is a constant $C$ such that   $$ \int_\Omega u^2\ dx\leq C\int_\Omega|Du|^2\ dx\quad \textrm{ for all   }\ \ \color{red}{u\in H_0^1(\Omega)}. $$   Here is my questions:    Can the condition $u\in H_0^1(\Omega)$ be relaxed so that the inequality is still true? More precisely, suppose $H$ is a subspace of $H^1(\Omega)$ such that for any $u\in H$, $u|_\Gamma=0$, where $\Gamma$ is a ([Added:]nonempty) closed proper subset of the boundary $\partial\Omega$ and the idenity is in the sense of trace. In other words, $u$ is only zero on a part of the boundary. Do we still have the Poincaré ineqaulity in $H$?    [Added:] This question is motivated by the following exercise


On Ubuntu 14.04, the internet kept disconnecting. So, I decide to restore connection ability, but I am new to linux. I typed:  sudo apt-get purge network-manager   The wifi icon on the top right was disinterested and I left with no internet. Since I have lots of software installed on my machine, I don't want to reinstall ubuntu. What would be the cure in this situation? FYI, I have another windows PC, so I can download.

Unfortunately, I uninstalled network-manager-gnome using sudo apt-get remove --purge network-manager. I was trying to reinstall it from but without internet connection I cannot do so. What is the solution for this?


I would like to make a request to Stack Overflow's gatekeepers.   I am not very good at asking questions and most of the time I do not know the right questions to ask.  I find it helpful to read lots of different opinions, and to listen to lots of past experiences before making a decision based on various trade-offs.  To that extent I'd really like to see opinions about a particular library, server, API usage.   I find myself using and reading a lot of posts closed as "not constructive". While these posts might be subjective, they are extremely useful to me.   Can another version of Stack Overflow be created which allows opinions about particular technology i.e. Server Fault, Super User?  On a lighter note, it would be ironic if this post is marked as not constructive. :)

Sometimes you just want to let out some steam, and troll about some technology or software. You are not looking for any answers, but for users with similar experiences and interesting stories. So why not create a separate discussion site (trolling.stackoverflow.com?), where you could ask questions like "why do you hate technology X" or "What are the stupidest bugs you encountered in X"?


MWE:  \documentclass{article} \usepackage{enumitem} \newcommand{\bulletlabel}{\raisebox{0.2ex}{\small$\bullet$}}  \begin{document}  \begin{enumerate}[label=\bulletlabel, topsep=0pt, leftmargin=0.3in, rightmargin=0.3in]     \item One     \item Two \end{enumerate}  \end{document}   As you can see, I've parameterised my enumerate environment to get the formatting I want. I use this set of parameters fairly often in my document, together with 2 other sets of parameters.  Is there a quick way for me to replicate this without having to copy/paste or type it out every time? I don't want to redefine the default enumerate environment, as there are 2 other sets of parameters that I need to handle as well. I'm just looking for a quick way to do it.  I tried this:  \newcommand{\paramone}{label=\bulletlabel, topsep=0pt, leftmargin=0.3in, rightmargin=0.3in}   But when I use:  \begin{enumerate}[\paramone]   It fails because it processes it as one parameter rather than 4.  How can I achieve this?

I'm using the following syntax for my code snippets  \begin{minipage}{\textwidth} \begin{lstlisting}[caption=<something>, label=<something>] The REST Endpoint URL     is http://api.flickr.com/services/rest/  To request the flickr.test.echo service,     invoke like this:    http://api.flickr.com/services/rest/       ?method=flickr.test.echo&name=value  By default, REST requests will send a REST response. \end{lstlisting} \end{minipage}   and I would like to have  \begin{code}[<caption>, <label>] ... code ... \end{code}   which would behave exactly the same.   So I tried this thing but it won't compile and I can't spot the problem  \newenvironment{code}[2][]%     {         \minipage{\textwidth}          \lstset{             basicstyle=\ttfamily,             breaklines=true,             captionpos=b,             frame=bottomline,             extendedchars=true         }         \begin{lstlisting}[caption=#1, label=#2]     }     {         \end{lstlisting}         \endminipage     }   Error when running pdflatex  ! Package inputenc Error: Unicode char \u8:�\expandafter not set up for use with LaTeX.  See the inputenc package documentation for explanation. Type  H <return>  for immediate help.


I am facing issue with my vs code application. Not able to run any commands in the terminal except sfdx. Unable to authorize org(Getting error- ended with exit code 127). I googled and tried most workarounds like re installing vs code application enter image description herecode, salesforce CLI, checked with IT team to see if it is firewall or proxy issue. But they confirmed it is not proxy issue . Not sure what is the exact issue here. Can anybody please assist me. sfdx update is also not working. I have attached 2 screenshots of the errors. It would be great if anyone has any inputs on this. When I try to authorize an org it redirects to browser , but when I enter my credentials getting localhost:1717 error as attached in the image. sfdx update : throws sfdx-cli: Updating CLI... ! »   Error: Channel "stable" not found. Please assist. Regards, Madhura

When I use SFDX:Authorize org command, it redirects me to Salesforce login screen. Then I enter my credentials. However I see only white screen and there is no response. From my home machine everything works fine. My OS - Linux Mint 20.


Let $f(x)$ and $g(x)$ be continuous non decreasing functions defined on $\Bbb{R}$ such that $f''(x)= g(x)$ and $g''(x)= f(x)$. Suppose $f(x)g(x)$ is linear in $x$ in $(a,b)$. Then prove that $$f(x)=g(x)=0 \quad\forall x\in (a,b)$$

Let:   $f(x)$ and $g(x)$ be twice differentiable, non-decreasing functions.  $f''(x) = g(x)$ and $g''(x) = f(x)$. $f(x) \cdot g(x)$ is a linear function.    Then we have to show that $f(x) = g(x) = 0$.  I am really not able to do anything useful, any help would be appreciated :)


I am loading an nc4 raster downloaded from a public dataset to QGIS and it first displays an error that the data does not have CRS. Then, it charges the map but the reference point 0 is shifted the map starts in Europe (I see most of the maps start in America on right side). Therefore, when I add an openstreet map layer, both maps don't match. I have tried changing the CRS but when I do that the map appears cropped.  I attach an image of the problem

I have a geotiff raster image that has a coordinate system with longitudes from 0 to 360. The horizontal center of the image is 180 longitude. See image below:    I want to transform it to EPSG:4326 SRS with -180 180 longtitude range.  And I want the center of the image to be at Greenwich meridian (0). I guess this srs is very widely used. I expect the result look like this:    So I use a gdalwarp command to reproject:  gdalwarp -s_srs '+proj=latlong +datum=WGS84 +pm=180dW' -t_srs EPSG:4326 test_col.tif test_4326.tif   But I only get a tiff with bigger dimensions (more pixels) and EPSG:4326 metadata. The image itself looks the same, as the initial one. But I expect it to swap the hemispheres.  How do I gdalwarp an image to be strictly -180 180 EPSG:4326 with the center in 0 longitude?  This is gdalinfo of my initial file:  Origin = (-0.102272598067084,89.946211604095552) Pixel Size = (0.204545196134167,-0.204423208191126) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=BAND Corner Coordinates: Upper Left  (  -0.1022726,  89.9462116) (  0d 6' 8.18"W, 89d56'46.36"N) Lower Left  (  -0.1022726, -89.9462116) (  0d 6' 8.18"W, 89d56'46.36"S) Upper Right (     359.897,      89.946) (359d53'50.18"E, 89d56'46.36"N) Lower Right (     359.897,     -89.946) (359d53'50.18"E, 89d56'46.36"S) Center      ( 179.8975000,  -0.0000000) (179d53'51.00"E,  0d 0' 0.00"S)   This is gdalinfo after gdalwarp     Origin = (-180.102727401932952,89.946211604095552) Pixel Size = (0.091397622896436,-0.091420837939082) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=PIXEL Corner Coordinates: Upper Left  (-180.1027274,  89.9462116) (180d 6' 9.82"W, 89d56'46.36"N) Lower Left  (-180.1027274, -89.9699975) (180d 6' 9.82"W, 89d58'11.99"S) Upper Right ( 179.8211116,  89.9462116) (179d49'16.00"E, 89d56'46.36"N) Lower Right ( 179.8211116, -89.9699975) (179d49'16.00"E, 89d58'11.99"S) Center      (  -0.1408079,  -0.0118929) (  0d 8'26.91"W,  0d 0'42.81"S)


Hello I was wondering where I could start with computing this limit $\sum_{n=3}^\infty \frac{n^2}{2^n}$ . This is a proof based intro analysis class and recently we were taught epsilon neighborhoods but in this situation solving for $n$ doesn't seem like it will work. Any ideas of other ways to go about this ?

I'd like to find out why  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6 \end{align}  I tried to rewrite it into a geometric series  \begin{align} \sum_{n=0}^{\infty} \frac{n^2}{2^n} = \sum_{n=0}^{\infty} \Big(\frac{1}{2}\Big)^nn^2 \end{align}  But I don't know what to do with the $n^2$.


I have a little question about the TOVn flag located in the TIFRn register.  The datasheet says, if the TCNTn counter overflows, then the TOVn flag located in the register TIFRn will be set to 1. (at the same clock cycle the overflow occoured).  The code to handle such event is the following:  /* Check if TOV1 flag is set */ if (TIFR1 & _BV(TOV1)) {     /* Since TOV1 is set, we know we missed an overflow interrupt */      /* Handle the event... */     // ... timer_ovf_cnt++;      /* Prevent ISR to be called, because we already handled the overflow */     TIFR1 = _BV(TOV1); // .. but TOV1 is already set in TIFR1? }   But what confuses me is: why should I set the TOV1 bit when its already set by hardware? Does setting the TOV1 flag in TIFR1 to 1 by user hand disable the timer interrupt? (Even, if the TOV1 flag is already set by hardware?)  EDIT: Found the answer:

Most of the interface devices have various flag bits (that can also raise interrupts if that functionality is provided) used to check the status of the device/operation.  Usually they are cleared by writing a '1' to said bit.  Just some questions regarding this ...   Why are they cleared by writing a 1? I mean if the flag is already set to 1 by the device, won't it make sense to clear it by writing a 0 to it? Lets say i have a 8 bit status register with bits distributed as (picked from datasheet of NRF24L01+)     If bit 5 (TX_DS) gets set (ie. turns to 1) and I want to clear it by writing 1 to it, what value do I write to the register.


I just started using Blender in the last few days and found some of it an exercise in frustration. I've watched a heap of YouTube tutorials on creating EEVEE fluid and I think I get it (for the most part). I can create the Domain and a Sphere as the inflow etc, and it all seems to work. I change the material to glass, etc, and I have all the EEVEE refraction settings set up to work. It all seems to look OK in Replay mode. I even can set up an HDR background. The thing is, is that if I view the fluid animation in Replay mode, it's fine, but if I go and change the Mesh Generator to 'Final' then the whole cube that is the Domain suddenly takes on the material properties of the fluid and just becomes one solid block of glass. And when I play, it just sits there as the block of glass. The same sort of thing happens if from the very beginning I start with 'Modular', and bake the data, particles, mesh etc separately - it all seems to work, but then if I free the data to change something, again, the Domain becomes a solid block of material, and even though it still has Domain properties etc, I can see that in wireframe mode it does not have that little cube in the lower corner that domains seem to have. The whole thing just not seem very consistent. Can anyone help?

Whenever I try to do a fluid simulation, the fluid domain remains visible.  I have tried:ctrl+a-scale, turn on/off visibility for render/viewport  Here's a video demonstrating my problem:   Here's the blend file in case I have messed up some settings:   Thank you for any help!


Let $p$  be a prime number. Prove or disprove that there exists $p\times p$ matrices $A$ and $B$ over a field $\mathbb F_p$ with $AB-BA = I$.   With the aid of MAPLE i was able to find out that this statement is valid for $2$ and $3$. But hadn't been able to prove it theoretically.  This is a homework question and we would receive extra marks if solved. Any hint(s) will be appreciated. Thank you.

Some days ago, I was thinking on a problem, which states that $$AB-BA=I$$ does not have a solution in $M_{n\times n}(\mathbb R)$ and $M_{n\times n}(\mathbb C)$. (Here $M_{n\times n}(\mathbb F)$ denotes the set of all $n\times n$ matrices with entries from the field $\mathbb F$ and $I$ is the identity matrix.) Although I couldn't solve the problem, I came up with this problem:  Does there exist a field $\mathbb F$ for which that equation $AB-BA=I$ has a solution in $M_{n\times n}(\mathbb F)$?  I'd really appreciate your help.


I've been trying to copy a 3D array but it seems like no matter what I do; amending the copy, amends the original as well.  I've tried multiple veriants of the top advice given on  question.  Can anyone explain to me why this code is amending the Clients array, after it's been copied and how to avoid this?  ##### This block is to get and save the information  import csv  import datetime  import glob import os  #import copy  from datetime import timedelta  list_of_files = glob.glob(r'U:\UEL\Sales and Marketing\Relationship - Sales\Team\Edinburgh Clients\Portal backups\Full export archive\*.csv') # * means all if need specific format then *.csv latest_file = max(list_of_files, key=os.path.getctime)  with open(latest_file, newline='') as csvfile:     data = list(csv.reader(csvfile))     Vheaders = data[0]     data.pop(0)  Clients = list(set(list(zip(*data))[9]))  i = 0 for line in Clients:     Clients[i] = [Clients[i]]     i = i + 1  Voids = [] CoTs = []  for row in Clients:     Voids.append(row)  for row in Clients:     CoTs.append(row)  #Voids = list(Clients) #This creates an array of arrays, an array of voids for each client  #CoTs = list(Voids) #Same as above for CoTs  #import pdb #pdb.set_trace()   i = 0  for row in Clients:     for line in data:         #if line[0] == '443179':             #import pdb             #pdb.set_trace()         if (datetime.date.today() - timedelta(days=7)) <= datetime.datetime.strptime(line[2], "%d/%m/%Y").date() < datetime.date.today():              if line[9] == row[0]:                 Voids[i].append(line)             else:                 pass         else:             pass     i = i + 1

I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it?


I was recently looking at why one of my answers turned out incorrectly using this  $(a^n)^m = a^{n\times m}$ .  Trying to solve $(-1)^{3/2} = ?$  I found that    $(-1)^{1/2\cdot 3}$ would become $((-1)^{1/2})^3$. This becomes $-i$.   and    $(-1)^{3*1/2}$ would become $((-1)^3)^{1/2}$. This becomes $i$.   I know how to solve both, and understand the answer should be $-i$.  Why can I multiply as $1/2 \cdot 3$ and not $3\cdot 1/2$ ? Are there additional conditions in the Power Rule that I have missed?

Regarding ,  it is not possible to combine complex powers in the usual way:  $$ (x^y)^z = x^{yz} $$  There was mention of multi-valued functions, is there some theory that makes this all work out correctly?


I need help, I am very new to Ubuntu and am running 14.04 LTS. the problem was that my password login screen would prompt me twice for my password, I could not find a solution so I decided to remove my password login completely. I found a web page telling me how to remove it and I succeeded in doing so, but now it prompts me twice for my keyring password.. I have looked for a solution to this but no luck, I have decided just to go back to having my normal password on the login screen and wait for a solution to the double login problem, but apparently I did not bookmark the site I used to remove it and I cannot remember how to undo it..  Any Suggestions?  output of cat /etc/lightdm/lightdm.conf in terminal is  [SeatDefaults] autologin-user=

I used to have a password prompt but then I, from somewhere in User Accounts, unchecked "Require a password for login." Now, I want Ubuntu to prompt for a password again at login screen, mainly because I have to manually unlock the login keyring whenever I access Dash or other services, which is a pain at best.  I also searched another question, namely . It was of no help because the OP's question is "I have a password but Ubuntu doesn't ask for it."  Also, the two answers provided there don't solve my problem at all. They discuss completely other things.  Is there no simple mechanism? Because intuitively, if there's a checkbox option to bypass password requirement, there should be an equally hassle-free facility to again require the password.


I got two emails this week from Gmail, claiming to have prevented "suspicious sign-in attempts" to my account. These emails came from the address: signins.activityalerts@gmail.com (using the name "Activity Alerts"), and were located in my inbox (not spam, where faked emails should go).  Image of one of the emails:    Text:     [My name redacted],      In the past 48 hours we have detected 6 failed sign-in attempts to your Google Account, [My email redacted]. We have prevented further sign-in attempts from the responsible address in case this was a hijacker trying to access your account. Please review the details of these attempts:      IP Address: [Redacted]      Location: [Redacted]      ISP: [Redacted]      Organization: [Redacted]      If you do not recognize this address, someone else might be trying to access your account. These sign-in attempts were unsuccessful, so no action is required. However, you may wish to reset your password for greater security. Find out how at       If this was you, you may safely ignore this email. The address will be allowed to sign in again within 24 hours.      Sincerely,      The Google Accounts Team   Are these legitimate? I've never seen the email address before, but the only link on it (to learn how to reset my password) goes where it says and doesn't ask for any login information. If it is legitimate, is my account safe or compromised?

I got 3 mails from Gmail today; one each for my 3 seperate Gmail accounts, saying someone from this IP: 109.200.4.130 tried to log-in and it was prevented, and that I should reset my password by following the given link if I don't recognize the address.   Is it real or is it phishing? Is this because I signed into one of Gmail accounts with a VPN? But then again why would I get notices for the other two?


Related:  Alchemical Savant reads:  You develop masterful command of magical chemicals, enhancing the healing and damage you create through them. Whenever you cast a spell using your alchemist’s supplies as the spellcasting focus, you gain a bonus to one roll of the spell. That roll must restore hit points or be a damage roll that deals acid, fire, necrotic, or poison damage, and the bonus equals your Intelligence modifier (minimum of +1).  Spell-Storing Item reads:  At 11th level, you learn how to store a spell in an object. Whenever you finish a long rest, you can touch one simple or martial weapon or one item that you can use as a spellcasting focus, and you store a spell in it, choosing a 1st- or 2nd-level spell from the artificer spell list that requires 1 action to cast (you needn’t have it prepared). While holding the object, a creature can take an action to produce the spell’s effect from it, using your spellcasting ability modifier. If the spell requires concentration, the creature must concentrate. The spell stays in the object until it’s been used a number of times equal to twice your Intelligence modifier (minimum of twice) or until you use this feature again to store a spell in an object.  So does a cure wounds cast using the spell-storing feature, and using the alchemist's supplies to store the spell, benefit from alchemical savant? I think to answer this question a few sub questions need to be answered: Does producing the spell's effect from the spell-storing item count as casting a spell? Because casting the spell is requisite for the alchemical savant feature to take effect. Another requirement for benefiting from alchemical savant is that you cast the spell using your alchemist's supplies as the spellcasting focus. In spell-storing item's case, you would be casting the spell using your alchemist's supplies as the 'spellcasting focus used to store the spell', according to the requirements set forth by the spell-storing item feature. However, does alchemical savant require that you cast the spell using your alchemist's supplies as the 'spellcasting focus used in place of material components'? because being cast from an item means that there are no material components.  Some magic items allow you to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn't expend any spell slots, and requires no components, unless the item's description says otherwise.

In  about a homebrewed Artificer subclass, I was asked in a comment how one of the abilities that modifies spellcasting would interact with casting spells stored within a my subclass's variant version of the Spell-Storing Item feature that all Artificers get. I'd not considered it before, but I suspect it should work the same as a normal spell cast from a normal Spell-Storing Item.  But as it turns out, I'm not actually sure how that works for normal Artificers either. The relevant rules text for the  feature says (from Eberron: Rising from the Last War, page 58, and the latest version of Wayfinder's Guide to Eberron, p. 179-180) says:     While holding the object, a creature can take an action to produce the spell's effect from it, using your spellcasting ability modifier. If the spell requires concentration, the creature must concentrate.    Notable in that rules text is that it does not say that the creature using the object casts the spell, only that it produces the spell's effect. This seems relevant because the top voted answers to  seem to mostly attach to the "cast" terminology used by most magical items that grant extra spells.  In combination with the answers to that question, it seems like the different language (not using "cast") may mean that using a Spell-Storing Item isn't spellcasting, and so no feature that modifies spellcasting will apply. But there's enough ambiguity that I want to ask about it here.  Do an artificer's spellcasting-related features apply to spells they store in an item? Do spellcasting-related features of the creature using the Spell-Storing Item (which may or may not be the Artificer themself) apply?  For a concrete example, if an Artillerist stores Scorching Ray in a wand, staff or rod that they had previously made their Arcane Firearm, would they get an get an extra d8 to add to one of the spell's damage rolls when they use the stored spell?


I hear people saying, "He said it to my wife and I" when they would never say, "He said it to I." Why are people so inconsistent?

I've always been taught to put myself last when referring to myself in the same sentence as others but the usage of "me and..." seems to be everywhere these days. The misuse of the word "me" instead of "I" aside, is there some new rule I haven't heard of? Shouldn't we put ourselves last regardless of the "me"/"I" usage?  Examples of "correct" usage:      My friends and I went for some ice   cream. Did you see my friends and me   at the ice cream stand?   Examples of "incorrect" usage:     Me and my friends went for some ice   cream. Did you see me and my friends   at the ice cream stand?   Note: I was also taught that the only person who could put themselves first was the queen.


How can I access my Ubuntu 18.04 desktop server with Windows? Which RDP and VNC are best suited?

I have Ubuntu installed on my work computer. I am wondering whether I could have access to it from another computer with Windows installed. If so, could you give a step by step guide?