(Proof-verification) Prove that a consistent linear system Ax = b has infinitely many solutions if and only if Ax = 0 has a nontrivial solution

Prove that a consistent linear system $Ax = b$ has infinitely many solutions if and only if $Ax = 0$ has a nontrivial solution.  (Note: A is a homogenous matrix)  In order to prove this, we have to prove two separate statements, namely:  1) If $Ax = b$ has infinitely many solutions, $Ax = 0$ has a nontrivial solution. 2) If $Ax = 0$ has a nontrivial solution, $Ax = b$ has infinitely many solutions.  Proof of statement 1: Since $Ax = b$ has infinitely many solutions, there are at least two distinct solutions, say $y_1$ and $y_2$, where $y_1 ≠ y_2$.  So $Ay_1 = b$ and $Ay_2 = b.$  Then, $A(y_1 – y_2) = Ay_1 – Ay_2 = b – b = 0.$ So $y_1 – y_2 ≠ 0$ is a nontrivial solution to $Ax = 0.$  Proof of statement 2: If $Ax = 0$ has a nontrivial solution $y$, then $Ay = 0$, where $y≠0$. If $Ax = b$, then $A(y+x) = Ay + Ax = 0 + b = b$ According to the uniqueness theorem, $A(αy) = 0$ for any scalar $α$ if $A(y) = 0.$ Therefore, $A(αy + x) = A(αy) + Ax = 0 + Ax = b$ for any scalar $α$ So if $Ax = 0$ has a nontrivial solution, $Ax = b$ has infinitely many solutions.  Proof by contradiction: If $Ax = 0$ has a trivial solution $y$, then $Ay = 0.$ Also, if $Ax = b$, then $A(y + x) = Ay + Ax = 0 + b = b.$ According to the uniqueness theorem, $A(αy) = 0$ for any scalar $α$ if $A(y) = 0.$ However, if $y = 0$, then $αy = 0$ for any scalar $α$, which implies that there is only one solution, not infinitely many.     Could someone verify my proof and see if I have worded anything incorrectly or missed anything?


.on(click) does not work after inserting html to the dom

After manipulating the dom, the click event does not work how can i fix this, i want to achieve a like and dislike action, sojust like the facebook like button on the styles if clicked.  HTML   <button type="button" id="style-like-{{$style->id}}" class="wider-button pb-skeleton-button-transparent pb-skeleton-button-tq-blue"><i class="fa fa-heart"></i> Like</button>   JQUERY  /* like style */  styleId = $('#style-id').val();  styleLike = $('#style-like-' + styleId); styleLikeUpdated = $('#style-like-updated-' + styleId); // styleLike.click(function(){ styleLike.on('click', styleLikeUpdated, function() {    styleId = $('#style-id').val();   styleIdAjax = $('#style-id-ajax').val();   userId = $('#user-id').val();   like = 1;    $.ajax({     url: "style@like@processing",     type: 'POST',     data: {'like' : like, 'user' : userId, 'styleId' : styleIdAjax},     headers: { 'X-CSRF-Token' : $('meta[name=_token]').attr('content') }, context: document.body   }).done(function(response) {  styleId = $('#style-id').val();  swal("Liked", "Wow you really like this style.", "success"); styleLikeButton = $('#style-like-' + styleId); styleLikeButton.detach();  console.log(styleLikeButton);  hrBeforeLikeButton = $('#before-like-button'); hrBeforeLikeButton.after(response.dislikeButton);  likeLabel = $('#like-label'); likeLabel.html(response.likeLabel);   });  });  /* /end like style */  /* dislike style  */  styleId = $('#style-id').val();  styleDislike = $('#style-dislike-' + styleId);         styleDislikeUpdated = $('#style-dislike-updated-' + styleId); // styleDislike.click(function(){     styleDislike.on('click',styleDislikeUpdated, function() {    styleId = $('#style-id').val();   styleIdAjax = $('#style-id-ajax').val();   userId = $('#user-id').val();   dislike = 0;    $.ajax({     url: "style@dislike@processing",     type: 'POST',         data: {'dislike' : dislike, 'user' : userId, 'styleId' : styleIdAjax},     headers: { 'X-CSRF-Token' : $('meta[name=_token]').attr('content') }, context: document.body   }).done(function(response) {      styleId = $('#style-id').val();  styleDislikeButton = $('#style-dislike-' + styleId); styleDislikeButton.detach();  hrBeforeLikeButton = $('#before-like-button'); hrBeforeLikeButton.after(response.likeButton);  likeLabel = $('#like-label'); likeLabel.html(response.likeLabel);   });  });  /* /end dislike style */


In Windows there is a straightforward "Format" option in a flash drive's right-click pop-up menu. Where's that in Ubuntu?


Yes, we all know that there are many questions asked that met the requirements for closing the question as stated here:   I agreed that some questions are totally "off topic".  But in some very rare cases, even though the question totally fits the requirements for closing or the definition of "off-topic", the question has a very high value as the answers gathered will truly benefit all the developers.  And sometimes, a closed question continues to receive lots of votes, or is highly upvoted already.  The number of votes these questions have already speaks for itself - it is a highly valuable question even if it is off-topic.  Closing a highly upvoted question makes no sense.  So, can we have another option for "voting for exception".  Lets say, maybe at 20 votes or 35 votes.  Example:


Define install folder on client ClickOnce

When clients install Click Once published program, it installs to clients'  Appdata folder such as C:\Users\USERNAME\AppData\Local\Apps\{ID here}  In every update it creates new folder named by NEW id..  How do set destination folder static for every update


Coloring a $3\times n$ board using $3$ colors

I have been reading about Combinatorial Material for a while now.  I also solved a few examples. However am stuck at this one.     Find the total number of ways a $3 \times n$ board can be painted using $3$ colors while making sure no cells of the same row or the same column have entirely the same color.  The answer must be computed modulo $10^9 + 7$.   I saw the solutions to $3 \times n$ using  colors but all these had the constraint that no adjacent cells were to have the same color. There's no such constraint here.  So am just not sure how to do this given the center row can have a bunch of options as well.  Thanks for any help.


sudo apt autoremove showing unmet dependencies I can't remove for mongodb

When I run autoremove I get the following. I am in root and have tried running sudo apt install -f without luck. This issue occurred because I ran sudo apt install mongodb and realized that the command installs v 3.6 and I needed the latest version, so I used mongodb documentation to install mongodb 4.4. Any suggestions would be much appreciated! mandi@mandi:~$ sudo apt autoremove Reading package lists... Done Building dependency tree        Reading state information... Done You might want to run 'apt --fix-broken install' to correct these. The following packages have unmet dependencies:  mongodb-org-tools : Depends: mongodb-database-tools but it is not installed E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution). mandi@mandi:~$ apt --fix-broken install E: Could not open lock file /var/lib/dpkg/lock-frontend - open (13: Permission denied) E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend), are you root?


Oracle SQL: Get top 3 results per "category"

I have an Oracle-db-table with multiple sportsteams and sports. Now I need to get the 3 teams (Or less if less than 3 teams) with the lowest id for each sport (based on their id).  (In my example Soccer: Barcelona, Real Madrid, PSG / Hockey: NY Islanders, Nashville Predators, Boston Bruins / Basketball: LA Lakers, Boston Celtics, Cleveland Cavaliers / Baseball: NY Yankees)  My table/entries:  Create Table Teams( teamid NUMBER, teamname VARCHAR(20), Sport VARCHAR(20) );    INSERT INTO Teams (teamid, teamname, Sport) values (1, 'Barcelona', 'Soccer'); INSERT INTO Teams (teamid, teamname, Sport) values (2, 'Real Madrid', 'Soccer'); INSERT INTO Teams (teamid, teamname, Sport) values (3, 'PSG', 'Soccer'); INSERT INTO Teams (teamid, teamname, Sport) values (4, 'Liverpool', 'Soccer'); INSERT INTO Teams (teamid, teamname, Sport) values (5, 'Bayern Munich', 'Soccer');  INSERT INTO Teams (teamid, teamname, Sport) values (6, 'NY Islanders', 'Hockey'); INSERT INTO Teams (teamid, teamname, Sport) values (7, 'Nashville Predators', 'Hockey'); INSERT INTO Teams (teamid, teamname, Sport) values (8, 'Boston Bruins', 'Hockey'); INSERT INTO Teams (teamid, teamname, Sport) values (9, 'Vancouver Canucks', 'Hockey'); INSERT INTO Teams (teamid, teamname, Sport) values (10, 'NY Rangers', 'Hockey');  INSERT INTO Teams (teamid, teamname, Sport) values (11, 'LA Lakers', 'Basketball'); INSERT INTO Teams (teamid, teamname, Sport) values (12, 'Boston Celtics', 'Basketball'); INSERT INTO Teams (teamid, teamname, Sport) values (13, 'Cleveland Cavaliers', 'Basketball'); INSERT INTO Teams (teamid, teamname, Sport) values (14, 'Huston Rockets', 'Basketball'); INSERT INTO Teams (teamid, teamname, Sport) values (15, 'Chicago Bulls', 'Basketball');  INSERT INTO Teams (teamid, teamname, Sport) values (16, 'NY Yankees', 'Baseball');    I have already tried this:  but i still get all the teams.  My Select Statement based on the example:  SELECT t.teamname, t.sport  FROM teams t   LEFT OUTER JOIN teams t2      ON (t.teamname = t2.teamname AND t.teamid <= t2.teamid)  GROUP BY t.teamid, t.teamname, t.sport HAVING COUNT(*) <= 3  ORDER BY t.sport asc;


Sort array by a specific key value in Javascript

I have an array of duplicate strings in no particular order or sorting. const array = ["Train", "Car", "Car", "Train", "Bicycle", "Car", "Bicycle", "Car", "Train"]  I would like to sort the array in a specific order, specifically Train, Bicycle, Car. So it should be sorted. ["Train", "Train", "Train", "Bicycle", "Bicycle", "Car", "Car", "Car", "Car"]  Also, if the array does not contain one of the string, it should still stick to the same order and just skip that string. I've tried a bunch of different ways to sort it, with no luck.


How to Reindex Removed URL in Google WebMaster

I requested from Google Webmaster to remove an URL called example.com/demo some months ago and the URL was removed from the search engine and now the status is expired.  Today I want to reindex the demo page  and have it appear in the search engine again but Google Webmaster is showing "301 Redurect html is corrupted" in the index request  .


Find all primes $p$ such that  $ p^3-4p+9 $ is a perfect square.   I tried a few different values for $p$, namely $2,3,5,7,$ and $11$. The prime $p =2,7,11$ all worked but $p =13$ didn't so it makes me wonder. How can I find all primes such that it is a perfect square?  EDIT: it turns out this is problem P25 in post number #63 at


My mother is given a UK tourist visa for 2 years with a duration of stay as 180 days. It is a c type multiple entry visa. Is this 180 days is the total stay she can take or is it duration of stay per visit.  Thanks in advance for your reply.


xubuntu 14.04 wont recognise my huawei e3372h 4g modem

good morning  I am trying tu use my huawei e3372h modem on my xubuntu 14.04 but it wont work. xubuntu recognise the modem as an usb flash memory. i really need some help  thanks


Lost my ability to add .tex and .sty files when upgrading to texlive 2016 on ubuntu

Using the instructions from  I upgraded from texlive 2014 to texlive 2016 on my second laptop. I did this because I am using some more recent packages and I don't think they will work with texlive 2014.    Now I do not seem to have the ability to add anything to my tex tree, which in my case is located at:  /usr/local/texlive/2016/texmf-dist*  So after adding to my tex tree, I did sudo texhash  kpsewhich picks up the 2016 packages fine, but I do not seem to be able to add anything.  I also tried adding a directory ~/texmf putting the files in there and then doing texhash ~/texmf and still no joy.  sudo texhash produced:  texhash: Updating /usr/local/share/texmf/ls-R...  texhash: Updating /var/lib/texmf/ls-R-TEXLIVEDIST...  texhash: Updating /var/lib/texmf/ls-R-TEXMFMAIN...  texhash: Updating /var/lib/texmf/ls-R...    Does anybody know what can be done to fix the situation?  I would be mightily obliged to any kind person who might help me figure out a solution.  Thanks.   Adding:  alias sudo='sudo env PATH=$PATH'   and then running  mktexlsr as suggested in  had no effect (I logged out and logged in again)


Simply connected does not imply contractible. Is there a nice counter example in $R^2$?

The standard counter example to the claim that a simply connected space might be contractible is a sphere $S^n$, with $n > 1$, which is simply connected but not contractible. Suppose that I were interested in a counter example in the plane - does anyone know of a subset of $R^2$ which is simply connected but not contractible?


Can I put a word count right into my LaTeX book?

I want to say inside my book how many words it has. Are you aware of any packages that can help me with this?


I have a brand new 14.04 LTS Lubuntu install on a Dell Inspiron 8600 which is getting wired internet connection, but not wifi. I've attempted some of the previous resolves for this, but seem now to have created a larger problem. At boot up, I get a system error message the detail of which reads  KernelOops, kernelBUG at include/net/cfg80211.h:3150!   I had previously tried to follow the .  Specifically the section dealing with Installing b43/b43 legacy firmware, but ran up against error messages trying to with the sudo apt-get update command, which ended in the error  E: dpkg was interrupted, you must manually run "sudo dpkg --configure -a"   When I do this, it appears to run a process relating to the Broadcom card, and appears to complete, but ends in Segmentation Fault.  Earlier in the process, I also had experience of the apt command meeting what appears to be an open lock issue, hence I explored , though I cannot tell if I resolved this issue, given the repeated Segmentation fault in response to the sudo dpkg --configure -a command.  With regard to the Broadcom driver, Software and Updates seemed to have installed the Broadcom STA driver and had it in use according to the additional driver info, but wifi was not working, nonetheless.


Show that a homomorphism of groups also has the property that $f(a^{-1})=f(a)^{-1}$ for all $a \in G$.


Does Legolas ever take arrows belonging to the enemy?

Been a while since I last read LoTR but I remember Legolas would sometimes take the arrows he loosed from the enemies' body. Obviously he has a limited supply and there are times where he couldn't retrieve some (enemies are too far high up or below, arrows "might" be damaged but they're Elvish so probably not etc).   Did he ever take and use Goblin/Orkish arrows or would that have been too frowned up as those arrows are used against the Free Races?


Column validation only when creating new item Sharepoint 2010

So I have a date field that needs to be a future date when the item is created.  The formula I have set up for that is:  =[Date Required]>TODAY()   This works well however I am running into an issue.  If the department is updating a List item after the Future Date it will still provide an error.  Is there a formula to use when the column validation can only be active when a new item is being created and not edited?    Thank you


ERROR: java.lang.IllegalArgumentException: invalid listener: null

I  use Database of Firebase to saved values of latitude and longitude, the problem is that send me this error:   Attempt to invoke virtual method 'double android.location.Location.getLatitude()' on a null object reference   I tried with used a class for methods of onLocationChanged but send the same error.  This is my code:  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     //Context Android     setContentView(R.layout.activity_);     Firebase.setAndroidContext(this);     //This  class is to connect with firebase     Firebase referencia = new Firebase(Path.URL_FIREBASE);      lat = String.valueOf(location.getLatitude());     lon = String.valueOf(location.getLongitude());      LocationClass ll = new LocationClass();     ll.setLatitud(lat);     ll.setLongitud(lon);       Firebase NuevaReferencia = referencia.child("Location").push();     NuevaReferencia.setValue(ll);         locationManager = (LocationManager) getSystemService(android.content.Context.LOCATION_SERVICE);      if (ActivityCompat.checkSelfPermission(this, android.Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED && ActivityCompat.checkSelfPermission(this, android.Manifest.permission.ACCESS_COARSE_LOCATION) != PackageManager.PERMISSION_GRANTED) {         // TODO: Consider calling         //    ActivityCompat#requestPermissions         // here to request the missing permissions, and then overriding         //   public void onRequestPermissionsResult(int requestCode, String[] permissions,         //                                          int[] grantResults)         // to handle the case where the user grants the permission. See the documentation         // for ActivityCompat#requestPermissions for more details.         return;     }     locationManager.requestLocationUpdates(LocationManager.GPS_PROVIDER, 0, 0, this.locationListener);         NuevaReferencia.addValueEventListener(new ValueEventListener() {         @Override         public void onDataChange(DataSnapshot dataSnapshot) {             for (DataSnapshot dataSnapshot1: dataSnapshot.getChildren()) {                  LocationClass LL = dataSnapshot.getValue(LocationClass.class);                 String string = "Longitude:"+LL.getLongituded()+"Latitude"+LL.getLatituded();             }         }          @Override         public void onCancelled(FirebaseError firebaseError) {             System.out.println("The read failed: " + firebaseError.getMessage());         }     });


Matrix reciprocal positive $5\times 5$, $6\times 6$ or bigger

Suppose we have $n\times n$ matrix $A$ having only positive elements and satisfying the property $a_{ij}=\dfrac{1}{a_{ji}}$ (a matrix satisfying this property is called a reciprocal matrix).  If its largest eigenvalue $λ_{max}$ is equal to $n$, then the matrix $A$ satisfies the property (consistency property) $a_{ij}a_{jk}=a_{ik}$ where $i,j,k=1,2,...,n$.    I already found an example of $5\times 5$ reciprocal matrix  to show this condition:  \begin{bmatrix}1&1/2&1&1&1/4\\2&1&2&2&1/2\\1&1/2&1&1&1/4\\1&1/2&1&1&1/4\\4&2&4&4&1\end{bmatrix}  It has simple characteristic equation $λ^5-5λ^4=0$, so the eigenvalues of matrix $A$ are $λ=0$ and $λ=5$ and it's shown that $λ_{max}=n=5$.  Is there anyone can help me to give another positive reciprocal matrix example  that has simple characteristic equation and integer number as its eigenvalues ($5\times 5$ or $6\times 6$ or bigger size matrix)?


Velocity of an satellite in an elliptical orbit

Consider some some satellite of mass $m$ around earth, traveling in an elliptical orbit about a focus (earth). Let's suppose at one point $A$ the satellite is a distance $a$ units away the focus at minimum distance, and at another point $B$  it is at a distance of $b$ from the focus, a maximum distance. Let points $A$ and $B$ be collinear with the center of the Earth. When the satellite is at a distance of $a$, it's speed is equal to $v_0$.    Calculate the speed of at the satellite a distance $b$ from the focus.  So first I approached this by the conversion of mechanical energy:  $$\frac{1}{2}mv_0^2-\frac{Gm_e m}{a}=\frac{1}{2}m v_b^2-\frac{G m_e m}{b}$$  I got,  $$v_b=\sqrt{v_0^2+2Gm_e(\frac{1}{b}-\frac{1}{a})}$$  But then I realized conservation of angular momentum gives,  $$mv_bb=mv_0 a$$  $$v_b=\frac{a}{b}v_0$$     I don't see how the two can be equivalent. Is one answer wrong? May someone please explain.


Why do these bash fork bombs work differently and what is the significance of & in it?

I get how a normal fork bomb works, but I don't really understand why the & at the end of the common bash fork bomb is required and why these scripts behave differently:  :(){ (:) | (:) }; :   and   :(){ : | :& }; :   The former causes a cpu usage spike before throwing me back to the login screen. The latter instead just causes my system to freeze up, forcing me to hard reboot. Why is that? Both continually create new processes, so why does the system behave differently?   Both of the scripts also behave differently from  :(){ : | : }; :   which doesn't cause any problems at all, even though I would have expected them to be alike. The bash manual page states that the commands in a pipeline are already executed in a subshell, so I'm led to believe that : | : should already suffice. I belive & should just run the pipeline in a new subshell, but why does that change so much?  Edit: Using htop and limiting the amount of processes, I was able to see that the first variant creates an actual tree of processes, the second variant creates all the processes on the same level and the last variant doesn't seem to create any processes at all. This confuses me even more, but maybe it helps somehow?


I searched on Detextify, but I cannot find the symbol      | |     | |     | |     | | -----------   in LaTeX. There is \perp with only one vertical line. I look for a symbol which looks exactly like \perp, but has two vertical lines.  Thanks in advance.


I want multiple references to appear like [8-10] instead of [8]-[10]. I am using \usepackage{cite}. I tried \usepackage[sort&compress]{natbib} but box brackets [] are replaced with round brackets () which is also undesirable.


There are too many options for "Solution/Answer" environments which we can use and I am adopting  for my "big" project that I am doing.  At the moment, it looks like the easiest one for me to implement, but there is just one function to be explored. How can I show/hide the solution environment, so that I can have a teachers' version and a students' version?  When the solutions are hidden, preferably that the space I used for these content are "reserved."  Thanks.


I have a date that is generated from the user side. However this date is in string format Here is an example below: period = '12-4-2020' how can I convert it to datetime format?


Area of triangle given 3 equations of sides, without finding points of intersection

Can anyone tell me a way to calculate area of a triangle given the equations of its 3 sides without sketching or finding the points of intersection?


Variable declearation and option explicit in vba excel 2013

I wrote some vba codes in excel 2010, it works fine in excel 2010, but now I have excel 2013 on my laptop and whenever I run my code, it gave me "Compile Error; Can't find project or Library" error and highlight the first undeclared variable! then if I declare variable, everything would be ok on that procedure; but I have too much codes and have no time to declare all the variables in it. there is no option explicit in my code and "require variable declaration" in editor option is unchecked. what should I do?


Compactness of the set of $n \times n$ orthogonal matrices

Show that the set of all orthogonal matrices in the set of all $n \times n$ matrices  endowed with any norm topology is compact.


Why does Windows think my phone has 52 GiB of internal disk space whereas my phone sees 64 GB?

From my phone:  From Windows 7 SP1 x64 Ultimate:


SQL Server equivalent to Oracle's CREATE OR REPLACE VIEW

In Oracle, I can re-create a view with a single statement, as shown here:  CREATE OR REPLACE VIEW MY_VIEW AS SELECT SOME_FIELD FROM SOME_TABLE WHERE SOME_CONDITIONS   As the syntax implies, this will drop the old view and re-create it with whatever definition I've given.  Is there an equivalent in MSSQL (SQL Server 2005 or later) that will do the same thing?


Is there a formulation of Noether’s theorem for the path integral formalism?

The notion that conserved quantities (or quantities for which there is something like a continuity equation) correspond to symmetries of the action of a physical system can be formulated in various different realms (classical mechanics, field theory, Lagrangian / Hamiltonian formalism, QM, QFT ...). When it is formulated in QFT / QM we usually employ the operator formalism, and see that operators that commute with the Hamiltonian generate transformations that are symmetries. I'd like to know if there is similar thing in the path integral formulation of quantum mechanics (which essentially doesn't know any operators).


A question should not be deleted by the user deletion algorithm if it has upvoted answers

As I found out earlier today, users who are deleted . This goes against established conventions, for two reasons:  As moderators, we constantly tell users that we won't unilaterally delete questions that have upvoted answers.  Even our . See also .   This 'delete my user' process allows a user to get around this policy by simply deleting their own account. Since nothing stops them from creating another account, it's quite possible this harms our mission of keeping good content around. Also, it allows users to delete their own questions whose answers have received bounties, which can take away the bounty award; this behavior was recently prevented for normal question self-deletions. I propose that we make changes to the user deletion algorithm:  If a user is deleted and they have questions with upvoted answers, those questions are disassociated from the user's account instead of being summarily deleted. Questions without upvoted answers are treated like they are currently: they are deleted when the user is deleted.  This should be the same for destroyed users as well.


I want to play on a LAN server with my brother, but I can't get it to show up on his MultiPlayer menu.  I made the server by clicking "Open to LAN", we both play on the same router, but it still never doesn't show up.  I have tried getting rid of all of the mods on his computer and my computer, both of us are playing on the same version.


Can I truncate very high bars in a pgfplots bar plot?

Please consider this code:  \documentclass[11pt]{article}  \begin{filecontents*}{table.dat} type    v1  v2  v3 v4 v5  v6 v7 t1 0 0 0 0 0 0 0 0 0 0 0 0 0 6 t2 5 17 4 0 0 0 21 0 133 4 91 0 1 93 t3 18 0 0 0 18 0 15 0 0 111 37 0 0 48 t4 12 0 14 0 0 0 18 0 38 0 38 0 0 30 t5 3 69 4 0 64 0 69 0 80 29 6 0 1 21 t6 28 4 10 0 10 0 33 6 58 0 48 0 21 29 t7 25 144 2 0 0 0 180 0 200 0 193 0 52 370 \end{filecontents*}  \usepackage{pgfplots} \pgfplotsset{compat=1.3}  \usepackage{lipsum}  \begin{document}   \lipsum[1]   \begin{figure}[h]     \noindent     \begin{tikzpicture}     \begin{axis}[       ybar=2pt,       bar width=3pt,       width=\textwidth,       height=3cm,       axis lines=none,       ytick=\empty,       symbolic x coords={ t1, t2, t3, t4, t5, t6, t7 }     ]      \addplot table[x=type, y=v1] {table.dat};     \addplot table[x=type, y=v2] {table.dat};     \addplot table[x=type, y=v3] {table.dat};     \addplot table[x=type, y=v4] {table.dat};     \addplot table[x=type, y=v5] {table.dat};     \addplot table[x=type, y=v6] {table.dat};     \addplot table[x=type, y=v7] {table.dat};      \end{axis}     \end{tikzpicture}   \end{figure}   \lipsum[1] \end{document}   As you can see, I have only two very high bars that make everything else indiscernible.     For various reasons I don't like the idea to use a log axis just for these two values.  Is there a way to truncate in some way the tall bars, so that they have a manageable height? In contrast to just tweak the data to have a smaller bar, I'm looking for something that visually hints at this truncation.


Is a person using the pronoun "I" uncapitalized considered rude or uneducated?

Like what i am demonstrating here. To be honest i didn't even know about it until much later when i discovered the Grammarly app and i was like "it even exists?". Now it has quite become my bad habit especially in real-time messaging. I am aware that it is incorrect but when the conversation is going fast i just kind of forget to give it one more keypress and bam there goes my grammar.  Again forgive me if the passage above sounds rude or something. I just want to clarify it once and for all.


Can a single particle create a black hole?

Let us suppose a particle with so much energy $ E= h \frac{c}{\lambda} $ so $ \lambda $ is smaller than Planck's length ?  Would it be possible? I mean if the particle has so much energy then its mass would be very huge and would itself collapse into a black hole  This means that we could not 'see' what is beyond the Planck's length because a very energetic particle would turn into a micro black hole before reaching 'Planck's lenght' am i right?  Is this fact supported by SR and GR? what would be then the Einstein equations ? $ R _{a,b} =0 $?


Formula for the coordinate of the midpoint in spherical coordinate system

Please let me know the formula for the coordinate of the midpoint of 2 points in spherical coordinate system . If possible , I want the answer includes the exact formula as ,   midpoint = point1 + ( point2 - point1 ) / 2 .  Thank you very much  Thank you very much for the answer.  Is it necessary to compute the Cartesian coordinate of the midpoint ? No means to compute directly the spherical coordinate of the midpoint ?  Thank you for the second answer . I am happy to know that I must use Cartesian coordinate system for the purpose .  Please someone let me know how to mark the answer as my accepted answer. There is no button for the purpose on my page .


Disable/modify middle-click-to-paste in X11/Xorg

I am using Slackware 13.1 (kernel 2.6) with FVWM as my desktop manager.  I have frequently had issues when coding where my over-sensitive mouse registers a middle-button (mouse-wheel) click while scrolling with the mouse-wheel.  Is there any way to modify the shortcut so that middle-click no longer pastes using the built-in clipboard with X11/Xorg/Xfree86? I would prefer if it were re-mapped to something like +MiddleClick, or something similar.  I have searched through the forums already, and have found some suggestions using XMODMAP, but none have worked so far.  Thank you all in advance for your time and assistance.


2D Circular View/Background Wrapping SDL for Game

In the games such as Defender (1980 arcade) and Defcon, the player can move/scroll in one direction infinitely because the level/terrain simply wraps over and over again(like if it was wrapped around the side of a cylinder).   I am more interested in the wrapping mechanics of Defcon which wrap(on the x-axis) and zoom the entire level. Here is a link to view the .  To make images(such as a background) wrap is it a per-pixel approach? Is there a function? What methods are there to achieve the circular wrapping of a level?


If I design a PC for use as an NPC, how much XP should he give when killed?

As part of an early quest, my PCs are likely to face off against a wizard.  The problem here is that the stat block for Mage NPCs listed in the Basic Rules has a Challenge Rating of 6, while the PCs are going to be five Level 1s. So, instead of messing with the stat block and risk weakening it too much/too little, I'm choosing to create a Level 1 Wizard PC and use it as an NPC for this quest.  The problem with that is that, as far as I can tell, there aren't any designated rules for assigning either Challenge Ratings or XP values to a PC. So, should I just give the wizard a Challenge Rating equal to his level (and thus have him give 200 xp when killed), or is there a better way to do this?  (This is different from , because he's asking for a way to assign a level to an NPC, while I'm asking for a way to assign an XP value/Challenge Rating to a PC (for use as an NPC). Similar questions, but different.)


I want to prove that $\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes. I know this was proved before for the generalized case of $p_{1},....,p_{n}$ primes here:    And every proof of this kind of equality involves Galois theory but I still don't know Galois theory and I'm supposed to prove this with only basic  Field theory(field extensions, irreducible polynomials, algebraic extensions, etc).  By definition $\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})$ is the smallest field containing $\mathbb{Q}$ and $\sqrt p_{1}+\sqrt p_{2}$, also $\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ is the smallest field containing $\sqrt p_{1}$ and $\sqrt p_{2}$. Or  $$\mathbb{Q}(\sqrt{p_{1}},\sqrt{p_{2}})=\{a+b\sqrt{p_{1}}+c\sqrt{p_{2}}+d\sqrt{p_{1}p_{2}} \mid a,b,c,d\in\mathbb{Q}\}$$   $$\mathbb{Q}(\sqrt{p_{1}}+\sqrt{p_{2}}) = \lbrace a+b(\sqrt{p_{1}}+\sqrt{p_{2}}) \mid a,b \in \mathbb{Q} \rbrace  $$  Also I know that $[\mathbb{Q}(\sqrt p_{1},\sqrt p_{2}):\mathbb{Q}]=4$ from this:    Still don't know how to proceed proving this two extensions are the same.


I'm looking into what upgrade options exist for the  lens. For me, this is a superb general purpose lens with a great walk-about focal range, which is why it's my default, go-to lens - it lives on my camera pretty much full time as part of the default trio I carry (with an EF-S 10-22mm and EF 70-300mm).  However, whilst I'm quite happy with this lens, recently I've been thinking that it would be nice to have something faster for use in lower-light scenarios (indoors, late evening), especially at the long end. I'm aware of the excellently regarded Canon EF-S 17-55mm f2.8, but would ideally prefer a bit more reach. I already have a couple of primes which I would use when I know in advance that such a situation will occur (or if I can carry more of my gear), so I'm only interested in the general purpose scenario.  My camera is a Canon 700D which I've had for just over two years and have no plans to upgrade in the near future. If I were to upgrade, it would not be to full frame (most likely it would be a 760D/77D).  I have seen , but a lot has changed in the 4 years since it was asked, plus the only recommendation was the 17-55mm (probably because there wasn't anything else at the time).  Summary of basic criteria:   Broadly similar focal length range. The wide end is more important to me than the long end, so it needs to be at least 18mm (sacrificing length is OK) Faster than f/3.5-5.6 (variable aperture is fine) Similar or better image quality (sharpness/distortion) 3rd-party lens are fine   I'm not going to put a price limit in place, because I'm OK with buying second-hand and/or waiting for a price drop. Plus, it's good to dream…


Suppose we have $$ x^{2} = (-x)^{2}.$$ I understand that this equation holds because $$\begin{aligned} (-x)^{2} & = (-1\cdot x)^{2} \\ & = (-1)^{2} \cdot x^{2} \\ & = x^{2}, \end{aligned}$$ and so $\sqrt{x^{2}} = \sqrt{x^{2}}$ becomes $x = x$ and everything is fine. But what if we just take the square root first, like so: $$\sqrt{x^{2}} = \sqrt{(-x)^{2}}.$$ Wouldn't this gives $x = -x$, which is a contradiction?


Reversing Extract by Mask in ArcGIS for Desktop?

I have a DEM and I want to apply some tools to it (fill and others). In my DEM I've zones (drawn as mask) that need to be exlcluded from that processing.  I don't want to apply the processing to the whole zone and then put a mask on it.  How do I get the zone where I can apply my tools? My masks are the zones I don't want to process.  I thought about Clip (data management) but it does not work, I also tried to substract this mask from the DEM, without success. Same with "Erase tool", it does not accept my DEM.  I'm using ArcMap 10.2.2.


Disclaimer: I am not asking about speculation on C.C's (or V.V's) real names  In Code Geass, C.C implies that she abandoned her real name and has since forgotten it     Lelouch, do you know why Snow is white? it's because it has forgotten it's name   When talking to Lelouch about if she was human she says that if she wanted to be seen as human she would have a more human name, as if she hinting that her name C.C was something she chose. V.V also shares the same kind of name but nothing is ever said about it.  in Etrian Odyssey Untold, the AI in charge for firing Gungnir and Ricky's friend is named Mike however is spelled as M.I.K.E which stands for Memetic Installation Keeper Engine.  So i am wondering, does C.C and V.V stand for anything?


how to remove html auto fill username & password?

Login form username and passwords are auto filled when i goes to login page.  I do not want to be filled automatically. User only should fill the form manually.  To solve this problem I have used  autocomplete='off'   but still I am getting same issue


What determines which questions are tweeted?

Some (all?) SE sites have a Twitter account.  A selection of questions are tweeted there. Here's an example:    What decides which questions are tweeted?  Is it automatic (done by a bot), or do mods do it manually?  Either way, what are the criteria?   View count? Highly voted question or answer? Evaluation by mods? Unanswered/needs attention? -Other factors?   Are these criteria the same for all SE sites' Twitter, or does it differ?


What is the best way to write a plural of a plural?

What started out as programming has turned into a curious language/grammar question. I'm writing a program and want to clearly specify a variable name. The variable will be a dictionary and each item in the dictionary stores the details of a "revision". variable = {     "revision_a": {"detail_a": "", "detail_b": ""},     "revision_b": {"detail_a": "", "detail_b": ""} }  I want to name the variable revision_details but I don't believe it clearly communicates what the list is. If I saw a variable named revision_details I would assume that it stores details about a single revision. revision_details = {"detail_a": "", "detail_b": ""}  In this case would revisions_details be correct grammar? If this is or something similar correct what is the official term for this and what does the correct version look like? Otherwise would I just need to find a different name like details_of_revisions or just revisions? To clarify, what is the right way to say "revisions details", i.e. multiple details about multiple revisions?


Rudin's PMA Exercise 2.18 - Perfect Sets

I've been working through Chapter 2 questions and have thought about Exercise 2.18 for a while, but couldn't come up with an answer.     Is there a nonempty perfect set in R which contains no rational number?   I had a look  but I think this is wrong because obviously the Cantor set is not a subset of the rationals * (See below). Another thing that the above "solution" states is that the Cantor set only has endpoints but this is not true, e.g. 1/4 is a member of the Cantor set but is not an endpoint (See ).  Other solutions to this question based on a quick google search also give the same - seemingly incorrect - answer.  I have thought about sets like {x: Only 4 and 7 are in the decimal expansion of x, and the decimal expansion of x is non-repeating}, but this set doesn't work because 4/9 is a limit point of this set but is not a member of this set and so it is not a perfect set.  Other ideas I have come up with include starting with the irrational numbers in [0,1] and taking away lots of irrational numbers systematically, but I couldn't make this work.  The denseness of Q has something to do with it but I can't figure it out...  Any ideas?  *I say "obviously" but I should really explain myself here. The Cantor set is a perfect set, and every perfect set is uncountable, but any subset of rationals is countable.


LSI RAID monitor reports "Consistency Check inconsistency logging disabled"

I have a server with a LSI MegaRAID 9261-8i controller. Recently I started getting alerts like this one:  Controller ID: 1  Consistency Check inconsistency logging disabled, too many     inconsistencies on VD: 0 Generated on:Sat May 12 04:06:40 2012   SYSTEM DETAILS--- IP Address: 192.168.1.29 OS Name: Windows 7 x64 OS Version: 6.01 Driver Name: megasas.sys Driver Version: 4.5.1.64  IMAGE DETAILS--- BIOS Version: 2.120.33-1197 Firmware Package Version: 12.12.0-0045 Firmware Version: 3.21.00_4.11.05.00_0x05000000   VD 0 is a RAID mirror containing the system disk.  I have searched and read, but cannot find any trace of how to actually do anything about this. I tried running a scandisk but that did not find anything (as I expected, since scandisk reads the disks as exposed by the controller, right?). The MegaRAID Storage Manager does not as far as I can see have any options for checking or fixing physical disks. The program claims the VD is "healty", and both disks have Error count 0.  Also a bit strange is the System details in the message... The IP address is associated with the RAS (dial in) interface, and the OS should be Windows Server 2011 SBS.  Has anyone else experienced this before? What can be done?


Somehow I created a nondeterministic sh script

I created the following script:  #!bin/bash cat > Top10 <<EOF Linux Mint 17.2 Ubuntu 15.10 Debian GNU/Linux 8.2 Mageria 5 Fedora 23 openSUSE Leap 42.1 Arch Linux CentOS 7.2-1511 PCLinuxOS 2014.12 Slackware Linux 14.1 FreeBSD EOF sed -ri "s/^[^0-9]*$//" Top10 sed -r "s/(.*)([[:space:]][[:digit:]]*.*)$/\2\1/" Top10 | sed -r "s/([[:space:]])([[:digit:]])/\2/" | sed -r "s/([[:digit:]])([[:alpha:]])/\1 \2/" > Top10 sed -r -i "s/(.*)/\L\1/" Top10 sed -r -i "y/[aeiou]/[AEIOU]/" Top10 sort Top10 -g -o Top10 cat Top10   When I run it a few times the following happens:     As you can see sometimes the Top10 file turns out empty and sometimes it turn out the way I needed it to be. I know that the command which replaces the extensions from the end to the front of a line is done poorly. I ran this script on a VMware virtual machine. Could that be the reason?


How to evaluate : $\lim_{n \to \infty}\sum_{k=0}^{n} \frac{{n\choose k}}{n^k(k+3)}$

Usually I would write the given sum in the form $$lim_{n \to \infty}\frac{1}{n}\sum_{r=o}^{n}{f(\frac{r}{n})}$$ and then approximate it with the integral $$\int_{0}^{1}f(x)dx$$ but it doesn't seem so easy to do with this question. The solution says that this sum is equal to the integral: $$\int_{0}^{1}x^2e^xdx$$ without any further explanation. I can't see how they are equal. Any help is appreciated.


Definition of Lebesgue Outer Measure: Given a set $E$ of $\mathbb R$, we define the Lebesgue Outer Measure of $E$ by, $$m^*(E) = \inf \left\{\sum_{n=1}^{+\infty} \ell(I_n): E \subset \bigcup_{n=1}^{+\infty}I_n \right\}$$ where $\ell(I_n)$ denotes the length of interval (bounded and nonempty interval).  Definition of measurable set: A set $E$ measurable if $$m^*(T) = m^*(T \cap E) + m^*(T \cap E^c)$$ for every subset of $T$ of $\mathbb R$.   If $E \subset \mathbb R$ with $m^*(E) = 0$ and $\exists$ finite interval $I,$ such that $E \subset I, $, then is $E$ measurable?  If $E \subset \mathbb R$ with $m^*(E) = 0$, then is $E$ measurable?


Where can I find all tables available to query?

I want to know where the source is to look all tables available to query. For example, a few months back I came to know we can query ApexClass, TestCoverage, etc.  SELECT Id, CreatedBy.Name FROM ApexClass SELECT Id, RecordType.Name FROM RecordType   Is there a way I can know how many tables are available to query through SOQL?


How to make /sbin/shutdown, /sbin/reboot etc. require sudo again in 16.04?

For whatever reason, we do no longer need to be root (or using sudo) to run /sbin/shutdown, /sbin/reboot etc.  This seems to be because those executables are now symlinks to /bin/systemctl which handles everything as normal user.  However, what if I want shutdown and reboot to require root authentication again? How can I achieve this?


I found this odd relationship, $x^2 = \sum_\limits{k = 0}^{x-1} (2k + 1)$.

I stumbled across this relationship while I was messing around. What's the proof, and how do I understand it intuitively? It doesn't really make sense to me that the sum of odd numbers up to $2x + 1$ should equal $x^2$.


How can I filter incoming email based on plus addressing in Gmail?

I currently have some basic filters in Gmail, but the other day I heard someone mention you could use a plus sign in your address to filter incoming email?  Can someone elaborate?


Calculating slope between two points on DEM using ArcMap

I'm a forester, and I do lots of work with LiDAR derived DEM's. I'm looking for a quick-and-easy tool to calculate the slope between two points. The application for this would be drawing a proposed road, where the slope of each road segment must be below a certain value. After quite a bit of searching, I'm unable to find a tool to accomplish this in ArcMap. Can anyone suggest an existing tool to accomplish this? I don't need the slope along the surface of a DEM; I simply need a FAST way to calculate the straight-line slope between two points. Currently, the only way I'm able to do this is as follows:  Load DEM into ArcMap. Create a new shapefile. Create a line feature with a single segment. Get the elevation values for the lines two vertices from the underlying DEM. Use math to calculate the slope of the straight line between the two vertices.  I'm looking for a workflow similar to the following:  Click on "slope" tool. Click on point A, then click on point B. Dialogue box displays the straight-line slope between point A and point B.  I've been looking for an existing solution to accomplish this, and have come up empty handed.


Find the shortest path in a graph which visits certain nodes

I have a undirected graph with about 100 nodes and about 200 edges.  One node is labelled 'start', one is 'end', and there's about a dozen labelled 'mustpass'.  I need to find the shortest path through this graph that starts at 'start', ends at 'end', and passes through all of the 'mustpass' nodes (in any order).  (  /  is the graph in question - it represents a corn maze in Lancaster, PA)


How to find event listeners on a DOM node when debugging or from the JavaScript code?

I have a page where some event listeners are attached to input boxes and select boxes. Is there a way to find out which event listeners are observing a particular DOM node and for what event?  Events are attached using:    Event.observe; DOM's addEventListener; As element attribute element.onclick.


Why there cannot be source-free spherical symmetrical EM disturbances?

On the paper by John Wheeler that first introduced the concept of , he states that when one tries to construct such geons with spherical symmetry, incoherence of the different EM modes is essential since  If all [disturbances] had the same frequency, they would add incoherently to form a single mode of electromagnetic field strenght. But there is no such thing as a nonzero source-free spherically symmetrical electromagnetic field disturbance.  Why is it that there cannot be a "a nonzero source-free spherically symmetrical electromagnetic field disturbance"? Where does this result comes from?


Unable to connect to friend's LAN server

I am unable to connect to my friend's LAN server, on the Technic launcher mod pack, "Vivacity".  When he puts it up, I can't even see it in my server menu. This has also been an issue when trying to use LAN servers for other games, such as Garry's Mod. When I enter the port number and try to direct connect, it says "java.net.SocketException:Network is unreachable:no further information".   I tried using our public IP as the port, in an attempt to add it to my server list, but it says "java.net.SocketException: Connection refused: no further information"  What am I doing wrong?


Describing groups with given presentation? $\langle x,y\ |\ xy=yx,x^5=y^3\rangle$ and $\langle x,y\ |\ xy=yx,x^4=y^2\rangle$.

I'm trying to describe the groups with presentations $\langle x,y\ |\ xy=yx,x^5=y^3\rangle$ and $\langle x,y\ |\ xy=yx,x^4=y^2\rangle$. I have some problems getting a good picture of what they look like...   For the first one, $xy=yx$ allows us to say that any element in the group can be written as $x^iy^j$ for some $i,j$. More precisely, using $x^5=y^3$, we can always reduce $j$ to $0,1$ or $2$, whereas $i$ could have any value. So I was thinking about $\mathbb{Z} \times C_3$. But the other way around (reducing $i$ this time) it's also $C_5 \times \mathbb{Z}$. But then I should be able to prove that both descriptions are equivalent, which I can't do...  For the second, I proceed similarly and get to the same kind of problem...  Could you tell me where I'm going wrong?  Thank you very much in advance!


I don't understand why the app closes:  java.lang.NullPointerException: Attempt to invoke virtual method 'double android.location.Location.getLongitude()' on a null object reference     private void getWeatherInformation() {         compositeDisposable.add(mSevice.getWeatherByLatLhg(String.valueOf(Common.current_location),                 String.valueOf(Common.current_location.getLongitude()),                 Common.APP_ID,                 "metric")                 .subscribeOn(AndroidSchedulers.mainThread())                 .subscribe(new Consumer<WeatherResponse>() {                     @Override                     public void accept(WeatherResponse weatherResponse) throws Exception {                         Picasso.get().load(new StringBuilder("https://openweathermap.org/img/wn/")                                 .append(weatherResponse.getWeather().get(0).getIcon()).append(".png").toString()).into(imageWeather);                          cityName.setText(weatherResponse.getName());                         description.setText(new StringBuilder("Weather in ")                         .append(weatherResponse.getName()).toString());                         temperature.setText(new StringBuilder(String.valueOf(weatherResponse.getMain().getTemp()))                         .append("°C"));                         dateTime.setText(Common.convertUnixToDate(weatherResponse.getDt()));                      }                 }, new Consumer<Throwable>() {                     @Override                     public void accept(Throwable throwable) throws Exception {                         Toast.makeText(getActivity(), ""+throwable.getMessage(), Toast.LENGTH_SHORT).show();                     }                 })          );


Internet is working, but Firefox 67 browser cannot connect after update

I have been using Firefox on Ubuntu 18.04 for several weeks. I currently have firefox 67.0 (freshly updated).  Since the update, firefox cannot connect to the internet anymore. The internet is working fine. I am writing this post from the Opera browser the I installed on Ubuntu 18.04 after the problems with Firefox.   I tried to follow the suggestions of this . Explicitly I tried the following:   Change proxy setting, in about:preferences Network Settings. I tried the options "no proxy", "Auto-detect proxy" and "Use system proxy" (the latter was the default). In about:config I set the "network.dns.disableIPv6" to TRUE In about:config I set the "network.dns.disablePrefetch" to TRUE   The issue seems firefox-specific. Opera does not give any problem. Pinging to www.google.it works fine (so no DNS problems).   I am fine using Opera, but I would also like to understand hwo to fix the issue in Firefox!


Adding dashicon fonts to the admin of pre 3.8 installs

I've started using the dashicon fonts in my theme options page for WP 3.8+ users. To take care of users on < 3.8, I've added the dashicon fonts to my theme folder and also an entry at the top of my custom admin stylesheet:  @font-face {     font-family: 'dashicons';     src: url('fonts/dashicons.eot'); }  @font-face {         font-family: 'dashicons';         src: url(data:application/x-font-woff;charset=utf-8;base64,xxx) format('woff'),         url('fonts/dashicons.ttf') format('truetype'),         url('fonts/dashicons.svg#dashicons') format('svg');     font-weight: normal;     font-style: normal; }   (I've left out the base64 encode for brevity)  This works great, however, I'm getting a bit of strange behavior with the fonts. When I leave the admin open in a tab and go away for a bit, then come back, every once in a while, the webfonts have turned to squares, as if the font is missing.  This does not happen every time. It appears to be somewhat random.  In those cases, simply doing a mouseover the page usually returns the webfonts to their proper symbols.  The screenshots below show the issue. The first screenshot is what I see when the problem occurs. The second screenshot is what I'm expecting to see when things go well.   Notice in the first shot, how the wordpress labels themselves have gone to a default serif font.


How to bind 'tab' and 'shift+tab' in GNU screen?

How do I bind the keys Tab and ShiftTab in screen? My problem is that I don’t know what to pass to the screen bind command to designate these keystrokes.  BTW, I’m aware of  but the answer is not there.  All of the following fail with the error -X: bind: character, ^x, or (octal) \032 expected:  screen -X bind "\033[Z" focus up screen -X bind "^[[Z" focus up screen -X bind "\t" focus up screen -X bind \033[Z focus up screen -X bind ^[[Z focus up screen -X bind \t focus up   Same thing if I hit CtrlA: to input the command.


Java, declaring static methods in interface

This subject already has questions and answers, none with conclusive results. If this is not possible, then can someone determine the best workaround? Some of the answers say that this is possible with Java 8, but my IDE (eclipse) is still showing errors even though it is set to compiler compliance 1.8. If someone can get it to work on their system, let me know and I'll fix the problems with my system.  Problem: I need to create an interface with both static and non-static methods. An example of this:  // I need to create an interface with both static and non-static methods. public interface TestInterface {      // No problem     int objectMethod();      // static is an illegal modifier in an interface     static int classMethod(); }  // TestClass is one of many classes that will implement the interface. public class TestClass implements TestInterface {      // static and non-static variables are no problem     private int objectVal;     public static int classVal;      // this method has no problem     public int objectMethod() {         return objectVal;     }      // this one has problems because it implements a method that has problems     public static int classMethod() {         return classVal;     } }   And I need a class that will use classes that implement the interface  // a class that will use classes that implement from the interface // what is the syntax for this? my IDE doesnt like the implements keyword public class TestGeneric <T implements TestInterface> {      // stored instances of the class     private T t;      public void foo() {         System.out.printf("t's value is: %d\n", t.objectMethod());         System.out.printf("T's value is: %d\n", T.classMethod());     } }   The only problems in the above code are with the static methods. The only workaround I can think of is to not declare any methods as static, but use them in the way most similar to static use.


Matrix multiplication is not commutative. If however $$ AB = BA $$for the matrices A and B with $$A, B \in M_{nn}(\mathbb{K})$$  Can I conclude that A has to be of the form $$A = B^{Ad} = det(B)B^{-1}$$? Or when is $$ AB = BA $$


Linux/bash does not execute the executable that "which" tells me

Observation: I have an executable named foo, located in /b/foo. It is compiled against an old header of a dynamic library, causing it to segfault when executed:  $ foo Segmentation fault. // Expected behaviour.   Now, I compile a new version of foo to /a/foo against the new dynamic library that should execute just fine. Directory a/ is in my $PATH before b/, so /a/foo should be selected:  $ which foo /a/foo   When I execute foo, the following happens:  $ foo Segmentation fault.   Therefore, it seems that /b/foo gets executed, whereas "which" tells me that /a/foo should be executed. To make things weirder, when I run the full path $(which /a/foo), things run fine:  $ /a/foo OK!  $ cp /a/foo . $ ./foo OK!     To go yet one step further, if I now delete /a/foo:  $ rm /a/foo   Then /b/foo must surely be chosen, right?  $ which foo /b/foo $ foo bash: /a/foo: No such file or directory $ $(which foo) Segmentation fault. // Expected result.   Nope!  Fix: Source .bash_profile and .bashrc and the problem disappears.  Reproducibility: Every time. Just remove /a/foo, source ~/.bash_profile, create /a/foo, and the above observation re-occurs.  Question: Does anyone have an idea what went wrong here?  Hypothesis: "which" is up-to-date, but the system chooses based on "what was used to be the case". In my example above, /a/foo did not yet exist when the terminal was opened: I had only just created it. Therefore, when /a/foo was created, "which" did detect /a/foo, but the system still chose /b/foo, because it was somehow out of sync? But why is the system out of sync?


univariable significance lost when combining variables together

Analysing data from a past experiment I found that size of animals and a level of serum biomarker were associated with time to death when considered separately. Though when combining them in a cox model both the variable lost significance. How should I interpret and report this? Is it correct (and also relevant in scientific terms) to affirm that univariable association is lost when analysing both variables in a multivariable cox model?


Is it possible to minimize by mouse click?

Is it possible to minimize or close any application or browser by mouse click.  If I click any icon on launcher then the application opens but if I click on the same icon then it does not get close or minimize.  I need to go to the minimize or close button for the same.  Please let me know.


Do Stack Exchange sites allow editing of comments and posts from other users?

Possible Duplicate:         Is this normal behavior in Stack Exchange sites that after just signing up one can edit not only his/her own comments / posts, but also others' comments / posts?  If so, then the Q&A does not look safe to me. Imagine someone maliciously modifying a post and bringing bad reputation on a Q&A member.  Can you check this and perhaps fix it?


Remove an item on list while doing foreach loop

I want to remove an object in a list while doing foreach loops Here's the code List<Book> listBooks = response.body().products;             for (Book book: listBooks) {                 if(!book.category.equals("scifi")){                     listBooks.remove(book);                 }             }  listBooks.remove(book) doesn't work.


Ubuntu boot process hangs on starting snappy daemon

TL;DR: Ubuntu boot hangs on starting the snappy daemon, takes roughly 5min to boot, reinstall doesn't fix, issue is caused by an update.    Backstory: I installed the vanilla-gnome-session and after deciding I didn't like it removed it again. I later had installed and removed ubuntu-gnome-session hoping that it would bring back the old login screen. After that I did an update before reboot. Upon shutdown the loading screen for ubuntu gnome appeared and was running a kernel upgrade. Then when booting again the loading boot screen for ubuntu froze, switching to TTY2 revealed that it hung on three jobs:  A start job is running for * Snappy daemon * Wait until snapd is fully seeded * Hold until boot process finishes up   It takes roughly 5min until this process is finished.  After some unsuccesful troubleshooting decided to reinstall. I first used the reinstall option from the live install disc and after finishing the PC booted fine even after a reboot. However as soon as I ran apt update && apt upgrade it would hang again.  Some goes after doing a complete reinstall (choosing "erase disk and install" on the install disc)


What are the advantages and disadvantages of transferring to a secondary vs. a long primary?

The conventional wisdom in homebrewing has been challenged in recent years.  This wisdom held that a beer should be transferred from the primary fermentation vessel to a secondary one after 7-10 days.  In recent years, many homebrewers have advocated for leaving the beer in primary until packaging, rather than racking to a secondary fermenter.    What are the advantages and disadvantages of the two methods? Are there limits to how long a beer should remain in primary, in the long primary scenario?


I need a VPS on Amazon AWS that can run Chrome and work with files

I am new to working with VPS (I'm a web developer), and I need a VPS from AMAZON AWS that can run Google Chrome, and download files (not big files).  Currently I have the free teir of Windoews Server 2008 R2 Base (Currently selected: t2.micro (Variable ECUs, 1 vCPUs, 2.5 GHz, Intel Xeon Family, 1 GiB memory, EBS only) - which I can't do anything there... So I guess I'll have to get myself a paid server.  Which AMI windows server fits my needs best(the last one I used is Windoews Server 2008 R2 Base)?  And whay type of AMI should work for me (currently using the free teir: t2.micro (Currently selected: Variable ECUs, 1 vCPUs, 2.5 GHz, Intel Xeon Family, 1 GiB memory, EBS only)?


Why global.asax Application_Error method does not catch exceptions thrown by ASMX service?

And how to fix it. I'd like to log every thrown exception for maintenance purpose.


How do i regain all my storage? I was running linux mint on MacBook Pro and have now gone back to Mac OS big sur and only have half the storage?

Last login: Mon Jun  7 22:43:40 on ttys000 samadams@Sams-MacBook-Pro-2 ~ % diskutil cs list No CoreStorage logical volume groups found samadams@Sams-MacBook-Pro-2 ~ % diskutil list /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *121.3 GB   disk0    1:                        EFI NO NAME                 536.9 MB   disk0s1                     (free space)                         60.5 GB    -    2:                 Apple_APFS Container disk1         60.1 GB    disk0s2  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +60.1 GB    disk1                                  Physical Store disk0s2    1:                APFS Volume MacOS Big Sur - Data    30.0 GB    disk1s1    2:                APFS Volume Preboot                 233.2 MB   disk1s2    3:                APFS Volume Recovery                652.6 MB   disk1s3    4:                APFS Volume VM                      1.1 GB     disk1s4    5:                APFS Volume MacOS Big Sur           24.4 GB    disk1s5    6:              APFS Snapshot com.apple.os.update-... 24.4 GB    disk1s5s1    7:                APFS Volume Untitled                860.2 KB   disk1s7


How to append two argument items into a stack (Python3)

So I'm currently practicing DFS & BFS approaches to binary trees and I am confused on how multiple arguments are being passed into the .append statements below. I know that .append can only take one argument and that when the the arguments are encapsulated in parenthesis they are treated as so, but what does it mean when you encapsulate them?   class Solution:     def maxDepth(self, root):         """         :type root: TreeNode         :rtype: int         """          stack = []         if root is not None:             stack.append((1, root)) # <---- Here          depth = 0         while stack != []:             current_depth, root = stack.pop()             if root is not None:                 depth = max(depth, current_depth)                 stack.append((current_depth + 1, root.left))  # <---- Here                 stack.append((current_depth + 1, root.right))  # <---- Here          return depth   To reiterate, what does .append((arg1, arg2)) mean? How are those args treated and what logic is behind it?


Recent Ubuntu Installation - No Wireless Network

I just recently installed Ubuntu 16.04 LTS as a dual boot with my Windows 7 computer. I got Ubuntu installed, but I can't connect to my wireless network. I tried checking out the network manager window, but the only option available is a wired connection.  I tried going through questions posted on here, but all the commands lead to dead ends such as "no such package exists" or whatever. The router is also in my landlord's control on the other side of the house, so connecting it via an ethernet cable is a no-go.  Can someone help me out? I'm stuck and have no idea how to get this thing working. :S


TextView.setText() Null Pointer Exception

I'm currently facing a problem when trying to edit the text of a TextView in the OnCreate method of an Activity. As I understand, setContentView must be called before trying to change the text, however I am still having trouble with this.  Here is the code in question :   @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_dash_board);      DrawerLayout drawer = (DrawerLayout) findViewById(R.id.drawer_layout);     ActionBarDrawerToggle toggle = new ActionBarDrawerToggle(             this, drawer, R.string.navigation_drawer_open, R.string.navigation_drawer_close);     drawer.addDrawerListener(toggle);     toggle.syncState();      NavigationView navigationView = (NavigationView) findViewById(R.id.nav_view);     navigationView.setNavigationItemSelectedListener(this);      userEmailtext = (TextView) findViewById(R.id.emailText);     mAuth = FirebaseAuth.getInstance();     mUser = mAuth.getCurrentUser();     userEmailtext.setText("This Does Not Work"); }   This Activity includes the Android Studio default sliding menu. The aim of this setText is to change the email address text of the sliding menu. I believe the problem may lie in the fact that the sliding menu is part of a different layout file, meaning there is no "emailText" textview leading to the null pointer exception, however I am still not sure how this would be rectified.  Any help is appreciated.


Derivative of series and series of derivatives

Let $f_n(x)$ be real functions. Given that the derivatives exist, and that the sums converge, is the following true? If not, what is a counterexample, and when is it true?  $$\frac{d}{dx}\sum_{n=1}^{\infty} f_n(x)=\sum_{n=1}^{\infty} \frac{d}{dx}f_n(x)$$


Custom cross-reference formats (e.g. "Equation 1" instead of just "1")

I have an equation system set up as below. When I reference it however, ie. with \ref{eqn:surfacetension}, it only prints the number '1', and not 'Equation 1'. How can I modify the code to do that? I apologise if I left out any key bits of code, I only put in the bits that I think are relevant  \documentclass[a4paper,12pt]{scrartcl}  \usepackage{amsmath}  \makeatletter \let\mytagform@=\tagform@ \def\tagform@#1{\maketag@@@{\bfseries(\ignorespaces#1\unskip\@@italiccorr)}\hspace{3mm}} \renewcommand{\eqref}[1]{\textup{\mytagform@{\ref{#1}}}} \makeatother  \begin{document}  \begin{equation} \Delta P = \frac{2\gamma}{r}  \label{eqn:surfacetension} \end{equation}  \end{document}


How to avoid the wrinkle at the poles of the UV sphere?

When I create a UV sphere and add the subdivision surface modifier, the following wrinkle appears.    How can I avoid it?  I've read the article  but there seems to be no clear solution.  UPDATE 1  I've used the word 'apply' in the first sentence of the initial version of this question. It's misleading since I want to preserve the modifier without 'applying' it. Rather, what I meant is 'adding' the modifier.  UPDATE 2  I followed josh sanfelici's solution, but still there is an artifact at the pole.  Here is the screen: (A rendered view with a sun lamp)    Maybe it's the limitation of the general-purpose subdivision modifier.  BTW, when the cast modifier is added after the subdivision modifier, the sphere becomes perfect (even for my original wrinkled sphere).  But since I want to edit the resulting sphere (for example, scaling X, Y, etc) while modifier is added but not applied, it's not usable.


How can I make an infinte terrain with object pooling in Unity?

I am currently making a 3D endless runner game in unity in C#. I now need to make the platform(3D Tiles) infinite but I don't know how. I already did some research but I don't find the right tutorial.   I already asked a  and I got the answer that I need to do it with object pooling but I don't find any good tutorial for object pooling. Does someone know how to make an infinite terrain with object pooling in unity?  Thanks  using System.Collections; using System.Collections.Generic; using UnityEngine;  public class TerrainScript : MonoBehaviour {     public GameObject[] tilePrefabs;      public Transform playerTransform;     private float spawnZ = 4500.56f;     private float tileLength = 2.0f;     private int amtOfTilesOnScreen = 2;      void Start()     {         for (int i = 0; i < amtOfTilesOnScreen; i++)         {             SpawnTile(0);         }     }      void Update()     {         if (playerTransform.position.z > (spawnZ - amtOfTilesOnScreen * tileLength))         {             SpawnTile(0);         }     }      private void SpawnTile(int prefabIndx = 0)     {         GameObject go;         go = Instantiate(tilePrefabs[prefabIndx]) as GameObject;         go.transform.SetParent(transform);         go.transform.position = Vector3.forward * spawnZ;         spawnZ += tileLength;     } }


Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable

Recall that a countable set $S$ implies that there exists a bijection $\mathbb{N}\to S$. Now, I consider (0,1). I want to prove by contradiction that $(0,1)$ is not countable.  First, I assume the contrary that there exists a bijection $f$, and I can find an element in $S$, but not in the range of $f$. But I can't find such element. How can you construct such $f$?


Creating arabic and alpha theorem numbering

For my Thesis I am stating a number of Theorems (Working Propositions actually). Using the theorem environment I do get some thing like:  WP1 My first WP  I create this by using   \begin{WP}    my first WP \end{WP}   I have defined the WP environment with  \newtheorem{WP}{Working Proposition}   However if I add a second (and a third etc) the numbering continues 1 , 2 ,3 etc  Occasionally I would like to be able to creat a WP2a and WP2b and then continue with 3.  When and where I extend to the a,b,c etc is random.  Help is appreciated.


How can I modify the size of swap with LVM partitions?

I'm trying to add/modify a swap partition on my LVM-formatted hard disk by using GParted from a LiveCD.  I only see one big partition taking up the whole disk.    Is there a hidden swap?    Does an LVM-formatted system even need a swap?  I'm using Ubuntu 12.10.


So basically what I'm trying to do is add an object to position 0 of an array then add another object and once I add that one I want to make sure that the NEW added object doesn't have the same first or second parameter but I keep getting a null pointer exception if I try to do that and I've been at it for hours and I can't seem to find the issue.   this is the first part of my method    public boolean hireUndergraduateTA(String firstName, String lastName,          double hourlySalary) {       boolean result=false;        /*     int nextPosition = 1;      boolean k = (taList[nextPosition].getTAFirstName()).equals(firstName);      boolean j = (taList[nextPosition].getTALastName()).equals(lastName);       */       for (int i = 0; i<taList.length; i++){               taList[i] = new TA(firstName, lastName, hourlySalary);            if (firstName.equals(null)||              lastName.equals(null)||             (hourlySalary<=0)){               taList[i] = null;              result = false;           }          /*          if (k || j == true){              taList[nextPosition] = null;              result = false;            }          */          else {               result = true;               numOfUndergradTAs++;          }       }       return result;    }   the commented out portions are the ones that are giving me the null pointer exception. I guess my question is this: how do I syntax-tically (word?) tell the commented out portions to not check until there's more than one object in the specific array?


How can I improve My reputation on Stack overflow?

I am new on this website. I have thirteen reputations on this website. I wants to ask that, how can I improve my reputations ? Sometimes I want to vote up for any question but website don't let me do that. Sometimes I want to share photo and solution for someone answer it don't allow me to do that. I always post productive questions and also make useful answer. Is there any way or tip so that, I can improve my reputation and become useful member for others ?


How can I use Windows in Ubuntu (not virtualized) to run an Adobe program?

I would like to use Windows (not virtualized) on a system based on Ubuntu 18.10. I need to use some Adobe program that I cannot use on Ubuntu, but at the same time I want the security that only Ubuntu can provide.  So I was thinking that I could run my Ubuntu system and within it run a Windows system, as there would be something like a "main system" (Ubuntu) from which I could use Windows. Is it possible?  I know that using Ubuntu (as an app) on Windows is possible, but I would like to know if the opposite is possible too.  Thanks!


Move position of div when breakpoint is triggered

I'm trying to create a layout where two divs are side by side when the page is larger than 900px but when the breakpoint is triggered then the divs are displayed ontop of each other.   Original layout:  --------   ------- | div 1  | | div 2 |  --------   -------  <900px:  ------- | div 2  |  --------   ------- | div 1  |  --------    This is really tricky to recreate because div2 has to end up on top of div1.  Current solution (sent via message to me). I'm not too bothered about the specific 900px breakpoint so I just used bootstrap md.

       div 2

       div 1


LaTeX - Let table be page wide in the IEEE template

I'm currently using the IEEE template, as it allows for the use of floats within a two column document. I am trying to make a table the width of the page (spanning both columns) at either the top or the bottom of the page. The code that I am using works fine in a normal document, but it fails in the IEEE template. Is there anyone who knows how to place a page wide table in this?  \begin{table}[b] \caption{A summary of the EMG sensor, marker cluster and probe position locations} \begin{tabular*}{\textwidth}{c @{\extracolsep{\fill}} ccccc} % The contents of the table are not that interesting \toprule {EMG Sensors} & {Marker Clusters} & \multicolumn{3}{c}{Probe points} \\     \midrule     Biceps femoris (L/R) & Foot (L/R) & Shoe tip (L/R) & Calcaneus (L/R) & Troch. major (L/R)\\     Rectus femoris (L/R) & Lower leg (L/R)  & Calcaneus shoe (L/R) & Maleolus lat. (L/R) & SIAS (L/R)\\     Adductor longus (L/R) & Upper leg (L/R) & CM1 shoe (L/R) & Maleolus med. (L/R) & SIPS (L/R)\\     Gastrocnemius medialis (L/R) & Pelvis & CM5 shoe (L/R) & Caput fibula (L/R) & Xiphoid proc.\\     Tibialis anterior (L/R) & Trunk & CM1 (L/R) & Epicondylus lat. (L/R) & Jugular notch\\     Gluteus medius (L/R) & Head & CM5 (L/R) & Epicondylus med. (L/R) & C7\\       &  & Occiput & Head vertex & Sellion \\     \bottomrule % but I included it to be complete as complete as possible \end{tabular*} \end{table}   The weird thing is that it does try to put it at the bottom of the page, but it's overlapping with the text that's already there.


How can I find the maximum value of $\frac{y}{xy+2y+1} + \frac{z}{yz+2z+1} + \frac{x}{xz+2x+1}$?

$x$,$y$ and $z$ are positive real numbers.  We have to show that $$\frac{y}{xy+2y+1} + \frac{z}{yz+2z+1} + \frac{x}{xz+2x+1}\leq\frac{3}{4}.$$ I am the equivalent of a senior in high school  (not a US citizen) and we didn't take a multi-variable calculus course. Is there a way this could be solved without it?   (It's a problem I found in a math olympiad somewhere,but I can't remember which one.)


How can I remove the first line of a text file using bash/sed script?

I need to repeatedly remove the first line from a huge text file using a bash script.  Right now I am using sed -i -e "1d" $FILE - but it takes around a minute to do the deletion.  Is there a more efficient way to accomplish this?


There are some excellent posts on various sites - both questions and answers; Of course, for the more technical it's harder to appreciate them but I would love to have a newsletter of "the best of SE".  Couple of posts I would like to see there:       Because someone personally checked the place for an answer and that's just the last two days.


I've installed Kali Linux (normally I use ArchLinux, but I need Kali for work) and every time I want to upgrade, a few packages can't upgrade and are kept back. To force them to update I have to manually select them and perform an installation.  To update, I use the following command:  apt-get update && apt-get upgrade   Even from a clean installation the problem persists. Is there someone with the same problem? How can I solve it permanently?


extremely strange logistic regression results

I am very new to r and statistics so excuse me if the answer to my question is very obvious. I have surveyed 64 people on their Facebook behaviour related to their political participation. One of my independent variables is how many Facebook friends the people have and i divided their answers into 3 categories: 0-500= 1, 500-1000= 2 and 1000+ = 3.The independent variable is whether or not they voted, coded 0= no and 1= yes. I have been trying to run this as a logistic regression but for some reason it is not working. This is my code:  #fit bivariate logistic regression model for amount of friends and voting fit3 <-glm(vote~as.factor(friends), family=binomial(link="logit"), data=politicalparticipation) summary(fit3) exp(coef(fit3)) abs(1-exp(coef(fit3)))*100 sjt.glm(fit3)   However, i continuously get the error message that there is a warning:  Warning messages: 1: glm.fit: fitted probabilities numerically 0 or 1 occurred   If someone could help me out, that'd be great!


I am doing the following exercise and I have some part of it Create a new column with a 1 if the country's % Renewable value is at or above the median for all countries in the top 15, and a 0 if the country's % Renewable value is below the median. My code: df = answer_one() print(df) mean = df['#% Renewable'].mean() df['ratio'] = df['#% Renewable'] > mean   I want to know if there is a way to create in one line a ternary operator, something like: If renewable > mean then 0 if renewable < mean then 1.  but not sure how to achieve this on python in one line


Flying with domestic with ID that expires on the trip

I live in Texas and I'm 17. A lot of my family and friends live in California. For my 18th birthday my family planned a trip to California. The problem is my license expires on my 18th birthday while I'll be in California, and with Texas I can't apply for my normal license until my 18th birthday or afterwards.  So since I'm turning 18 while on my trip and my only real form of ID will expire during it, will I have problems on my return flight using a recently expired ID? Will having my birth certificate, social security card, and diploma help?  Thanks for any answers you can provide!


Let $p$ be the probability that a man aged $x$ years will die in a year time.Then what is the probability that out of $n$ men $A_1,A_2,....,A_n$ each aged $x$ years,$A_1$ will die and will be the first to die?  The probability that a man aged $x$ years will die in a year time$=p$  The probability that a man aged $x$ years will not die in a year time$=1-p$  But from here on,i got stuck.Some hints and suggestions are welcome.


Factorize $z^5 - 1$ using $\cos$ function

This is a problem from an exam, with which I am struggling for over a month, and trying over and over. I've given up... The problem states (and my exam is tomorrow where I could expect even same problem):  $(a)$ Prove that: $$z^5 - 1 =  (z-1)(z^2 +2z\cos(\frac{\pi}5) + 1)(z^2 - 2z\cos(\frac{2\pi}5) + 1)$$ $(b)$ Find the values for $\cos\frac{\pi}5$ and $\cos\frac{2\pi}5$.  I've managed to prove $(b)$ using $(a)$, and to find all roots for the polynomial $z^5 - 1$. Also, I've managed to prove $(b)$ using "double angle formula" and then use it for $(a)$. However, I cannot prove it in the stated order (I hope it is possible).


TCP DOS: How to terminate CLOSE_WAIT connections?

One of my servers is getting DOS'ed - there are a large number of connections in the CLOSE_WAIT state which are preventing legitimate users from connecting to the system.  So is there any way to close the CLOSE_WAIT connection without killing the underlying server process? Killing the process would result in downtime which I want to avoid.  Is there any other way?


Unreachable 'yield' still strangely affects function

If you run the following snippet, it will ignore the 'print' on line 2 and 'exit' on line 3.  However, if you comment out the already unreachable 'yield' from line 4, lines 2 and 3 will execute normally.  This makes me think that Python (3.5.2) looks for a 'yield' anywhere in the function, and if one is found, even an unreachable one, nothing is executed until a next() is called on the returned iterator.  Up until now, I was under the impression that the function would execute normally up until hitting a yield, at which point it would begin acting like an iterator.  def func():     print("> Why doesn't this line print?")     exit() # Within this function, nothing should matter after this point.  The program should exit     yield "> The exit line above will exit ONLY if you comment out this line."   x = func() print(x)   Does this seem strange to anyone else?  Does anybody have some insight to share here?


How to deal with spam user posting ad in their profile page

At our Stack Exchange site we have some users created recently that have no activity, simply a name and profile which contains an add for some car insurance quotes. How can we deal with users like that? Are there tools to report them to moderators and for moderators to flag them somehow or remove them?  Examples:          This question is not actually answered in the question:   As the answers deal with automated detection of those users or some other algorithmic approaches. I'm wondering about the lack of moderation tools to allow flagging user profiles directly for spam and for moderators to delete flagged accounts. While this might seem a time sink for some bigger sites, it still should be an option for those who want to keep their SE site clean.


Is conjugation in infinite groups well behaved?

A question from earlier today made me start to think of this question. Let $G$ be an infinite group with infinite subgroup $H$. Can the condition below ever hold?  \begin{equation*} \exists g\in G \text{ such that } gHg^{-1}\subset H \end{equation*}  where the containment above is strict.


How do I turn on phonetic typing for Tamil?

Is phonetic typing for Tamil available in Ubuntu 12.04?  How can I install it?


Cannot write to NTFS data partition possibly because of lack of permissions?

I have Ubuntu 18.04 installed on a SSD with a larger separate HDD with 1 partition that contains Windows 10 and another NTFS partition that I use for storing all sorts of data. I have added the NTFS data partition to mount at startup using the Disks Utility in Ubuntu, it auto mounts just fine but only has read access. I would like to have this partition also have write access from Ubuntu. But I cant figure out how. (Fast Startup in Windows 10 is disabled)  Heres my fstab file (The last entry, dev/sdb4, is the NTFS data partition):  # /etc/fstab: static file system information. # # Use 'blkid' to print the universally unique identifier for a # device; this may be used with UUID= as a more robust way to name devices # that works even if disks are added and removed. See fstab(5). # # <file system> <mount point>   <type>  <options>       <dump>  <pass> # / was on /dev/sda3 during installation UUID=0e4a3e97-171f-4c96-9260-e2eb217f4302 /               ext4    errors=remount-ro 0       1 # /boot/efi was on /dev/sda2 during installation #UUID=1022-A48D  /boot/efi       vfat    umask=0077      0       1 # swap was on /dev/sda1 during installation UUID=c59f57b3-26c6-4fb1-82ae-29e676a973b1 none            swap    sw              0       0 UUID=1022-A48D  /boot/efi   vfat    defaults    0   1 /dev/sdb4 /mnt/sdb4 auto defaults,x-gvfs-show 0 0   These are the permissions for this partition    Also please explain how this drive can be added to the Favorites (the side bar which shows the running apps or apps that you have marked as favorite) in 18.04?


Is the Doppler effect for sound symmetrical for observer or source movement?

It makes intuitive sense to me for the apparent frequency of a sound as modified by the Doppler effect to be based entirely on the speed at which the observer and the source get closer or farther apart, regardless of whether the source or the observer is moving, based on the principle of relativity. However, the general equation I receive from every source $$f'=f((v±v_o)/(v∓v_s))$$ does not have this property. For example, if the speed of sound in the medium is 2 units and the observer and source are coming closer at a rate of 1 unit, then if we take the observer to be moving then we get $$f'=f(3/2)$$ but if we take the source to be moving then we get $$f'=f(2/1)$$ What is the difference between these two cases?


How to make my OSX app to open files of particular types?

I have custom made files that were created by my app. I want to be able to double-click on these files and make them open through my app. How can I achieve this?!


Is cross-validation enough to prevent overfitting?

If I have a data, and I run a classification (let's say random forest on this data) with cross validation (let's say 5-folds), could I conclude that there is no over fitting in my method?


Tax implications of non-US person family member gifting big amount of money to US resident

Let's say person A is person B's dad. Person A lives in Europe and is not in any way a US citizen/resident etc... Person B is a US resident (is there a difference between citizen and just a resident?).   Person A wants to send person B a gift of 1 million US dollars. This money was earned by person A outside the US and income tax was paid for it outside the US.  Does person B have to do anything specific so that he won't be taxed in the US for this gift? I have read online on multiple sources that all gifts over $100,000 have to be reported to the IRS via form 3520. But it's not clear to me if this absolves person B of paying anything for this gift?


The image of bounded linear operator is closed iff the image of its subspace is closed

Banach space $E$ is the direct sum of its closed subspaces $L$ and $M$. $M$ is finite dimensional. $T:E \rightarrow E$ is a bounded linear operator. I'm asked to prove that $T(E)$ is closed iff $T(L)$ is closed.  I have only learned the open mapping theorem and closed graph theorem, and have no idea how to prove that the image is closed. Any hint will help. Thank you.


I followed a recipe for cruelers that came out delicious! Unfortunately they didn't puff the way I was expecting them to. Just wondering if Anton might know why or have some tips for getting them to poof.


This is displayed when I try to install Snaphu in Linux  E: Unable to lock the administration directory (/var/lib/dpkg/), are you root?   How can I solve this problem?


Howthe body differentiate between foreign and native protein? How does it know when to create an immune response?

How the body differentiate between a foreign and a native protein? Suppose there is a bacteria, it has lot's protein on its membrane, with specific structures. How does our body know it's the foreign protein? How does it know, the particular configuration is native or foreign?


Are metals more heavy due to the Earth's magnetic field?

Non-metal objects are attracted to the Earth due to gravity. So the weight of non-metal objects can be only dependent on their mass.   On the other hand metals can be attracted to the Earth's magnetic field, with the Earth acting as a giant magnet; causing metals to weight more than they normally should.   In other words the weight of metals and magnetic objects would be the sum of the magnetic force plus the gravitational force, is that correct?  If that effect is true, would it be more clear as we go closer to the magnetic poles, and metals would weigh different in different locations on Earth?


How to lock aperture using Reverse ring with Canon 600D?

Is there anyone using reverse ring and know how to lock the aperture.   I tried doing the techniques provided on youtube. First connecting the lens on original positions then lock the aperture by pressing the AE lock button on the camera. after that reverse the lens.  But this method is not locking the aperture.  Help if anyone know how to lock in reverse.  Thanks.


Where should I ask questions about hardware?

Questions about hardware like:   If I put Visual Studio on an SSD, does it improve the speed of the software?  Which brand of SSD is better, Samsung or Kingston?


Sed Usage: Add shebang missing from first line of script

I have a *.sh script that's missing the shebang from the first line. Can I fix it with sed?


php - MongoDB\BSON\Regex - How Do I Set a regex for not a character?

I have a query that searches text using a regex:  $filter = ['word' => new MongoDB\BSON\Regex("some text","i")]; $query = new MongoDB\Driver\Query($filter);   I now want to be able to search for text that does not contain the text: e.g. [^(some text)]  The first issue I'm having is that I can't get the NOT to work, it appears that ^ can only be used to force the start of the string. Here is what I tried to find text without the letter 'a' in:  $pat = '[^a]'; $filter = ['word' => new MongoDB\BSON\Regex($pat,"i")]; $query = new MongoDB\Driver\Query($filter);   That just returns all documents with a value set for 'word'  I also tried:  $pat = '^a';   But as expected, that returns all documents that start with an 'a'.  How can I get this to work?


Travelling to Italy without my spouse who is a UK citizen

I am India citizen married to a UK national who has been issued a Schengen Visa from the Italian consulate as a spouse of a UK national. My husband was supposed to travel with me but now can’t. We have decided that I should still pursue the trip without him as I will be joining our friends there. Please can someone let me know if I will still be allowed to travel to the Schengen region with a valid Schengen Visa issued as a spouse of a EEA national but without my husband joining me there in person ?


I am running a processing PyQGIS script with grass i.pca but I am not getting results in my output folder

It runs without problem but I don't get the expected pca bands, my output folder is empty, I don't know what to test. path ='C/Users/Manuel/Documents/INPUT' output='C/Users/Manuel/Documents/OUTPUT'  bandList = [band for band in              os.listdir(path) if              band[-4:]=='.TIF'] input = [os.path.join(path,band)for band in bandList]  def PCA_GRASS(input,output):     processing.runAndLoadResults("grass7:i.pca",\     {'-f': False,'n':False,\     'GRASS_REGION_CELLSIZE_PARAMETER' : 0,\     'GRASS_REGION_PARAMETER' : None,\     'input': input,\     'output': output,\     'percent': 99,\     'rescale':[0,400]})   outList=[band for band in os.listdir(output) if                        band[-4]=='.tif']   new_output = [ os.path.join(output,band) for band in                                 outList ]   for band in new_output:            iface.addRasterLayer(band,band)  PCA_GRASS(input,output)  When I run the script I open log message and an ogr error appears (can't open _ address of input files_) I don't understand why () I am working with Landsat 8 band and I have tried other images to see if the code works.  Using processing whit grass I have performed other tasks satisfactorily but this one is causing me many problems.  The images are not the problem when I perform the operation (i.pca) from the processing toolbox, it is done without problem. I have also changed the syntax with which I enter the input data but nothing.


Estimated probability looks too large, what I am doing wrong?

A factory produces links for heavy metal chains. The research lab of the factory models the length (in cm) of a link by the random variable ${X}$, with expected value ${E(X) = 5}$ and variance ${Var(X) = 0.04}$. The length of a link is defined in such a way that the length of a chain is equal to the sum of the lengths of its links. The factory sells chains of 50 meters; to be on the safe side 1002 links are used for such chains. The factory guarantees that the chain is not shorter than 50 meters. If by chance a chain is too short, the customer is reimbursed, and a new chain is given for free.  Give an estimate of the probability that for a chain of at least 50 meters more than 1002 links are needed. For what percentage of the chains does the factory have to reimburse clients and provide free chains?    Number of links in a chain: ${n = 1002}$  Mean lengh of 1002 links: ${ \mu = 1002 \times 0.05 = 50.1 }$  We know variance, so we can find the standard deviation: ${ \sigma = \sqrt{0.04} = 0.2 }$  We are interested how often chain is shorter then 50 meters: ${ \bar{x} = 50 }$  Thus let define an appropriate test statistic: ${ \displaystyle z = \frac{ \mu - \bar{x} }{ \sigma } = \frac{50.1 - 50}{0.2} = \frac{0.1}{0.2} = 0.5 }$  Probability of getting value in a lower tail is: ${ \displaystyle P(z < 0.5) = \frac{1}{2} + \frac{1}{\sqrt{2\pi}} \int\limits_{0}^{0.5} e^{-\frac{z^2}{2}} dz }$  By making the substitution ${ z = \sqrt{2} x }$, we get:  ${ \displaystyle \frac{1}{\sqrt{2\pi}} \int\limits_{0}^{0.5} e^{-\frac{z^2}{2}} dz = \frac{1}{\sqrt{\pi}} \int\limits_{0}^{\frac{0.5}{\sqrt{2}}} e^{-x^2} dx }$  As we can not solve integral above, let's consider ${ e^{-x^2} }$ as a Taylor series: ${ \displaystyle \sum\limits_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{n!} }$  Then the approximate probability is: ${ \displaystyle P(z < 0.5) = \frac{1}{2} + \frac{1}{\sqrt{\pi}} \sum\limits_{n=0}^{\infty} \frac{(-1)^n (\frac{c}{\sqrt{2}})^{2n+1} }{ n! (2n+1) } \simeq 0.691462 }$    But this probability looks too large. What I am doing wrong?


How can I automatically group each shape with the text inside it for a huge collection of rectangles?

I have a .dwg (AutoCad file) map full of fields (rectangles) that I'm manipulating with Illustrator. Each rectangle has a text inside it that indicates its number. The problem is that there is no association between the rectangle and its number and that's what I'm trying to do. Also the order or drawing is not the same, when I check the layers.  Is there a way with Illustrator that can group each rectangle to the text inside it and this for all the fields? It is possible manually, but impossible to do it for every single field: about 40,000 rectangles.   I guess the approach should have something to do with "closeness" since it's the only data that tells us the correspondence between a rectangle and its number.


We have ground-truth data $\mathbf{x}^* = (0,0)^T \in \mathbb{R}^{2}$. Furthermore, we have $N$ measurements $\mathbf{x}_i \in \mathbb{R}^{2}, i\in \{1,\ldots,N\}$. We calculate the $N$ error vectors $\mathbf{e}_i = \mathbf{x}_i - \mathbf{x}^*$. We assume that the two components of $\mathbf{e}_i = (e_{x,i}, e_{y,i})^T $ are independent of each other and normally distributed with equal mean $\mathbf{\mu} = (0,0)^T$ and variance $\sigma^2$. The absolute errors $e_i = \sqrt {e_{x,i}^2 + {e}_{y,i}^2} $ follow a Rayleigh distribution, is that correct?  The probability density function (PDF) of the Rayleigh function is zero at a value of zero. Why is this the case (intuitively)? I would assume that our errors should most likely be 0 (i.e. PDF should be highest at 0)...


How can I change the variable in $$\int_{0}^{1}\int_{0}^{1} \frac{x-y}{(x+y)^3} dxdy$$ to computer the value  I tried to let $u=x+y$ and $v=x-y$  But I have no idea for next step   Can you give me some suggestion,thank you!!!


How can I find unanswered questions of interest, that I have not yet answered?

I can search for is:question intags:mine hasaccepted:no and add other criteria as I wish, but there's no way to express 'that have no answer by me'.  That seems like a useful addition to me, since if I'm looking for questions to answer, I have no use to questions I've already written an answer for.  Is there any way of doing this, short of the Data Explorer (which of course lags behind the main sites)?


Is faithful flatness implying $M \otimes_{S^{-1}R} S^{-1}N \cong M \otimes_R N$?

Assume that $M$ is faithfully flat $S^{-1}R$-module, for $R$ commutative ring and $S \subset R$ a multiplicative subset. Furthermore, let $N$ denote an $R$-module.   Is it true that $M \otimes_{S^{-1}R} S^{-1}N \cong M \otimes_R N$?


Why are primes of the form $6k+1, 6k-1$ where the prime is $\geq 3$

I recently came to know that primes are of form $6k+1,6k-1$ for primes greater than three. Why is this so? I tried my hand on it could not really understand about it. I have also heard of Dirichlet's theorem but can there be any elementary such way to show this?


For a few months now I was using both Linux Mint and Windows 10 through a dual boot setup and a grub loader on startup. Suddenly this morning I can no longer see my grub loader or any boot options and am automatically booting into Windows.   I have checked the UEFI boot options and I can no longer see a grub/Linux option. I currently do not have access to the USB I used to initially install Linux. I am wondering what the best course of action is to recover the grub loader and boot into my Linux partition. I am also concerned that the Data may be corrupted or lost.   Any insight on what to try/how to proceed would be very helpfull. I have read a little about using bootrepair after booting using a USB, but I currently don't have access as I mentioned and would like to see if there are alternatives as I require access asap.


What words should never be capitalised in a title or heading?

Are there any exceptions to the rule? Sometimes song names will have "the" with a capital "T".


Does the circuit with qubit-wise CZ gates compute the inner product of two states? If not, is there another circuit that does?

I've been searching for a quantum algorithm to compute the the inner product between two $n$-qubit quantum states, namely $\langle\phi|\psi\rangle$, which is in general a complex number. One can get $|\langle\phi|\psi\rangle|^2$ through thte SWAP test for multiple qubits, but this is not really the inner product as the information of the real and imaginary parts are lost. I came across this , which claims that the task can be done by simply using CZ gates. I'm not sure if I am mistaken, but it seems to me that such a circuit works for computational basis states, but not for general quantum states. Could somebody help me confirm if this is actually the case? If the above algorithm doesn't work for general quantum states, what algorithm would you suggest?